Teaching Physics Blog

AP PhysicsChallenge Circuits

2012-01-17T17:18:00.000-08:00

Learning Objectives

Students will build several circuits using switches and principles of series and parallel circuitry.

Activity Type
This activity would best be used as an introduction to circuits and electricity. No previous experience in electricity or circuits is required for students to complete these challenges. This activity could also be used as a practicum component to a unit test on circuits and electricity.

Assignment Details

Teams of students will use a variety of simple circuit equipment (batteries, bulbs with holders, wires, alligator clips, and SPDT switches) to complete four circuit challenges.
Circuit Challenges:

String of Lights: Create a string of three lights that could be used for a Christmas Tree. If one of the three lights breaks (or is loosened from its socket) the other lights should still stay on.
Lighting a Tunnel: Designing lights for a tunnel, you would like to be able to control two lights with one switch, which both turns on the light in front of you and turns off the light behind you. Create such a circuit.
Lighting a Stairwell: In this case we want to control one light with two switches - one at the top and one at the bottom of a stairwell. Wire a circuit with one bulb in which either switch can turn the bulb on or off at any time.
Dimmer Switch: See if you can make a switch that would not only allow you to turn on and off a light, but also control how bright the light bulb gets. Try to create such a circuit.

After a team completes one of the challenges, the team must demonstrate the function of the circuit to the instructor. Then, each student on the team must draw an accurate diagram that would allow them to rebuild the working circuit.

Instructor's Notes

The circuit challenges are listed in order of difficulty with the easiest circuit first. It is acceptabe if some of the groups never reach the last two challenges, which are particularly tricky.
As you review the student circuits, be sure that they are not using a short in the circuit to make the light go out. Each of these circuits can be built without a short circuit.
Proper understanding of SPDT (single pole double throw) switches is important for completing challenges #2 and #3. The "off" position of the switch must still make an electrical connection in order for students to create these circuits.
Students do not necessarily need to know about proper circuit diagrams before making their circuit drawings. In fact, it may be helpful for students to experience the difficulty of drawing a circuit before learning about circuit diagram conventions.
Creating a dimmer switch (challenge #4) will require some way to change the current of the circuit. This could be accomplished by adding more than one bulb, or by adding a potentiometer (adjustable resistance device) to the circuit.

Hippocampus Correlation
This activity would be an appropriate introduction to the "Electric Circuits" unit of AP Physics B.

AP PhysicsThe Physics of Osmos Contest

2011-12-16T06:38:00.000-08:00

Join the Contest!

The makers of Osmos have sponsored a contest open to all physics enthusiasts - students, teachers, everyone. Here's how it works:

Create a one-minute video illustrating a physics concept that you discover in the game. The top entry will receive a $500 gift card to Amazon.com. The top three runners up will also receive prizes.

To submit your entry, follow the instructions below.

Download and install the Osmos free demo. (Or purchase Osmos from the App Store.)
Experiment with your gameplay to illustrate physics concepts using Osmos as your virtual lab.
Review the official contest rules.
Create a video illustrating a physics concept.
(If you want to record your screen, try Jing or ScreenChomp)
Upload your video to YouTube, Vimeo, or Screencast.com
Complete the submission form by 11:59PM PST, January 2, 2012.

Winners will be announced on January 4, 2012.

Teacher Notes

This contest would make a great activity for the final days before the holiday break from school. It would also be a fun project for advanced physics students over the break.

Hippocampus Correlation
Review some of your physics knowledge using Hippocampus.org.

AP Physics:How Do Pulleys (Do) Work?

2011-11-16T04:20:00.001-08:00

Learning Objectives

Students will explore the significance of work by experimenting with pulleys.

Assessment Type
This activity is meant to partially replace a traditional lecture on the topic of work. It can be used as a brief hands-on laboratory activity, or it can be completed using the provided simulation in an online or hybrid classroom. The purpose of the activity is to generate class discussion and is best left ungraded.

Assignment Details

Work is a difficult concept for students to understand, even the second or third time they encounter it. Simple machines in general, and the pulley in particular, provide excellent tools for exploring work since simple machines allow us to trade force for distance to transfer the same amount of energy.
Begin the lesson by introducing the concept of work and providing students with the equation for work.
Without making any apparent connection to work, introduce students to the pulley. This can be accomplished with a set of physical pulley systems around the classroom (1-, 2-, and 4-pulley systems would work best). Alternatively, you can use the pulley gizmo with its 5-minute free trial.
Do not over-introduce how pulleys work - simply point out that pulleys can make it easier to lift heavy objects, and that the more pulleys there are, the easier it is to lift the object.

Pose this question to students: How can simply adding pulleys make something lighter?
Ask students to work in teams of 2-3 to investigate this question and write out their explanation (including a drawing) on a white board or sheet of paper.
When students are complete, ask a few groups to share their work with the class and discuss.

Instructor's Notes

To make the investigation more quantitative, provide students with force meters and meter sticks. Students should be able to show that the same amount of work is done with each pulley configuration.
A good transfer of knowledge question (in class, on homework, or on a test) would be to ask why pushing a cart up a ramp is 'easier' than lifting it straight up. You could follow up by asking whether we measure the difficulty of a task by the amount of work required or by the force required (the answer is not trivial).

Hippocampus Correlation
This activity would be appropriate either before or immediately after the Hippocampus lesson on work.

AP Physics:Is Momentum Conserved in Osmos?

2011-10-16T19:12:00.000-07:00

Learning Objectives

Students will design an experiment to determine if momentum is conserved in the video game Osmos.

Assessment Type
This activity can be used as a formative assessment, extracurricular project, or challenge problem for advanced students. There are multiple methods that could be used to answer the question. The ultimate goal is to promote student creative thinking and problem solving.

Assignment Details

Students should begin by downloading and installing the free demo of Osmos, which is available on a variety of platforms including Windows and Mac computers (http://www.hemispheregames.com/osmos/). Osmos is also available for purchase through the iTunes App Store for iPad, iPhone, and iPod Touch.
Students should experiment with the game to learn how it works. In particular, students should recognize how the conservation of momentum is essential to motion within the game.
Students are challenged to answer the following question: Is momentum conserved when the mote propels itself?
Students are asked to design an experiment to answer this question. In particular, they must clearly outline:

The process they followed to reach their conclusions.
The data they collected
The assumptions they had to make.
The calculations they performed.

Students should submit their solution in the form of a 2-page report or a 2 minute video.

Instructor's Notes

In order to answer this question, students will have to wrestle with these additional questions:

How does the mass of the player mote compare to the mass of the expelled mote?
How can we determine the velocity of the motes?
Do we need to know the absolute velocity or will relative velocity suffice?

You may recommend that students use video analysis software to collected data on motion within the video game. By using a combination of screen capture software (such as Jing) and video analysis software (such as Tracker) students can extract numerical data to draw their conclusions.
A few well-timed screenshots could also be used instead of video analysis to measure the recoil of each mote and ultimately answer the question.
The following could be used as a simple rubric for evaluating this student project:
(10 pts) - Process for solving the problem is clearly outlined and accurate
(5 pts) - Assumptions are appropriate and data is collected
(5 pts) - Calculations are accurate and solution is correct.

Hippocampus Correlation
This activity should be completed after students have reviewed the Hippocampus lessons on momentum.

AP Physics:Newton's Laws in Three Pictures

2011-09-15T12:07:00.000-07:00

Learning Objectives

Students will be able to recognize Newton's Laws of Motion in ordinary situations.

Assessment Type
This activity can be used as a formative assessment to check student's conceptual understanding of Newton's Laws of Motion.

Assignment Details
Ask students to go around the school, looking for examples of Newton's Laws of Motion. When they find a situation that illustrates one of Newton's Laws, students should take a photograph using a digital camera (cell phones would work fine).

After returning to the classroom, students should write a brief description of how each image illustrates one of Newton's Laws. For example, a student description for the images above may look like:

1st Law: A stapler is sitting on a desk illustrating that objects at rest will stay at rest.

2nd Law: When pushing someone on a swing, a greater force must be applied to someone with a greater mass in order to achieve the same acceleration.

3rd Law: When the hamster runs in his wheel, there are two forces between his feet and the wheel -- one pushing his feet forward and the other pushing the wheel backward.

Instructor's Notes
Students can use one of several free online tools to create an animated .gif of their images (as above). The student's work can then be added to a class website, showing all the different ways Newton's Laws can be found in everyday life.

This same activity can be used to check student understanding for a wide variety of conceptual topics in AP Physics. For example, conservation of momentum, oscillations, refraction, and resonance would all make for an interesting series of photos.

As a formative assessment, this activity could be graded on a completion basis. Rewards, such as placing the best examples on the class website, could be used to motivate students toward excellent work.

Hippocampus Correlation
This activity could be used as after working through the Newton's Laws lessons (1st, 2nd, 3rd) in AP Physics B or AP Physics C: Mechanics.

AP Physics:The Kinematics of Plants vs Zombies

2011-08-15T12:28:00.001-07:00

Learning Objectives

• Students will be able to apply equations of motion to the video game, Plants vs Zombies

Assessment Type
This lab activity asks students to use video analysis software to address several questions related to the motion of zombies in the popular video game, Plants vs Zombies. This activity could be used as a formative or summative assessment of students' knowledge related to constant-velocity motion. It could also be used as an introductory review activity for AP students prior to starting the first unit.

Assignment Details

Before beginning this activity, students should download and install the required software:
Tracker: This is a powerful open-source video analysis tool for physics teachers. It makes a great free alternative if you do not have Vernier's LoggerPro software, which can also perform the same video analysis.
Plants vs Zombies: While the video snippets needed for this activity can be downloaded below. It will be helpful for students to have some experience with the actual game. It can be played in the web browser or downloaded as a free demo.
The activity can be presented to students as a series of questions. Students are directed to collect data that clearly and convincingly answers the following questions.
Question 1: Does the pea shooter slow down the zombies?
Question 2: At what position and time will the javelin-carrying zombie pass the cone-wearing zombie?
Question 3: By how much does the frozen pea shooter slow down the zombie?
Students will create a lab report or a brief video that presents their data, describes their analysis, and explains their conclusion.

Instructor's Notes

If you have screen recording software available, you can ask that students make their own videos for analysis, otherwise students can use the following videos to address each of the questions.
Question 1 Video
Question 2 Video
Question 3 Video
Students could be assigned to answer all three of the questions or given the option of choosing just one question to answer. Question 2 is the most open ended and would require students to make careful choices regarding their frame of reference for measurements.
Students can compare their prediction in Question 2 to this video, which shows the javelin-carrying zombie passing the cone-wearing zombie.
The following could be used as a simple rubric for evaluating this student activity:
(10 pts) - Clear and convincing conclusions are drawn that are consistent with the data
(5 pts) - Data analysis is correct and appropriate for the question being addressed
(5 pts) - The data was collected accurately and illustrates the motion shown in the video.

Hippocampus Correlation
This activity could be used as an introduction to the One Dimensional Kinematics lessons in AP Physics B or AP Physics C: Mechanics.

AP Physics:The Physics of Osmos

2011-07-15T11:57:00.000-07:00

Learning Objectives

• Students will be able to recognize and explain physics concepts in novel situations.

Assessment Type
This activity asks students to recognize physics concepts within the video game Osmos. Students are then asked to use the video game to demonstrate and explain the concept that they have identified. This activity can be used as a formative assessment of student understanding or as a summative assessment after a comprehensive introduction to kinematics or momentum.

Assignment Details

Students begin by watching the following YouTube video: http://www.youtube.com/watch?v=FWlP9ix3ukg

Students should then download and install the free demo of Osmos, which is available on a variety of platforms including Windows and Mac computers (http://www.hemispheregames.com/osmos/). Osmos is also available for purchase through the iTunes App Store for iPad, iPhone, and iPod Touch.
Students will experiment with the game, looking for physics concepts that could be demonstrated using the video game as their laboratory.
Using screen capture images or free video screen capture software (such as Jing: http://www.techsmith.com/jing/), students can create their own video demonstration and post it to YouTube as a response to the original "Physics of Osmos" video.

Instructor's Notes

There are a wide variety of concepts that can be demonstrated with this game. If students' need help identifying possible topics, direct them toward: Newton's 1st, 2nd, or 3rd law, elastic collisions, inelastic collisions, conservation of momentum, or rocket propulsion.
Using later levels of the game, students can also explore gravitation and orbits, these levels could be used as a demonstration of Kepler's Laws, uniform circular motion, or simple harmonic motion.
As a possible follow-up to this activity, include screenshots from Osmos on an end-of-unit test or final exam. Ask students to solve a problem involving the glowing orbs or to explain a concept in the context of the game.
The following could be used as a simple rubric for evaluating this student project:
(10 pts) - Physics concept is named and explained in the video
(5 pts) - Concept is convincingly demonstrated using the game
(3 pts) - Video is clear, concise, and easily understandable
(2 pts) - Student showed creativity or insight in their demonstration

Hippocampus Correlation
This activity could reasonably be included anywhere in the first semester of AP Physics B, or in AP Physics C: Mechanics.

AP Physics:Air and Fluid Pressure Activity

2011-06-14T07:46:00.000-07:00

Learning Objectives
From Chapter 7 of AP Physics B

• Understand and apply the relationship between pressure and depth in a fluid.

Assessment Type
This activity challenges students to explain very familiar phenomena using the concept of fluid pressure. In the process, even advanced students will have their misconceptions about pressure revealed. This activity can be used as a formative assessment of conceptual understanding or even as "practicum" component on a test or quiz.

Assignment Details

Provide students with a few basic supplies: 5-10 plastic straws, a small cup filled with water.
Ask students to perform the following three experiments and record their observations as well as a detailed explanation using the concept of pressure.

Experiment 1: With the straw only in air, place a finger over the top of the straw, closing the top end off. Put the bottom end of the straw into the cup of water and record your observations and explanation.

Experiment 2: With the straw open on both ends, put the straw halfway submerged into the water. Place a finger over the top of the straw, closing the top end off. With a finger still over the top, remove the straw from the water and record your observations and explanation.

Experiment 3: Make an extra long straw by connecting two straws together in a chain. Place the straw in a cup of water and attempt to move the water up the straw to your mouth with a single long and constant draw. If you are successful in getting water all the way to the top, then add another straw to your chain and try again. Find the highest straw length where it is no longer possible to move the water to your mouth with a single constant draw. Record your observations and explanation.
Allow the students to experiment, providing as much autonomy as possible and trying not to influence their observations or explanations.
After students have completed the experiments, ask them to share their observations by facilitating a class discussion. Go through each experiment one-by-one, with students sharing their observations and then discussing their explanations of the results.
Use leading questions to correct misconceptions and always return to the experiment when there is disagreement about what actually happened.
As a final test of their understanding ask students if there is an absolute limit to the height of a usable straw (even if a machine used the straw instead of a person). If so, what would cause this limitation? and how high would the maximum height be?

Instructor's Notes

Each of these experiments demonstrates the strong influence of air pressure. Students will be tempted to explain the experiments in terms of "vacuums" and "suction." Feel free to forbid the use of these two terms at the start of the lesson.
When "sucking" water up the straw, be sure that students keep the straws vertical, so that they do in fact reach a limit. Students will reach various limiting heights with their straws. This height is limited by the degree to which the pressure in the straw is lowered below atmospheric pressure. In some sense, this height can be used as a measure of lung strength.
The absolute limiting height up to which a straw can be used is determined by atmospheric pressure. The pressure caused by the weight of the column of air above the surface of the water can push the water up the straw until the weight of the fluid in the straw matches that of the column of air. Estimates on a numerical value for this height can be performed using the densities of air and water as well as the approximate column height of the atmosphere.

Hippocampus Correlation
This activity would be well-placed either before or after AP Physics B Lesson 21.

AP Physics:Free-Fall Motion Inquiry Activity

2011-05-15T15:55:00.000-07:00

Learning Objectives
• Understand and apply the principle of free-fall motion in a uniform gravitational field.

Assessment Type
This inquiry activity is a wonderful launch point for a discussion on free-fall motion and particularly the non-negligible role that air resistance play in free-fall acceleration. The activity can also be used as a formative assessment of students' abilities to design an experiment, generate and test a hypothesis, and make careful observations.

Assignment Details

Provide students with just a few basic supplies: manilla folders, empty film canisters, and pennies.
Ask students to collect data using these simple tools to answer the following two questions:
a) Does mass impact the rate at which objects fall?
b) Does shape impact the rate at which objects fall?
Allow students to experiment, provide as much autonomy as possible and try to accommodate student requests for other resources (rulers, timers, tape, etc) as they carry out their experiments.
After students have experimented for some time, ask them to share their conclusions by facilitating a class discussion. Any statement made by a student or group should be confirmed by a simple experiment shown to the class.
Through the process of testing one another's conclusions, work with the students to generate a statement describing the conditions under which mass and shape seem to impact the rate at which objects fall, being sure that everyone agrees to the language used.
As a final test of their conclusions, choose two new objects that the students have not experimented with -- say a styrofoam cup and a plastic cup. Ask the students to discuss which would hit the ground first when dropped from the same height, and under what conditions the opposite result could be achieved.

Instructor's Notes

Physics instructors often teach students that mass does not impact an object's free-fall rate. While this is true in the absence of air resistance, it is not true under normal circumstances. This activity can be used to demonstrate why Galileo's understanding of free-fall motion took thousands of years to emerge.
The joy and challenge of this activity is the open nature of the experimentation. Allow students to pursue experimental dead ends and even to make incorrect conclusions from their experiments. Through the class discussion, students will confront their misconceptions and be forced to reconcile them with the experimental evidence.
This activity can be used as an introduction to free-fall motion, before the simplifying assumption of ignoring air resistance is made. It could also be used after free-fall motion has been studied in detail and as an introduction to friction and/or terminal velocity.

Hippocampus Correlation
This activity can be used as an introduction to free-fall motion, which is covered in section 4 of AP Physics C Lesson 1 or AP Physics B Lesson 1.

It could also be used as an introduction to frictional forces, which are covered in sections 2 and 3 of AP Physics C Lesson 6 or AP Physics B Lesson 6.

AP Physics Exam Review:Physics in the News

2011-04-15T03:25:00.000-07:00

Learning Objectives
• Conduct a review of the topics discussed throughout the year.

Assessment Type
This review activity serves the dual purposes of reviewing physics concepts and applying this knowledge to current events in world news. This activity would be used as a formative assessment as well as a break from the traditional review routine.

Assignment Details

Students begin by searching various new sources to explore current events. Helpful resources could include Google News, Wired, Scientific American, or USA TODAY.
Students find an article that is related to a physics concept they learned this year.
Students write a brief description of the news article.
They explain what makes physics relevant to this story, using specific examples of physics concepts they learned in class.
Students create an AP Physics review problem related to the news story that they chose.
Students write the complete solution to their problem.
The student-written problems are redistributed around the classroom, and students try to solve a classmate's review problem, checking their solutions when finished.

Instructor's Notes

You may choose to use this worksheet to guide your students as they work.
Consider redistributing the student created problems two or three times for additional practice and review.
To increase the incentive for creating a quality review problem, tell them that you will include one of the question they create on the final exam.

Rubric
Students can be assessed on the following criteria.
1 pt - Students provide a concise and clear summary of the news article.

3 pts - Students correctly describe a physics concept and make a reasonable connection to the article.
6 pts - Students create a problem related to their news story that is of suitable difficulty and include a complete and correction solution.

Total = 10 pts

AP Physics B:Exploring Models of the Hydrogen Atom

2011-03-13T13:08:00.000-07:00

Learning Objectives
• Explain qualitatively the origin of emission or absorption spectra of gases

Assessment Type
This activity can be used to introduce atomic models and serve as a formative assessment of students' understanding of alternate models of the Hydrogen atom.

Assignment Details

Begin by watching NROC AP Physics B II Lesson 52: Atomic Energy Levels
Direct students to the "Models of the Hydrogen Atom" simulation from PhET.
Click "Run Now" to begin the simulation.
Ask students to explore the various atomic models under the prediction setting, trying to decipher what distinctions can be made between the models.
Students, working in pairs, should examine at least three atomic models in detail (Bohr's model and two others of the students' choosing). Student pairs are asked to discuss the models and create a two-to-three sentence description for each of their three models explaining how the model can be employed to explain the emission of light.
Ask students to turn on the spectrometer and collect spectral data for each of their three atomic models.
Students should then compare the spectra from the three models, and record at least one similarity and/or difference between each pair of models that they observed.
Turning the dial to "Experiment," students can collect spectral data on a 'real' Hydrogen atom.
After sufficient data is collected, the students will compare the experimental data to the predictions of their three models and rank them from most accurate to least accurate.

Instructor's Notes

Use the slider at the bottom of the simulation to make time go faster, making it possible to collect data more quickly.
Encourage students to use the camera button on the spectrometer to record their spectral data sets.
Ask students to speculate why the spectra from each model differ in the ways they do.
A particularly worthwhile discussion could be focused on the relative merits of the Bohr and deBroglie models.

Rubric
Students can be assessed on the following criteria.
6 pts - Students provide accurate two-to-three sentence descriptions for each of their three atomic models.
3 pts - Students correctly describe at least one similarity and/or difference between each pair of models they observed.
1 pt - Students properly rank their three models in order of accuracy.

Total = 10 pts

Reviewing for the AP Physics Exam

2010-04-26T11:26:00.001-07:00

It is the time of the year where us AP teachers are now taking our students through the review process for the AP Exam given in early May. So it is appropriate that I focus this late April blog on the topic of AP testing and the resources available online. I realize that AP Physics teachers that have taught AP Physics for some time are aware of the information below. But my intent in writing this blog is to provide information that would be helpful to AP Physics teachers doing this for the first time, to physics teachers who aren't offering an AP Physics course now but are considering doing it, and to students who are taking physics that may or may not be in an AP classroom.

Fortunately I had the opportunity to attend an AP summer workshop in AP Physics as well as AP Calculus a couple of summers ago, and I found that to be time well spent. Since attending these workshops is not a requirement for teaching AP courses, it might be helpful to a number of AP Physics teachers to once again take a tour of the College Board web site. At the College Board web site is an area for teachers , this area requires that you have completed the AP Audit. In this blog, I'm going to confine my comments and link to areas that both you and your students can get to.

The main links to come into for the AP Physics courses are:

Prior to the student taking the test, consider it a MUST to have them read the rules for what happens on exam day. Without this, especially if your school is new to the AP testing, your students could completely be missing what to expect on test day.

During the year, hopefully you have been having your students use the Table of Information and Equation Tables for the AP Physics C Exams so that they are familiar with what is on it and how it is laid out.

Samples of past Multiple Choice questions can be found in this document , but it is not very extensive. If you as a teacher have attended one of the AP sponsored workshops, you will likely have been given a CD containing two or three complete previously released Multiple Choice tests with all 35 questions on each of the C exams and the 70 questions on the B exams.

Your students don't have access to this large a database of multiple choice questions, so unless you have been using questions from material you picked up in the summer workshops, your students will have had a limited amount of practice with these. It is possible to order up printed copies of previous AP Exams. With the printed copies of the exam you have all 70 of the AP Physics B, 35 of the AP Physics C: Mechanics, and 35 of the AP Physics C: E&M multiple choice questions. The 2009 released exam can be ordered at the College Board web site.

While the College Board does not release the Multiple Choice questions each year, they DO release the FRQ questions for each year along with solutions and scoring rubrics. Both you and your students have access to these. The links to the FRQ questions used over the past eight years are as follows:

The 2009 released exam book linked to above is more than just the questions themselves. In addition it gives solutions, scoring guidelines, examples of good responses to the FRQ questions, and a statistical breakout you can use to determine after doing a practice test what the AP score would have been.

There are other review books out there that you, your students, or your high school library might want to pick up for test preparation.

These are not easy exams, and any advantage you can give your student by giving them access to back exams will be helpful.

Labs using the Exploration Activities from TI

2010-04-12T10:10:00.001-07:00

A good source for some lab activities for Physics class is the Texas Instrument calculator web-site. I'll use this blog post to describe a couple of labs you might be interested in using from the TI web-site.

About fifteen years ago, pre web-browsers, I used to buy these Exploration books from TI that had the labs in them that I used in my classroom with a rather minimal investment in equipment. TI now, in addition to still selling the Exploration books, also makes these materials available for free on their web-site. I first came across the materials as a math teacher looking for ways that I could better relate the math I was teaching to the real world. At the TI web-site (I'll link to it later), under the "Algebra" area is a book called "Real World Math Made Easy". I suspect that if you only teach Physics at your school, and not also some math, you could easily miss knowing these materials are available.

We are in the spring of the year when the AP Physics B teachers are usually covering heat, and the AP Physics C teachers are dealing with electricity, let's take a look at a lab dealing with each of these topics.

As you begin to cover specific heat with your students, a nice introductory lab is the one called Mix it Up: Combining Liquids of Different Temperatures . In this lab students mix two containers of water into a single container, by knowing the mass and temperature of each of the beginning two containers of water, they predict and then measure the temperature of the resulting combined combination. The lead in web-site to this activity, can be found here . At this location you will find more details about equipment as well as the teacher's edition of the lab.

Students taking physics in high school, almost always will have a TI-83 or TI-84 calculator that they purchased for use in their math classes. To use the lab as it is written, you would need to purchase the CBL2 at a cost of about $160. The CBL2 comes with the temperature probe. As you look over the equipment needed for this particular lab, it doesn't take a lot of imagination to imagine how you might still be able to do the lab without a CBL2. However, as you start to do these labs, you will find the CBL2 a nice piece of equipment to have. Next I'll link to a lab where the CBL2 plays a more important role in gathering the data.

Finding labs to go with the unit on capacitance in AP Physics C is bit harder than finding labs for many other units in the physics course. A relatively simple lab, one that let's students work with a capacitor, can be found in the Exploration book listed for Algebra. The lab is called Charging Up, Charging Down: Exponential Models . In this lab, students hook a capacitor and a resistor in series, and then charge the capacitor with a 9-volt battery. Students then take voltage readings as the capacitor discharges through the resistor. The lead in web-site to this activity can be found here . The voltage probe described comes as one of the probes bundled with the CBL2, just as the temperature probe does.

Of course I should indicate that "TI" and "CBL2" are registered trademarks of Texas Instruments. As a teacher, I have always found the support from TI, their documentation, and their understanding of the high school classroom to be excellent. In some future blogs, I'll plan to highlight a few more of the labs from TI that I have found very workable in the classroom.

Content related to this blog posting can be found at HippoCampus under Specific Heat, Water-Ice Mixture - Simulation, and Capacitor & Resistor Circuits.

Pulleys and Mechanical Advantage

2010-03-29T11:12:00.001-07:00

One of the problems on an FRQ in my course that gives students more trouble than I would expect is the following question:

The first question that gets asked is "What is the mass of the bucket and the sand?"

It usually isn't dealing with the component of the weight on the ramp and the friction that cause students their problem, it is dealing with the pulley system. There are two different approaches that I feel can help students understand how the pulleys are working, if they didn't get to play with and talk about pulleys in junior high. I am going to assume we are in a steady state condition.

The first is to think in terms of forces. In figure B, since a rope transmits the same force throughout it's length, as it passes over the pulley, the pulley is doing nothing but changing the direction of the force, T on the left of Figure B is equal to T on the right of Figure B.

The second is to think in terms of the distance things are moving. In a simple machine, which a pulley is, if you can make the input distance your input force works through be twice the output distance the object you are doing work on moves, you have a mechanical advantage of 2. In figure B, if you have a meter of rope come out the left side of the pulley, you also have a meter of rope that went into the right side of the pulley. That is a 1 to 1 ratio, and therefore the mechanical advantage of the pulley in Figure B is 1.

Applying the force argument to the pulley in Figure C, we see that we have two forces each of strength T pulling up, and they counterbalance the single force Ws acting down. We could write an equation about that 2 T = Ws . We can write an equation about Figure B also, T = T, but that doesn't do us much good.

Applying the distance argument to Figure C, if you think about it you can see that because the rope on the left side is fixed, that is what the horizontal bar on the top of the rope means, for every 1 meter of rope we pull through to the right side of the pulley, the weight hanging on the pulley only goes up by 1/2 of a meter. This may not be completely obvious, so visualize a specific situations to think about it. In moving from the arrangement in Figure D below, to figure E, we have dropped the center of the pulley (and therefore the suspended mass), a distance of 1 meter. How much rope did it take to do that? Clearly we added 1 meter of rope on the left of the pulley in Figure E and also 1 meter of rope on the right of the pulley in Figure E. So we have to let 2 meters of rope out to get 1 meter of movement, this is a mechanical advantage of 2. Thus the tension in the rope is 1/2 the weight of the sand bucket, or T = (1/2) Ws, and 2T = Ws.

In figure A, we have two forces trying to keep the block from moving up the plane, the component of gravity down the plane which I will call Fx and the frictional force. Fx = Wb*Sin(30), since that force would be zero if the angle were zero, and it would be the full weight of the block if the angle were 90 degrees. The frictional force is the coefficient of static friction times the component of the weight of the block creating the normal force between the plane and the block of f, where

We can now write our second main equation stating that the forces acting along the x-axis (taken to be along the plane) for the block in Figure A:

Do we have enough equations to solve for the weight of the sand? We'll look at this more next time. Meanwhile see if you know what the following item is. The small photo on the right is a close up of the item being pointed to.

Content related to this blog posting can be found at HippoCampus under Pulleys.

Physics on the Farm

2010-03-14T08:24:00.001-07:00

I've often felt that growing up on a farm gave me an advantage when it came to understanding physics. The next statement is a bit "tongue in check", but I think you could make a case for allowing farm students to be exempted from the AP requirement that AP Physics have a lab component.

Below is a picture of a John Deere tractor, the actual one that I used to work with as a kid growing up in Iowa. I'm not the one on the tractor, I'm the one behind the camera taking the picture. Dad restored this tractor. It didn't look this good when I used it.

The John Deere Tractor Physics Lab.

Each year during cultivating season you had to slide the rear tires out to widen the spacing between the rear tires for cultivating the corn. The tires had to be spaced so that as you drove through the field the tires would fall between the corn rows, and not trample the corn plants. In the picture of the tractor you can see an extended axle shaft that allows for widening the spacing between the rear tires. You could slide the rear tire in and out along this shaft.

The tractor weighed about 4,000 lbs, to adjust the wheel spacing you had to lift that wheel completely up off the ground. Below is a picture of what was affectionately know as "The John Deere Jack". I expect it must have been sold right along with the tractor. It was a very ingenious yet simple device.

Just looking at the background in the picture, you can tell this machine shed is really a "lab".

The lifting handle on this jack was about two feet long, when you pumped it up and down the distance the tip of the handle would travel going from the up position to the down position was also about two feet, and that movement from the up position to the down position is what raised the upright by one notch, I'll call that distance the "throw". The item labeled "lifter" in the figure is a U shaped latch that would catch on one of "notches" on the upright in the jack. You can see this lifter is a pretty heavy piece of metal, it had to stand a force of 4,000 lbs. Well, not exactly 4,000 lbs because you only lifted one wheel off the ground at a time. So if the weight was distributed evenly between the front tires and the two rear tires, it had to lift 1,333 lbs. The spacing on the notches was approximately 1 inch.

The free response question to answer on this lab is, "How can the farm kid lift the rear wheel off the ground using less that 100 lbs of force?"

Answer: The mechanical advantage of this jack is how far the handle moves (the throw) divided by how much the upright in the jack moves. That would give you 24 inches divided by 1 inch for a mechanical advantage of 24. For every 1 lb of pressure you applied to the handle, you could lift 24 lbs of tractor. Ten pounds of pressure on the handle could lift 240 lbs of tractor. Sixty pounds of pressure on the handle could lift 1,440 lbs of tractor, that would do it.

In junior high a farm kid would weigh 60 lbs, and sitting on the handle was allowed. By the time you were in high school, you could even do the algebra, x * 24 = 1,333, so x = 56 lbs.

Perhaps the farm students are the ones that most enjoyed the lab component of the physics course, and they would refuse to be exempted from that component of the class.

Content related to this blog posting can be found at HippoCampus under Work.

The New MathPrint on the TI-84 Calculators

2010-03-01T11:58:00.001-08:00

This past week Texas Instruments released a new operating system (OS) for their TI-84 series of calculators. The new operating system is free, free is good in education.

It surprised me to see this new release. I have owned my TI-84 for at least five years, making it long past when I thought I would see a major change in the OS. The new operating system has a feature called MathPrint that displays the mathematics on the calculator screen in a format that more nearly matches what you would see in a textbook.

Figure 1 below is what the calculation of the sum of the numbers from 1 to 100 looked like on the previous OS that was originally released with the calculator. On the right is what the calculation of the sum of the numbers from 1 to 100 looks like in the new OS.

Figure 1 Figure 2

Working from the idea that distance is the integral of the velocity, the calculation for the distance an object that is released from rest falls under the influence of the Earth's gravity in ten seconds would be:

What this looks like in the old operating system is in Figure 3, in the new operating system is in Figure 4

Figure 3 Figure 4

I think it may take a bit more time to enter expressions in the new operating system, but I think that will be time well spent. When writing equations in physics you can better illustrate the physics behind the mathematics if you can keep the numbers and the expression in the equation written in a form that corresponds to the role those numbers play in the original problem.

Let me illustrate this in a task as simple as graphing the motion of a long pendulum that completes 1 cycle every 5 seconds and has an amplitude of 1/2 of a meter. From mathematics, students will know that 1 cycle is 2 pi radians. But there are several equations that come to bear on this problem.

It is not all that obvious how the numbers in the problem go into the equations above, but by simple recalling that omega is the angular rate of rotation and is measured in radians per second, it seems very natural to say that we cover 2 pi radians per every 5 seconds. That translates rather easily into the expression:

When t = 5, we have completed one revolution (2 pi). When t = 10, we have completed two revolutions (4 pi). With that in place it seems reasonable to write:

The beauty of writing it in this form rather than as

is that it then allows you to see the physics. As t goes up we wind off more and more revolutions. If the 5 became a 10, then it would take 10 seconds to make one revolution. And let's look at the screen shots in the two different operating systems.

The new operating system can be downloaded from TI's web site, by going directly to this link. The operating system is called "v 2.53MP".

I believe seeing the math in this form on their calculators would help students.

If you want the next blog to talk more about how you get the new operating system off the Internet into your calculator, drop a note in the comment section below for this blog post.

In future posts, I'll plan to spend some time talking about other resources TI has for physics on their web site.

The 64 Year Old Teachers Meets the iPod Touch - part 2

2010-02-15T07:04:00.001-08:00

The iPod Touch makes me feel like a kid again! Not so much because it came with white ear buds, which I understand is part of the coolness factor for the teenager, the white ear buds signify you are using an iPod, that's like wearing the right brand of jeans for a teenager. It makes me feel young again because it pulled me out of my comfort zone, I had to learn some new techniques to operate it.

When I watch my own daughters work on a computer, it is obvious that they are seeing more on the screen than I am. When we are trouble shooting something an unusual icon in the corner of the screen, that to me is seemingly unrelated to the problem we are working on, will catch their attention. Yet that unusual icon or message, along with a couple of other clues, will lead to the solution. It must be a generational thing. My approach is to read a book about how it is supposed to work, then try to use it. Their approach is to try it, and if it doesn't work to search the Internet for suggestions on how to make it work.

The iPod Touch's manual was just a few paragraphs telling me to install iTunes and hook the Touch to the computer, following that they asked me to open the Safari browser on the Touch and one of the choices became "iPod Touch User Guide". That contained a "Getting Started" and a "Basics" section, they were not extensive. What I did find, is that I was now learning by immersion, not just by reading. The whole idea of tap, tap and hold, tap and drag, spread two fingers to widen the screen, where to touch to go back a menu level, these were all new to me. I learned them by playing with them, not by reading about them.

Now think back about the two different approaches to learning that I've described above and ask yourself, "Which of these is closer to what we call the scientific method"? I believe the answer is clear, and it is not the way I learned when I would first study what to expect, and then for the most part only see the parts that conformed to what I was expecting to see.

This has implications for how we teach physics. We need to let the students "experience physics", that involves labs, that involves posing questions not just giving answers, that involves having students work problems that the student can't solve on the first try. It involves not teaching dogmatically, and turning physics into an exercise of how many equations can you memorize and then see if you can pull the right equation at the right time.

Just for the record, I now have my iPod connecting to all of my email services and coordinating with the email accounts on my computer. I can make phone calls over the Touch to any place in the world using my previously existing Skype account (no additional fee). I can sync documents I have on my computer with the Touch, so that I have the documents/spreadsheets with me when I travel. I can bring up any stocks I own and get detailed charts, current prices, breaking news, and Morningstar reports. I have detailed star charts for my location and time. I don't need to wait for tomorrow's mail to arrive to read about what happened today. I can read the major breaking news stories from the New York Times, the Chicago Tribune, and USA Today instantly, I have available all of the approximately 150 Sirius-XM radio channels that used to only be available to me in the car, and I can connect the Touch to the stereo system in my living room if I want to listen to them that way. I can watch video lecture presentations from any of 1,900 courses from MIT through the MIT OpenCourseWare initiative, and if I like I can hook the Touch to my 32" HD TV to watch them in that format. Not bad for a 64 year old!

The 64 Year Old Teacher Meets the iPod Touch

2010-02-01T11:04:00.001-08:00

Many teachers say "I've learned a lot from my students". If they are talking about course content, I think that is a travesty. If they are talking about learning from their students what common misconceptions are, or how to explain the material - fine.

While I usually don't make the claim that "I learned a lot from my students", one of my "most challenging to teach" students, because he wouldn't do his homework even though he had been accepted by MIT, did convince me I needed to get an iPod. This is the student I referred to in the Oct. 20, 2009 blog, and by the way he did email me back a couple of days after my post in the Nov. 2 blog where I indicated he hadn't emailed me back.

Now my need for an MP3 player is to listen to podcasts (I can listen to my music on my CD player). For the most part I like technology, in fact I had two MP3 players ahead of picking up my iPod Touch for Christmas this year. Very briefly, the first MP3 player I bought was in 1997, but it very soon became obsolete because they were still changing the MP3 formats. About half the material I would download wouldn't play on it, although the material was supposed to be MP3 content.

The second MP3 player was more of a name brand unit, a SanDisk with 1GB of memory, that was a lot of memory for the time. It cost me about $100. This MP3 player had four buttons on it and a small joystick type button. It also had a small screen that could display text. One button was for recording external sound, I didn't need that. One button was for going between point A and B in a song, and then repeating that section, I didn't need that. One button was "hold" to pause the music, I didn't need that either. That left one button and the joystick control to run the unit with, and this is where the problem begins.

I grew up with on-off switches that had two states: on, off! I've taken on-off switches apart, and there are contacts inside, either the contacts are open, or the contacts are closed, this is what on-off means. On this $100 MP3 player, sometimes the on-off button would turn it on, sometimes it would activate (start playing) the podcast that was in the display, sometimes it would pause the podcast mid-stream, sometimes it would shut the unit off. Sometimes (most of the time) it would take me out to an area where I could adjust the equalizer. Count them! That is six different things happening, and all happening with a single button that to me should simply be turning the unit on and off! A good on-off switch is up for on and down for off, or clockwise for on and counter-clockwise for off. This one had one direction of travel - down, and when you did that it did any of one of six or more tasks, and the motion for each task was essentially the same - push the button down.

Then there was the joystick, up-down, left-right, punch the center. Yes, I know it is supposed to choose the directory I'm in, choose which song in the directory I want to play, adjust the volume, fast forward or rewind. However, just like the on-off switch, the same motion would produce different results. Yes, I know that all of this depends on how long you hold the button down and what the player is already doing at the time you press the button. The manual was extensive, but pretty much incomprehensible, apparently written by somebody for whom English was a second language.

I was finally reduced to just punching buttons, observing what they did, and trying to write my own manual on a 3x5 index card about what this thumb size MP3 player was going to do when I pushed the two buttons I had to control it with. Need I tell you more about why my next player had a larger touch screen, the iPod Touch?

Again, I'm 64 years old. My late Dad had limited his out of town driving to distance he could reach on 1/2 a tank of gas because he couldn't figure out how to use the newfangled gas pumps to add more gas to get home on if he used more than 1/2 the tank on the way out.

When I opened the iPod Touch, I pealed off the paper that it was wrapped in, and then there was this piece of plastic over the screen. I expected it was a screen protector, as I pulled that plastic off, all of the approximately 20 icons I could see on the screen come off with the plastic. My initial thought was this must not have been a screen protector! It must have been the labeling for the buttons on the unit. I had now managed to remove all of the labeling. $380 down the tube in the first minute! At this point it is time for a 64 year old to get out the manual. The box wasn't that big, but I did find a manual. The manual for this $380 piece of equipment was a 3.75 inch by 12 inch strip of paper, folded over four times. The washing directions in the pocket of my new coat were more extensive than the directions to operate this iPod Touch.

This blog post is getting too long again, I'm going to have to wait for the next post to let you know how the iPod Touch is working out.

I do need to explain how this blog ties to the Physics. My student above had told me about the MIT open courses that include the MIT lectures on Physics by Walter Lewin . I have since learned that the Bill Gates has funded placing the Richard Feynman Lectures Online. In future blogs I expect to tie some of these lectures more directly to the specific topics in the HippoCampus online content.

Oh, and yes, I can learn some content from Walter Lewin and Richard Feynman.

Applied Physics - Applied Math - The Radio Inside Your Boom-Box.

2010-01-18T09:59:00.001-08:00

In this posting, I will continue discussing the physics and math going on inside the disassembled boom-box that I talked about in the last blog. In the previous blog, I had looked at the audio section of the boom-box, and in there we dealt with frequencies ranging from 20 Hz to 20,000 Hz.

After doing the audio section, I took the oscilloscope and hooked into the RF section of the AM radio in the boom-box. The AM dial on your radio is likely labeled from 550 to 1600, that stands for 550 kHz to 1600 kHz. I tuned in the local AM radio station at 1240 kHz and we looked at that on the scope. It is my recollection that we could also see the amplitude modulation on the 1240 kHz signal, where the amplitude of the 1240 kHz wave was varying with the announcer's voice. We then hooked into the RF oscillator in the radio that is adjusted with the variable tuning capacitor when you turn the tuning dial, allowing you to select among the various radio stations. Here we had another example of an application of changing the value of B in:

f(x) = A sin (B x + C)

By making changes to B, we were able to pick from the various radio stations that were broadcasting. Next we looked at the intermediate frequency of 455 kHz, and then on through the detector stage to the audio amplifier. Some links you might visit to learn more about how a radio works and about using an oscilloscope are How Radio Works, Explain that Stuff - Radio, Wikipedia - Superheterodyne receiver, and YouTube on Using an Oscilloscope.

We also calculated the wavelength of the local radio station using: wavelength * frequency = speed of light, so wavelength = (speed of light)/frequency = (186,000 miles/second)/(1.240 * 10^6 seconds) = 0.15 mile.

Next we talked about the FM section of the radio. The FM dial on your radio is likely labeled 88 to 108, these numbers are in terms of megahertz (MHz). Our local radio station is at 94 MHz on the dial, we then calculated that signal's wavelength.

As a physics student, and also as a physics teacher, I am often reminded of the significant difference between studying something in the textbook, doing the written homework problem on paper, and then going into the lab and looking at what should be the same topic. When you first sit down in the lab to apply it, the topic has a tendency to seem to be completely different than the paper and pencil version.

Let me describe my oscilloscope and then ask you some "lab related questions".

The horizontal speed control on my oscilloscope ranges from 0.5 seconds per division to 0.5 microseconds per division. The divisions run in steps of .5 s, .2 s, .1 s, 50 ms, 20 ms, 10 ms, ....., 0.5 microseconds. Thus, the fastest horizontal speed on the scope is 1,000,000 times as fast as the slowest speed. The width of my oscilloscope screen is ten divisions.

Let me pose some very practical questions, the answers of which should seem obvious from your textbook study, but I suspect many an A level student measured only on written tests, might have trouble with these when they are sitting in front of the oscilloscope in the lab.

Applied Questions:

1) What is the setting just ahead of the 0.5 microsecond on my scope going to be labeled as?

2) Assuming the boom-box is able to play a 20 Hz tone, if I want to display two complete cycles of a 20 Hz sine wave across the face of my scope, what should I have the horizontal frequency on the scope set to?

3) What is the wavelength in meters of our local FM radio station that is broadcasting at 94MHz?

4) Is my oscilloscope (specifications above) capable of displaying the 94 MHz signal in the RF section of the FM receiver? Why or why not?

The students in my math class gave me a round of applause at the end of the period, they had enjoyed this elaboration on how this mathematics relates to the real world.

I'll post the answers to the above four questions in the next blog, in about two weeks. It wouldn't be much of a challenge if I posted them below. They are not particularly hard questions, but you do have to apply some basic math and the concepts of sine waves to get the answers.

Content related to this blog posting can be found at HippoCampus under Period & Frequency and Wave Function - Simulation.

Applied Physics - Applied Math - It is ALL in your Boom-Box.

2010-01-11T08:36:00.001-08:00

I tend to be a rather practical person, if you can't give me an answer to "Where am I ever going to use this?", I'm probably going to look for something else to spend my time on. The activity I'm going to relate below, I did in my face-to-face Pre-Calc classroom when we were studying trig functions. I wasn't teaching physics at the time, although I think it would work very well in a face-to-face physics classroom.

I've always been interested in electricity and electronics, but when I was in high school I never had any money to spend on it (or anything else for that matter). I talked the local TV repair shop into giving me some junked TV chassis, and I took them apart using a soldering iron that was meant for doing plumbing work. That gave me a source for some wire, resistors, tubes, capacitors, etc. I could play around with those items.

After I started teaching, I happened to meet a person who did repair work for the local hi-fi store in town This was at a time when CB radios were in their prime. He was having trouble keeping up with the repairs and asked if I wanted some part time repair work. It sounded like a good idea to me, I saw it as a way to rationalize buying (and paying for) some of the electronic test equipment and hi-fi equipment I always lusted after.

During those years a local doctor in town who was into "green" in the late 70's, would bring in equipment to be repaired. I got to know him pretty well. One day be brought in a boom-box, that looked like it had been dropped from about ten feet, he indicated he wasn't asking that I repair it, but thought I might be interested in having it for parts. The door hung open on it, the front of the case was broken, the circuit board was cracked. I kept that boom-box in my garage for about a year, and then one day it occurred to me that my students might like to see and have an explanation of the inner workings of a boom-box, boom-boxes were in now and CBs were out.

I hauled my voltmeter and oscilloscope into school, along with the old boom-box. I had removed the screws holding the outer case in place. The students walked in and saw this in the front of the math classroom, the whole front side was hanging off of it. They weren't quite sure what to make of it. I had them come up around the desk, and then we did the following with this busted up boom-box:

1) I unplugged one of the speakers and then hooking the oscilloscope to the speaker, used the speaker as a microphone. I explained I could whistle a perfect C, and was probably the only person in Illinois that could do that. I whistled into the speaker and got a wonderful looking sine wave on the oscilloscope screen. They had been graphing the sine function in their math work, and mine looked just like their graphs, so they were convinced and nobody asked if the frequency was right. Of course several of them wanted to try it also, but with not having had any practice, their patterns would usually break up.

2) I then put in the audio cassette test tape I had, it had varying frequencies on it for testing frequency response. The tape would announce, "A 20 hz tone for checking frequency response" and that would be followed by the tone, the announcements and the tones would move up in frequency from the 20 hz to 20,000 hz. We watched the test tones on the oscilloscope and listened to them simultaneously. Math and science teacher know that as we move up through the frequency spectrum, the wavelength of the pattern on the scope gets smaller and smaller. Of course this corresponded nicely with f(x) = A sin (B x + C), where B is being increased.

3) Later came a section of the audio tape where they played a constant 330 hz tone for about a minute. This was for aligning the tape pickup head. I was able to use the steady tone, and adjust the volume so that students could see and hear the effect of changing A in the above equation.

4) On one side of the cassette head, there is a small screw that is used to align the tape head so that it is parallel to the direction of the travel of the tape. If the head is not parallel, the test tone from one channel will get picked up ahead of the matching test tone from the other channel, so on the scope you see the phase of the sine wave from one of the channels fall ahead of the phase for the other channel. By adjusting that screw, I could shift the phase over a range such that the right channel sine wave was ahead of the left, then to where they were the same, and then to where the left channel was ahead of the right channel. So now they were hearing and seeing the effect of C in the equation above.

I do believe the students left with a new perspective on the A, B, and C in the equation f(x) = A sin (B x + C), and why they might be of some practical value.

So far I have only talked about the cassette player in the boom-box. In the next blog posting I'll spend some time describing the AM, FM, and power supply sections of the radio that we were also able to look at and relate to the trigonometry we were studying.

Content related to this blog posting can be found at HippoCampus under Period & Frequency, Wavelength, and Sound Waves.

Centripetal Acceleration - A Banked Turn - No Friction

2009-12-27T12:01:00.000-08:00

In the previous blog I talked about the classic problem of a car going around a banked frictionless curve. There were two web sites I used, that I will place in links below to make it easy to follow along with this blog post.

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In order to drive a car around a curve, there must be a frictional force between the tires and the road, or the road must be banked. Consider a 1250 kg car traveling at a speed of 25.0 m/s around a curve with a radius of 175 m.

b.) If the curve is banked and the road surface is frictionless, what must be the angle (with respect to the horizontal) of the road surface?

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At http://mtl.math.uiuc.edu/~t-anders/blog/road_slope_problem.htm is a dynamic free body diagram of this problem. (This diagram relies on your browser being able to handle Java, most newer browsers can.)

At Batesville.k12.in.us web site is a static sketch and the algebraic solution of this problem, resulting in the equations:

Equation 1

And therefore the needed angle::

Equation 2

The physics of the solution is that the gravitational attraction on the car shown by vector GF must be balanced by the upward component of the normal force shown by vector GC. We know that vector GF and GC must have the same size because the car is not accelerating in the vertical direction. Notice that both vectors GF and GC are the same length, and will remain the same length throughout the problem. This argument corresponds to the Batesville equation N cos(theta) = m g, where m and g are constants.

Because the road slopes down as you move from point B to O, on the frictionless surface the car would want to slide towards point O. The component of the force pushing it to the right is the horizontal component of the normal force and is shown by vector GE. When done at the correct speed with the correct bank in the road, the car will make it around the bend despite it being a frictionless surface. Vector GE is the force that is supplying the centripetal force that when things are balanced, will keep the car coming around the curve in the road without sliding up towards B or down towards O, vector GE providing the force for the circular motion:

For additional understanding, and to help students check the reasonableness of answers they have arrived at, I like to have students look at the ends of the domain of the situation as well as in the middle of the domain to see if the solutions they got make sense. I will move along that line of questioning as we look at the correct solution given above.

Here would be some questions to ask your students:

1) If you drag point B down to point A so that the surface of the road is horizontal, what will happen to the car as it tries to round the curve? (Ans: The car will continue in a straight line, thus slipping off the road in the direction of point B.)

2) If you drag point B up to where angle AOB is a 45 degree angle, and then you drive very slowly around the curve, what will happen? (Ans: Due to the slope of the curve, gravity will drag the car downward towards point O, causing you to slip off the road towards the inside edge of the curve.)

3) If you drag point B up to where angle AOB is a 45 degree angle, what is it in the free body diagram that displays the centripetal force that is going to bring you around the curve? (Ans: As point B moves up to 45 degrees, the horizontal component vector GE becomes longer, indicating there is more centripetal force, which is the force needed to make the car follow a circular path.)

4) If you drag point B down to point A so that the surface of the road is horizontal, what is it in the vector diagram that supports the answer you got in question 1? (Ans: All of the centripetal force shown by vector GE disappears, so there is no force present to make the car follow a curved path.)

5) Does equation 1 also support the same result that you answered for questions 1? (Ans: Yes, when theta = 0, tan(theta) = 0, and v = 0 becomes the velocity needed to stay on the road. The car can only stay on the road if it is stopped. If it is moving, with no traction supplying a horizontal force, and being on a frictionless surface the car can not go around a bend. )

6) As you increase angle AOB by giving more slope to the road, does equation 1 reflect that the velocity would need to be higher to make it around the bend? (Ans: Yes, as theta increases, tan(theta) increases, r g tan(theta) increases, and that increases v.

7) If you increase the velocity in equation 2, how does that change the angle theta in equation 2? (Ans: As v increases the argument of the tan function, v^2/(g R), increases. As the argument increases the value of arctan increases, so theta increases.)

8) Sketch me a graph of arctan(x) to explain why your statement in 7) is true.

9) When you drag point B upward until you get an angle of 80 degrees, you see vector GE becomes extremely long, explain why this is the case in terms of what is happening with the car. (Ans: As the road becomes very steep, the car a large tendency to want to slip to the inside, moving down towards point O. The faster the car goes, the more of tendency it has to slip outwards towards point B. To overcome the extreme slope in the road created by an 80 degree angle, the car has to go extremely fast to get a large enough component of the tendency to want to slip out to B to overcome the slope of the road and gravity trying to push it toward O.)

10) How fast does the car have to go to stay on the road if the angle of the bank becomes 90 degrees? Support you answer with common sense, with the vector diagram, and with equation 1. (Ans: At 90 degrees there is no vertical component to the normal force being supplied by the road. In the vertical direction only gravity is acting, and the car will fall towards point O. The vector diagram is saying the horizontal component of the normal force would have to become infinite (notice how long vector GE becomes). In effect the vector diagram as it is drawn becomes inapplicable at 90 degrees because there should be no vertical component vector GC, and we can't have an infinite normal force. Equation 1 agrees with these results, because as theta becomes 90 degrees, the tan(theta) becomes infinite, and the equation says we would need an infinite velocity to be able to stay on the road.)

11) When the carnival used to come to town they had a silo with a sloping base and vertical walls. As the viewer, you would go up a platform to the top of the silo, about 15 feet up, and look down into the silo. A motorcycle rider would start riding on the sloping base, increase his speed, and finally circle inside the silo on the vertical walls. How could he do that based on the previous ten answers? (Ans: His surface wasn't frictionless! I doubt that he would try this on a rainy day.)

Content related to this blog posting can be found at HippoCampus under Uniform Circular Motion, Centripetal Acceleration, and Racetrack - Simulation.

Using Multiple Representations in Physics

2009-12-14T11:41:00.001-08:00

The National Council of Teachers of Mathematics has placed a lot of emphasis on using multiple representations when teaching mathematics. By that they mean students should be able to deal with mathematics by writing about it, talking about it, viewing it visually such as when graphing or as in geometric drawings, and by viewing it algebraically as in equations and functions.

One of the classic problems in first year physics is to calculate the amount of bank needed to prevent cars from sliding off the highway when they round a curve at a given speed. This problem can benefit from multiple representations.

This problem comes up in my AP Physics C course from Monterey Institute, it is problem 2 part b) on the end of Chapter 5 FRQ. Here is how it is stated there:

--------

b.) If the curve is banked and the road surface is frictionless, what must be the angle (with respect to the horizontal) of the road surface?

--------

If you search the Internet, you will also find a good drawing and a good explanation of the solution to this problem at the Batesville.k12.in.us web site , explaining why the relationship between the velocity, the radius of the curve, the acceleration of gravity, and the need angle will be given by:

Equation 1

And therefore the needed angle will be given by:

Equation 2

In addition to looking at the problem in terms of equation, I also want to look at this problem graphically in a free body diagram, and I want to suggest how we might relate these either by asking the students to write about their solutions, or to discuss their solutions in class. When looking at the free body diagram, there is now software out there that will allow you make a dynamic free body diagram that can be manipulated to see how things change with the amount of bank in the road.

The equations themselves, and where they come from, are nicely covered at the above Batesville.k12 site. By looking at this graphically we can go farther, getting an even deeper understanding of the physics that is happening in the problem, getting a feel for the underlying mechanics.

I have added a "dynamic sketch" of the situation at http://mtl.math.uiuc.edu/~t-anders/blog/road_slope_problem.htm . (This diagram relies on your browser being able to handle Java, most newer browsers can.)

Line segment BO represents the bank on the road. If you drag point B you can change the angle of the bank on the road (angle AOB). The car is located at point G, and vector GD represents the normal force exerted on the car by the road. As you move point B, try and relate what you are looking at in the free body diagram, to what you are seeing in the Batesville equations, and to the description of the original problem. See if what you are looking at visually makes sense. Think about questions you might ask your students as they look at the multiple representations.

In the next blog, I will talk about the underlying physics, and suggest some questions you might ask your students, either in class, or in a written exercise, to cause them to think about whether a particular solution really makes sense.

Content related to this blog posting can be found at HippoCampus under Uniform Circular Motion, Centripetal Acceleration, and Racetrack - Simulation.

Finding Your Way Around the Winter Sky

2009-11-30T09:58:00.001-08:00

There is nothing that is more awe inspiring to me than to go out on a very clear night and look at the stars, realizing that each of them is the equivalent of our sun. It puts things in perspective for me. I believe an appreciation for the magnificence and immensity of the universe is something every parent should share with their child and every physics teacher with their students.

In June of 2009 I did a blog posting regarding finding your way around the summer sky. As we move into December 2009, this posting is going to be about finding your way around the winter sky (if you live north of the equator).

In The Stargazer's Bible by W.S. Kals that I referred to in the June posting (I believe it is out of print), the author presents a mnemonic for finding your way around the winter sky, it reads:

"CAPtain, ALL DE RIGging SEEms PRoperly POLished."

This stands for the names of the six bright stars that make up the winter hexagon, Capella, Aldebaran, Rigel, Sirius, Procyon, and Pollux. In Figure 1 below, I've placed a wide view of the night sky to place the winter hexagon in context, I followed that by Figure 2, where I have enlarged just the winter hexagon.

Figure 1

Figure 2

The chart above is what the sky will look like at midnight near the middle of December, facing south. How high the pattern is in the sky will depend on your latitude, the curved arc you see in Figure 1 is the path the sun would have taken through the sky that day, known as the ecliptic. Knowing how high the sun was during the day will give you an idea how high up to look in the southern sky at night for these stars. This is a very large pattern in the sky spanning about 60 degrees of arc from one side of the hexagon to the other.

Each of the major six stars in it is associated with some of the best known constellations, the names of which are highlighted in yellow above. The three stars that form the belt in Orion, are one of the easiest objects to spot in the winter sky, and you can use those as a jumping off point to find the six very bright stars named above. From those six bright stars, you can more easily locate each of the constellations.

As the map shows, the constellations are near the ecliptic. I've highlighted the names of the constellations and the stars in the above map. Capella is the bright start in the constellation Auriga the Charioteer, Aldebaran is the bright star in the constellation Taurus the Bull, Rigel is the bright star in the constellation Orion the Hunter, Sirius is the bright star in the constellation Canis Major the Big Dog, Procyon is the bright star in the constellation Canis Minor the Small Dog, and Pollux is the bright star in Gemini the Twins.

I wish to acknowledge that the above star charts came from the "Free Star Charts" link of the web page for The Department of Physics and Astronomy at Stephen F. Austin State University .

Making use of Mathematica in Physics

2009-11-15T18:10:00.001-08:00

It's never easy to know how much technology to use when teaching science and math. I'm coming over to the philosophy that an appropriate aspect of the process of thinking about that is to factor in what I do myself, when I'm working the problems sets for myself. I don't balance my check book without reaching in the drawer and getting out a calculator. If I have "modeling" to do for personal finances, I'll use a spreadsheet. If I'm working a physics problem set, I'll often turn the mathematics over to a piece of software called Mathematica.

When I'm trying to explain the physics to a student, I want to focus on the physics concepts, and not spend a lot of time going though algebra steps or graphing steps the student already knows, but we all know can take quite a bit of time. Mathematica allows me to use my time to focus on the physics.

Some Basics of Mathematica

To solve an equation, we use the command Solve, the syntax of which is

Solve[the equation written with a double equal sign, the variable to solve for]

For example the equation for the time it takes an object dropped from rest to fall 100 meters, under the influence of gravity would be:

The work above is the physics, solving for t is the mathematics, and that we can turn over to Mathematica by using the Solve command.

Here is this equation solved in Mathematica, what you input is shown in the line called In[1], the solution you get back is shown in the line called Out[1].

And here is a quick and easy plot of the distance an object falls under the influence of gravity in time t.

The command is Plot. One way to handle the syntax is to define the function using an underscore after the variable name on one line, and then use the Plot command in the next line. The syntax of the Plot command is:

Plot[ name of the function to plot, the domain you want it plotted over]

I did leave off the labels for the axis to make the syntax easier and to save time.

With a graph quickly in place, now you can talk about the physics that is going on in the graph. Does the object fall the same distance during each one second interval? And then on to another question about the physics, does the velocity change by the same amount during each one second interval?

Recall that velocity is the derivative of the position, so let's make a graph.

And what is happening to the acceleration, which is the second derivative of the position?

Or maybe you have a more complicated problem where you want to focus on conservation of momentum and not have the focus be on the mathematics. Two objects of mass m1 and m2, each 10 kg collide. The initial velocity of m1 was 20 m/s, and m2 was sitting at rest. After the collision m2 is observed to leave at an angle of 30 degrees above the horizontal with a velocity of 6 m/s. What will the velocity and angle of departure for m1 be after the collision.

From the conservation of momentum, the physics is:

Turning the algebra over to Mathematica looks like this:

I'd be interested in hearing if other physics teachers agree or disagree with these thoughts.

Content related to this blog posting can be found at HippoCampus under Equations of Motion.

Linking in the MIT Physics Video Presentations

2009-11-02T10:27:00.001-08:00

As you might have guessed, my "errant" student, mentioned in the previous blog, didn't email me back. Given the amount of arm twisting I had to do last year to get assignments turned in, my prediction would have been "no reply".

In this blog, I'll finish off describing how I have linked the MIT content into my course and also explain why I did it the way I did. If you do a Google search on (MIT open courseware physics) you will get in excess of 200 hits.

My initial thoughts were that I would link to the "YouTube" version, certainly the students would relate to that. However, what I found is that while the video was there, it still needed to be selected out of a group along the right side of the screen. Of course I could drill down further, and get the URL to the specific lecture I wanted, but I didn't find the material at this site to be organized in the topic order that reflects the order concepts are typically taught in most physics courses. I also found I had to watch much of the video to identify the topics that were covered in the video and I needed to know those topics to link it correctly into my course as an enrichment activity.

I found it much more convenient to go directly to the MIT web site for the course I wanted. At that site, the content was laid out in a way that made it easy to identify what the lecture was about, and then to slot it in as an appropriate link in my course (graphic of the MIT site below).

Doing it this way, when I click on one of the above links, I am able to give my students several choices in how they might view the lecture (shown below).

My course is based on the National Repository of Online Courses (NROC) and the free online HippoCampus content. Because this MIT web site had the traditional naming of the topics, as well as the traditional ordering, it made it easy to link specific videos into my course at appropriate locations.

My course as originally supplied, has its own set of videos, as well as examples, and practice problems. After the material has been presented, students take a Self Check Quiz over what they learned, I use the Self Check Quiz solely as a practice area. But following the Self Check Quiz is the real Quiz that becomes part of their grade. I wanted my students to do the Self Check right after they had gone through the original material. But then I felt that after the Self Check would be a good time to give them the opportunity to also see a second, but somewhat different presentation of the same material. If they choose to watch the MIT lecture, my expectation is that this would help them on the Quiz. Below is a graphic of the slotting into my course:

Before leaving this topic, I also want to add a more general link to the MIT content. Here they give more details of what all is on their site that pertains to physics. I've circled in green the course title of the material I'm linking in as enhancement/supplemental materials to my AP Physics C - Mechanics course.

The MIT materials, as you should expect, is written, selected, and presented at a level that targets the average MIT student. That makes it a notch above what an average AP level course would be taught at, and that's OK. We still have students in our classes that can benefit from this as an enrichment/supplemental activity.

Linking the MIT Physics Lectures into My Online AP Physics Course

2009-10-20T18:01:00.001-07:00

One of the changes I'm making in my online AP Physics C course this year, in keeping with my previous blog suggesting that you should try to improve your teaching and/or course each year, is to create links in my course to other related quality content on the Internet. As a physics student at the college level in the 1960s, I remember seeing a 16 mm film from the The Feynman Lectures on Physics series. I expect it would have been presented to us in an evening enrichment session rather than used directly in our physics classroom; we didn't spend our physics classes watching movies.

I had never seen anybody that could talk about physics the way Richard Feynman could. I thoroughly enjoyed watching his films and seeing the additional insights that Feynman could pull out of the topic; insights that I was not getting as I attended class, read the textbook, and did my homework. His lectures were both helpful and entertaining, and I in no way am I indicating that my college instructors weren't doing an excellent job. There aren't going to be more than a handful of people in the entire USA that can present the material like Richard Feynman did.

A few years back, MIT adopted the policy that they would make all of their course content freely available on the Internet. I had made excursions out to their site over the past few years, but I never found quite what I wanted. Last spring their site came up in a search I was doing and their site seemed better organized than it had been on my previous visits. So in April I sent an email to my students that there was an MIT lecture on Ampere's Law on the Internet. Ampere's Law is a rather abstract topic, and I thought the video lecture would be helpful to my students, so I added it and treated it as an enrichment activity.

This year I'm linking the MIT lectures directly into my online Illinois Virtual School AP Physics C course, and now I'll explain why. I had one recalcitrant student from the Chicago area, that I had a heck of a time getting any homework out of and getting him to attend the online screen shares. Every week for most of the semester I had been sending updates to the student, the parent, and the school indicating that the student had an F going in the class. I had been told by the student's local school that the student had all kinds of ability, that he was planning on attending MIT, and that he had already been accepted at MIT. I couldn't have gotten into MIT, but that didn't diminish my willingness to give the F if I didn't receive the work

It turns out that just I was emailing the link to the MIT lecture on Ampere's Law to my students, this student was visiting the MIT campus. Below is part of the Email exchange I had with this student after I sent the link to the MIT web site. My April 25 email struck a chord with him!

--------------------------------------------------

From: [Student's name removed]

Sent: Tuesday, April 28, 2009 10:17 AM

To: Tom Anderson

Subject: Re: The MIT Open Course Web site

Hi Mr. Anderson,

You can actually download all the physics lectures through iTunes for free and use it either on the computer or an iPod (and don't have to rely on You Tube). I actually downloaded these already too.

Sincerely,

[Student's name removed]

On Sat, Apr 25, 2009 at 3:00 PM, Tom Anderson wrote:

Hi Folks,

As I've been searching for some other materials on the Internet this morning, I tracked back further on the MIT web site where I had found the video on Ampere's Law that I sent earlier today.

I have found the videos presented by MIT correspond almost chapter by chapter with what we have studied this year.

--------------------------------------------------

In the next blog I will give the web site that I have been using to get to the MIT Physics lectures, and also talk about how I'm linking them into my online course. I will also email the student above and see how it is going for him at MIT, I can't guarantee that I will get a response, but I will let you know in the next blog if I get a response.

Changes I'm making to AP Physics C this year.

2009-10-05T10:57:00.001-07:00

In the last blog, I talked about the idea of the "10% Solution", referring to the idea that to improve your teaching/courses you should try to change about 10% of what you do each year. I remember reading about an employer who said he gets applications where the person says "I have have 20 years of experience", and it would have been more correctly stated if they had said "I have 1 year of experience, and I have experienced it 20 times". The 10% solution can prevent this.

This year in my AP Physics C class, I'm changing (or adding) three main components. The first of these is feedback on quiz questions. The original course did not have feedback on the questions in the quizzes. When a student finished a multiple choice quiz question, he would know the answer was for example "A", but had no other feedback supplied. I had always told my students that if they had questions in the online quizzes that they couldn't figure out after they had seen the correct answer to the multiple choice question, they should email me and I would provide additional explanation. Unfortunately, the reality was that there were not many of the students who would take the time to do that.

Since I had worked all of the problem myself when I first taught the course, I had solutions. The problem was that they were in my three ring binder, and that didn't help the students much. In replying to a student's email request regarding a particular question, in the past I would write up that particular solution and send it back as an email reply. This year, I am scanning all of my solutions for each individual quiz into a pdf file, and then I use a screen capture utility where I pull off one solution at a time, and paste that solution into the "feedback" box provided in the online quizzing program. It's not fancy, but it sure takes a lot less time than typing the math out for each solution to each question, or responding to requests by students on a question by question basis. Pasted below, as an example, is what I have captured and pasted into the "feedback" area for an individual quiz question.

I do think that making this change in my course will help my students. Using this method I can supply "feedback" like this for a 15 question quiz in about 30 minutes. If I were to try to type up the solutions, it would probably take about three hours. I'm planning to do this for all of the Quizzes and Self-Check Quizzes in my course over the duration of the school year.

Below is an unsolicited email I got back from a student after he hit the first quiz where I had made this change, there had been a Self-Check Quiz ahead of this that the student had taken that didn't have the change made in it yet, so it was clear to the student that something had changed.

From: [Student Name] [mailto:name@sbcglobal.net]
Sent: Friday, September 18, 2009 7:51 AM
To: Anderson, Thomas
Subject: [Student Name]-Quizzes

Hi,

Thank-you for posting the questions and answers to the first quiz, but I was wondering whether you could do the same thing with all the other quizzes, so that I know where I went wrong.

Thanks,

[Student Name]

In the next blog, I'll move on to the other changes I'm making in my AP Physics C course this year.

The 10% Solution

2009-09-18T12:41:00.001-07:00

Ah! A summer off!

I know that there are a lot of people in the private sector that envy us teachers during June, July, and August; not so much during the rest of the year. The great teachers I know are usually individuals who are interested in so many varied things, that if they didn't have three months in the summer to explore them they would go crazy.

Believe it or not, a welcome summer vacation activity for me is to attend a week long AP conference. Two years ago I was able to attend a week long AP Calculus AB conference in Connecticut and a week after that attend a week long AP Physics C conference in Denver. I enjoyed meeting with and observing some very good teachers 25 to 30 years younger than myself, teachers that were both knowledgeable in their subject matter and enthusiastic about teaching.

As we start the new school year, if you are a teacher, I hope you are thinking about what you will do differently this year to improve on the good job you did last year. A few years back I had the opportunity to be part of a team of mathematics teachers, working on behalf of the University of Northern Iowa, that were involved with a grant to provide professional development to the math teachers that teach on our military bases around the world. About seventy-five teachers that teach for the Department of Defense would come to the Iowa campus for a week in the summer, and the UNI staff would work with them during that week. Then at one point during the school year we would travel to their schools to team teach and work with as many of them as we could in their own classroom on the military bases. In my case the bases I visited were in Germany and Japan.

Throughout that process Jack Wilkinson, who directed the project for UNI, stressed a concept he called the "10% Solution". The "10% Solution" refers to trying every year to change 10% of what you do in the classroom to improve your teaching and the classroom experience. While I think I probably had done that during most of my years of face-to-face teaching, I never had heard it expressed as elegantly as it was with the simple phrase "The 10% Solution".

In two weeks, I'll post a blog talking about the changes I'm making in my online courses for the 2009-2010 school year.

iLabs - Remotely Controlled Science Labs from Northwestern and MIT

2009-06-08T07:06:00.001-07:00

Those of you who teach an AP science course online know the frustration of trying to meet the College Board's lab requirement that the labs for your course must be "wet labs" as opposed to "dry labs". "Dry labs" is a term used for labs such as those that would be a simulation done on a computer, often done over the Internet. During the year I included in the blog some of my favorite online simulation, these were activities that I felt were very beneficial for helping students understand the material they were studying.

HELLO NORTHWESTERN AND MIT! Northwestern and MIT have an NSF grant to produce nine Internet based labs where students work with REAL EQUIPMENT, but they do so remotely over the Internet. This year I had the opportunity to be one of the early teacher testers of the first lab they have brought up. This first lab uses a radioactive Strontium-90 sample located in Australia, and students can take measurements of the amount of radiation given off from this sample at various distances from the sample. Try doing that as a wet lab in your high school classroom and you won't be teaching long!

The science behind the lab focuses on how rapidly the level of radiation from a point source falls off with distance. To increase the student level of interest, they pose the questions "Am I frying my brain with my cell phone?" Then the fall off with distance of the radioactive radiation from a Strontium-90 source is used to model the rate that electromagnetic radiation from a point source would fall off at.

When I submitted my course syllabus for AP Physics C, it was initially rejected because I was making use of "virtual labs - simulations" for some of the labs that went with various units. I wrote the lab portion of my curriculum over to only using "wet labs" in order to satisfy the AP Audit committee. In the original rejection the College Board had written:

"The panel that reviewed the submitted labs found examples of virtual schools' labs that provide a college-level lab experience for their students. However, there is insufficient evidence in your course's case that the learning experiences provided by your virtual labs meet the goals identified in the National Research Council’s America’s Lab Report."

I asked the Audit Committee to please share with me some examples of the virtual schools' labs that did meet their requirement. Despite numerous emails, phone calls, and discussions with College Board representatives at national conventions, I never did get from AP Central a single example of a virtual lab that meets their requirements.

Below I'm going to paste write ups from three of my Illinois Virtual HS students in Calculus II that did the radiation iLab experiment. The first post is from Jacob, a senior at a high school in Illinois who took AP Calc AB as a Junior. The second post is from Max, a sixth grader in Illinois. I meet Max a year ago when he was in 5th grade, he took AP Calculus AB from me as a 5th grader and scored a 5 on the AP exam. The third post (it is still coming in) is from Joe, a high school senior who is an Illinois resident but spent the past two years in Vietnam because his parents were working there. Joe is flying across the Pacific to day as I post this, he is on his way back from Vietnam (as I expect his write up is).

I will be watching to see if the College Board is prepared to say that labs using real equipment from Northwestern and MIT, taken by students like these, won't meet their lab requirements. I think it's time we look for ways to provide a meaningful education to these students, and I invite the College Board to join me, my students, Illinois Virtual High School, Northwestern, and MIT in that venture.

The home page for the iLabs project is at http://ilabcentral.org/ .

***********************************

From Jacob - 12th grader in Illinois taking Calculus II

Radiation from Cell Phones

Recently I was part of a lab that was taking a look at the effects of cell phone radiation on the body. Specifically, our lab focused on the effect distance has on radiation. We were allowed control over a Geiger counter that was monitoring a sample of radioactive strontium-90. We could change the distance between the sample and the counter. I used distances of 15 millimeters, 25 millimeters, 35 millimeters, and 45 millimeters. I did ten trials, where the counter would take a reading at each distance and then report the totals to me. I then charted all of these values compared with the distances, and I got this:

(Click on any of the graphs to get enlarged copies.)

As you can see for each trial, there seems to be a general rule. Next, I took the average of all the values of each distance and came up with a single chart of the averages.

The next step was to try and find an equation that matched this curve. For our lab, we tried a linear function, an exponential function, and a power function. We then compared these graphs to the average to see which function best fit the rule.

Each function was given an R^2 value. This value measures how closely the estimated function fits the given information. The closer R^2 is to 1, then the closer that function fits. The function that had the R^2 value closest to 1 for my graph was the power function, with a function value of y = 26818 x^(-1.4841). What this means is that as the distance increases, the value of y, or the particle count, will continue to decrease at a predictable rate. With this information, we can make the following statements in addition to the facts already established about cell phones and radiation:

· The more distance between a cell phone and a cell tower, the more radiation emitted between the phone and the tower.

· After the initial connection is made between the cell tower and the phone, the amount of radiation being emitted is decreased.

· The closer the phone is to the person while this connection is being established, the more exposure that person will receive.

· Wireless headsets are another source of radiation, but wired headsets do not emit radiation of any kind.

After analyzing these statements, the following precautions can be taken to ensure safety:

When first placing a call, do not hold the phone directly up to your head. Instead, wait until the phone begins to ring to hold it up to your ear.
Do not use wireless headsets. While the amount of radiation being emitted is extremely minimal, it is still safer to use either a wired headset or no headset at all.
Place calls in urban areas. With the closer proximity to cell towers, the phone has to put out less radiation to establish a connection.
Texting or other forms of short messaging is safer than making calls. Simply sending a message requires less radiation than establishing a connection for a phone call.

Hopefully this post will be helpful in promoting proper cell phone usage.

***********************************

From Max - 6th grader from Illinois taking Calculus II

Radiation from Cell Phones

Cell phones do emit radiation. The gadget uses electro-magnetic microwaves to communicate with the cell phone tower. If you want to reduce the risk of cell phones, there are a couple of things you can do. You could use speaker phone instead of talking directly into the phone. In our experiment it was shown that the radiation level from a radioactive sample is modeled by d^(-k) where d is distance and k is 2. This was done by measuring the radioactivity from a Strontium-90 source at different distances using a Geiger counter. I then plotted the data and added best-fit curves. Here is a plot of my data.

Another way is to text people instead of calling them. This helps because the phone is much farther away from your head. Also, the time where there is the most radiation is at the beginning of a call. At this time, you could avoid keeping your head close to the phone. Or, you could wear a lead suit, but then you will die of over-heating.

***********************************

From Joe, an Illinois resident who completed his Junior and Senior year in high school as a home schooled student in Vietnam.

Radiation from Cell Phones

Research shows, by the end of 2009, half the world’s population will be using cell phones (Source A). This extraordinary statistic means it is now more important than ever for users to be informed of the safety risks extensive cell phone use can bring, and even more importantly how these risks can be lessened or avoided.

While the risks involved with using a cell phone are extremely small in the first place, there are health issues that can be caused by the radiation from the cell phone which include tumors and growths (Source B). However these issues have only been found in those who use their cell phones extensively, such as heavy use for ten or more years. While the average user generally doesn’t have much to worry about, it is important to be informed.

Radiation from a cell phone, firstly, is not what most people associate it with. Radiation is “the process in which energy is emitted as particles or waves” (Source C) There are two types of radiation, ionizing and non-ionizing respectively. Ionizing radiation is the dangerous type of radiation that comes from sources such as plutonium. Non-ionizing radiation includes radio waves, visible light, and cell phone transmissions. However it Non-ionizing radiation can still have long term negative effects, and therefore as with all radiation it should be avoided when possible.

I conducted a study on a Strontium-90 sample, which is radioactive, to get a better understanding of how radiation works and to see how radiation exposure can be reduced.

Since distance is the best way to lessen the exposure of any radiation, the tests I conducted are strictly of that nature. I set up an experiment to test the radiation levels of the Strontium-90 sample at 15, 25, 35, 45, 55, 65, 75, and 85 millimeters away using a Geiger counter. I ran each of these tests for five seconds. The graph below is the data I collected from this experiment.

As you can see from the graph, as the distance increases the amount of “hits” or simply put the amount of radiation decreased. Anyone who has taken math through Algebra might recognize this plot as a power decay graph. And they would be right. As it turns out as the distance you put between you and the radiation source increases the amount of radiation you receive is a power decay graph. This is shown in the graph below.

So in light of these findings there a few steps you can take to decrease the amount of radiation you receive when you use your cell phone.

The amount of radiation emitted by your phone is greatest when you first make a call (this is because the cell phone works at maximum power when first used in order that it may connect to the tower, once connected it will decrease the radiation emission depending on how far you are away from the tower in order to conserve its battery) therefore one way to decrease the amount of radiation your head receives is to remove the phone from your head until it is connected.
Use text messaging. When sending a text there is no need to put the phone to your head, and it also does not work as hard to send the message out, as it only needs a short burst of radiation to send the message.
Use a speaker phone or hands free, this again removes the phone from your head, greatly reducing the amount of radiation you receive.
Last but not least, use your phone in moderation. When you don’t have to use your phone for long periods of time, then don’t.

As stated earlier, the amount of radiation you receive when using a cell phone is minimal and does not do much short term damage. The only problems occur when you use your cell phone heavily for long duration of time, such as ten years. In conclusion, cell phones are safe, and just as anything else in life, need to be used in moderation.

Source A: http://www.mobiledia.com/news/43104.html

Source B: http://well.blogs.nytimes.com/2008/06/13/the-well-podcast-answers-to-your-cellphone-questions/

Source C: http://dictionary.reference.com/

Content related to this blog posting can be found at HippoCampus under Radioactivity.

Finding Your Way Around the June Sky

2009-06-01T08:08:00.000-07:00

While I own a number of astronomy books, my favorite astronomy book is one of the more simpler ones titled The Stargazer's Bible by W.S. Kals. The price tag on my copy, purchased in 1986 was $5.95. It looks like it is out of print, but I did find used copies still for sale when searching the Internet. Several were available for $1 plus shipping and handling. The triangular pattern and mnemonic I will be describing below come from the Kals book.

The web site SkyMaps.com makes available a monthly sky chart for free. They are the source for the image below. I went out under the download latest issue link, and then scrolled down the page to where I could select the June 2009 PDF downloads link on their page. The Sky Map also contains a short narrative of interesting things to look for in the June 2009 sky.

The above sky map is for June 2009, I've highlighted the big dipper in green. The first constellation most people learn about is the big dipper, to often it ends there. If you follow the curve of the handle of the big dipper around (my blue arrow) you will come to the bright start Arcturus and if you keep going you will come to Spica. To the right of Spica is a bright star Regulus, and to the left of Spica is a bright star Arcturus. These four stars form two large triangles in the sky. To help remember the names of these four stars remember the phrase "Regular Spices And Arsenic", using the phrase to remember the names of these four bright stars as you travel around the triangles in a clockwise direction leaving from Regulus.

These four 1st magnitude stars will also help you locate four of the constellations along the ecliptic. I've highlighted the names of the constellations in the above map. Regulus is the bright start in the constellation Leo the Lion, Spica is the bright star in the constellation Virgo the Virgin, Antares is in Scorpius the Scorpion, and Arcturs is in Bootes the Herdsman.

In a future blog posting I'll move to another part of the sky and we will learn the names of six more of the brightest stars, how to locate them, and some major constellations they are associated with.

Basic Astronomy

2009-05-17T11:00:00.000-07:00

With the AP tests for the 2008-2009 year having taken place, we now have a bit more latitude in what we want to cover in our physics class for the remainder of the year. My feeling is that we need to spend some time in classes like physics talking about very interesting topics, and those are often the topics that attracted you to teaching physics in the first place.

I was attracted to science early on because it explained things in the world around me. The stars in the night sky will capture any youngsters attention, it's only as we grow old that we take them for granted. I remember how interesting it was in grade school when we first started studying about the solar system, gaining some understanding of what you were looking at when you looked up at the night sky.

During my second year of teaching high school physics (1971) I decided to hold an evening session where we went out and observed the night sky. I had recently bought an empty lot in the country, about five miles out of town, to build on. Part of my selection criteria was that it was dark out there, no street lights and at that time no yard lights, providing me a good view of the night sky. The physics department had a very moderate 1.5 inch diameter telescope and I brought that along. I also asked students to bring binoculars if they had a set. I also invited another teacher to help chaperon.

Because we only had one telescope, and only one student could be viewing through it at a time, I spent a good portion of the evening pointing out various planets, how the sky was moving, some of the major constellations, and the milky way. One of the items that I remember about the session almost forty years later is that most of my students had never seen the milky way. Even though I was teaching in rural Illinois, in a community of about 30,000 people, many of them had never observed the sky from a location other than in town. Being five miles out in the country made all the difference in seeing the milky way, as well as vastly increasing the number of stars they were seeing in the sky.

About 15 years later, in 1986 when Hale's comet was due to return, one of the local banks ran a promotion that if you took out a four year CD one of the gifts that you could select from was a Bausch & Lomb telescope. Thus I acquired my first telescope in 1986. It was a Bausch & Lomb 4000 Schmidt-Cassegrain telescope, it had a 4 inch objective lens, a motor drive to track the stars, a spotter scope, several different eyepieces - it was a nice scope. I've spent many enjoyable hours exploring the sky with that telescope.

What I did learn about teaching astronomy from that first outing is that with a high school physics class, you don't need to have a good telescope. You just need to have a telescope to entice them to come join you for a stargazing session. Giving them a visual tour of the night sky, talking about what they are looking at, and watching how the sky moves makes for a good session.

In the next blog posting I'll talk about how to find your way around the night sky, learning the names of some of the brightest stars, then from those stars how to locate some of the major constellations.

Open Courseware at MIT

2009-05-04T13:49:00.000-07:00

While I was putting together last weeks blog on the 10-minute electric motor I was searching the web looking for a picture of Cenco's electromagnetic cannon, the electromagnet that I had used in my face-to-face classroom, I came across a copy of the "electric motor" activity at MIT. Finding that link into a specific topic in a course at MIT, a little further looking brought me to videos available freely on the Internet of their Physics 8.02 Electricity and Magnetism class. You might enjoy a short clip from MIT of the results of the electric motor competition in Physics 8.02, it comprises the first 6 minutes of Lecture 19.

With many things on the Internet, you go looking for one item but before you are finished you have found others that are as good or better than what you started out looking for. I think this is why I would rather surf the Internet where I can choose the path, than watch TV where somebody else has determined the path. Last weeks discovery of the lectures at MIT have to rank as my best find on the Internet in the past year, especially as related to the AP Physic C course that I teach over the Internet for Illinois Virtual HS.

A few years back I had read in newspapers and computer magazines that MIT had required their instructors to make all of their materials available on the Internet - FOR FREE. I had connected to them at that time, and my recollection is that I was getting copies of notes, homework, and perhaps some of the tests. When I found the electric motor clip, a side panel opened on my browser with listings of several other lectures that were available. For this weeks blog, I thought these videos might make a good topic. However, I was finding bits and pieces, and as I tried to compile all of the lectures in a chronological order, I was finding some on You Tube, some on Google Videos, but I continued to have gaps in the topics. After about two hours, I don't claim to be a fast learner, I found the mother lode.

For AP Physics C - Mechanics, you want to go to: http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/index.htm . There you will find all 36 lectures (1 introduction and 35 lessons) in a chronological order.

For AP Physics B - Electricity and Magnetism, you want to go to: http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/VideoAndCaptions/index.htm . There you will find all 37 lectures in chronological order. In addition, at these sites you also get a printed transcript of the lectures. I'm going to paste in the transcript of the first 1 minute of Lecture 1. Teachers will relate to the last item in the transcript below.

-------------------------

Transcript - Lecture 1

I'm Walter Lewin.

My lectures will in general not be a repeat of your book but they will be complementary to the book.

The book will support my lectures.

My lectures will support the book.

You will not see any tedious derivations in my lectures.

For that we have the book.

But I will stress the concepts and I will make you see beyond the equations, beyond the concepts.

I will show you whether you like it or not that physics is beautiful.

And you may even start to like it.

I suggest you do not slip up, not even one day, eight oh two is not easy. We have new concepts every week and before you know you may be too far behind.

-------------------------

I have certainly found Electricity and Magnetism more difficult to teach than Mechanics. You can bet I'm going to put links in my online course next year at appropriate places to the corresponding videos from MIT. While your students would probably think you were "hip" if you linked to the You Tube version of these rather than the MIT site, remember that some schools block You Tube. Oh - and teens today don't use the expression "hip". In addition to the videos being good explanations, the videos can give your students a glimpse into what a course is like and the expectations at a our leading educational universities.

Content related to this blog posting can be found at HippoCampus under Torque.

Build an Electric Motor in 10 Minutes

2009-04-25T09:15:00.001-07:00

For those of us teaching AP Physics C, the last couple of chapters in the spring deal with magnetism and more specifically with Ampere's Law - detailing how a current in a wire creates a magnetic field. For those who teach in a brick and mortar school, the standard experiment is usually to place a compass near a wire and then send a current through the wire, showing the current swings the needle on the compass, or to use a current balance and measure the force between two parallel wires carrying current. The other demonstration that is common is the "electromagnetic cannon", a picture of which I found on the University of Illinois web site. While the U of I cannon appears to be built in their well equipped labs, commercial ones can be purchased from sources like Cenco, at Cenco it is called a "ring thrower". The electromagnetic cannon is a convincing experiment, with a lot of drama, that demonstrates current carrying wires can produce magnetic fields.

All three of these activities are rather impractical if you are teaching online. The ring thrower is too expensive and too bulky to ship out to each individual student. The compass near a wire requires a dc current source with a relatively high current rating. The parallel wires require both a good DC current source and a sensitive balance. Because AP Central wants the labs to be hands on, finding an online video demonstration of these experiments is not considered satisfactory.

For my online course, one of the labs that I have settled on relating to Ampere's Law came from an web site that I came across a few years ago, that features "Science Toys". The site has examples of simply things you can build at home that demonstrate science principles. Their 10-minute electric motor meet my needs for an experiment relating to Ampere's Law. I have bought small spools of the appropriate size magnet wire. Each year when I send out my business size envelope to each student containing the resistors, capacitor, and LED talked about in the previous March 29th blog, I also include the wire they will need for the motor. The postal service won't let me send magnets through the mail, the magnets stick to their equipment. The students have to spend about $2.00 and buy a magnet at Radio Shack if they don't already have one.

To convince the students that, "yes", I also do these labs as the instructor. Here is a stationary screen shot of my motor. The electrical tape is just a weight to make the upright pieces of wire stay in position.

My Sony still shot camera also allows me to do very short video captures, so below is a video of my motor running.

Now least you think "I've lost it", in putting together this weeks blog I came across much the same activity at MIT. Not bad company! Here is the course syllabus where they use it , you will need to go most of the way down the page to where they reference it. Here is a pdf of the motor activity as used by MIT.

Content related to this blog posting can be found at HippoCampus under Loop of Wire , Torque , and Ampere's Law.

Studying for the AP Physics Exam

2009-04-20T06:27:00.001-07:00

We are at that time of the year when you hope to be winding up covering new material in your course, and if all has gone as planned you will be entering the final stage of review for the AP Exam itself. When I plan my online course syllabus and schedule, I try to wrap up my new content and the main exam for my course so it falls two weeks ahead of when my students will take their AP exam. In my teaching situation, an individual student may be taking AP exams for more than just my physics class. By having the main exam for my course occur two weeks ahead of the AP exam, it allows my students to get feed back from my semester exam and have a reasonable amount of time for the final push of reviewing for the AP Exam.

My strategy throughout the year has been to at the end of every chapter have a series of 10 to 15 multiple choice questions drawn from old AP exams that I ask the students to work. Then I also select an FRQ question for the chapter from released previous AP exams, a question that is representative of the chapter, and I also ask the students to work that. In a follow up online screen share session we then go over both the multiple choice and the FRQ questions.

I feel that going over the multiple choice questions is particularly helpful, the students often begin physics thinking the course is about how many formulas they can memorize and learning to pull up the right formula at the right time. Because the multiple choice questions on the AP tend to be conceptual questions, like "how does this change if that changes", for most questions you do not need to be substituting numbers into a memorized formula to get the correct answer. It is more a matter of, "If A increases, does B also increase, remain the same, or decrease?" "Will the change be linear, quadratic, or exponential?" When I go over these problems with the students, they are surprised at how simply the solution can be found by using fundamental ideas with very few calculations.

In the final two weeks ahead of the exam, it is my feeling that the most effective review is going to have to be carried out by the student themselves. By this time in the year I've spent thirty-two weeks, every week helping them as much as I can to learn this material. They need to take responsibility for the final push, some students will and some won't. My recommendation to students for an effective final push is to utilize three resources:

1) The Key Concept documents at the HippoCampus web site.

2) Review the old AP Multiple Choice questions that I have been providing and going over at the end of each chapter.

3) Use the previously released AP FRQ questions and the solutions/grading rubrics provided at the College Board web site.

I find the Key Concepts documents at the HippoCampus web site to be very well written and very concise. To get to them, after going to the HippoCampus web site: 1. select your course, 2. select the Course View, 3. select the chapter, 4. select Key Concepts. They will come up as a pdf file that you can then print out.

I can't post the old AP Multiple Choice questions I use with my students here, they are copyrighted by the College Board. You are allowed to use the questions with your students. You can get back copies of these released multiple choice questions by attending AP workshops.

The previously released AP FRQ questions along with solutions and grading rubrics are freely available on the College Board's AP web site.

Online Circuit Design Kits

2009-04-13T06:42:00.001-07:00

As much as I have advocated in the previous two blog postings how important I feel it is that we use real meters, real batteries, real resistors, etc. in the classroom, I'm also intrigued by how far the online simulations of basic electric circuits that we see in an AP Physics B or C course have come. In this blog, I'm going to talk about two that I feel are very well done. I can see a teacher deciding to do a mix of the "virtual" circuits and the hands on circuits. The virtual circuits would save time, allowing students to explore more combinations of circuits in the same length of time that they might need to just do one or two hands on circuits.

A relatively simple, but realistic looking, online circuit construction kit can be found at the Ohm Zone . Below is a screen shot of their web site.

At the bottom you have your battery, several color coded resistors, light bulbs, wires, and switches. You also have a voltmeter and an ammeter to use to take measurements. By dragging the various components onto the circuit board, you create your own circuit, and decide where to place your meter to take measurements.

I've yet to see a student burn one of these meters out, or break it by dropping it on the floor. If another teacher is using the physics room to teach Earth Science in ahead of you, the lab setup time for these circuits is a lot shorter than for the physical alternative. The Ohm Zone construction kit does not allow you to change the values of the resistors or the battery. Under the "hand icon", they have fourteen exhibits of some sample circuits; circuits demonstrating series and parallel resistance, Ohm's Law, and Kirchoff's Law.

A more complex and rather elegant circuit design kit can be found at the PhET site sponsored by the University of Colorado at Boulder.

With this circuit kit, in addition to batteries, resistors, and light bulbs, you also have capacitors and inductors. You get to change the values of the batteries, resistors, and other circuit components. When I first came across the site, the item I liked best was the voltmeter, it looked so real and the student had to decide how it should be hooked into the circuit to take the voltage and current measurements. It has been my experience that understanding the need to hook the voltmeter in parallel for voltage measurements and in series for current measurements is one of the items students usually have trouble with in "real" circuit work. So seeing the student have to make that decision themselves here is a plus for this circuit design kit. I wish students would also have to change where the leads are plugged into the meter itself, as well as set the dial on the front of the meter to the appropriate setting.

But I see a lot of advantages in doing a blended approach to the circuit work, where some circuit work is done with real equipment, and other circuits are explored with quality simulations.

The circuit below is from an old AP question I gave my students on the midterm. The students had a lot of trouble with this question. The question asked what is the voltage between points X and Y.

(Click on the picture for an enlarged view.)

Perhaps if we had spent more time modeling some of these circuits using simulations like these, the students would have found this question easier.

Content related to this blog posting can be found at HippoCampus under Single Loop Circuits, Multiloop Circuits, Measuring Current & Voltage, Capacitor & Resistor Circuits, and LR Circuits.

Physics Labs with a Digital MultiMeter

2009-04-05T08:00:00.000-07:00

I have four labs that I have my students do with a digital multimeter (DMM). Because some of them are copyrighted, I can't just go ahead and post them here. However, I'll describe the labs in general, and then give you URL links to labs already posted on the Internet that would be similar. When you find a lab on the Internet, you can often copy and paste the materials into Word and then make the specific modifications you want for your own classroom.

The first chapter in my AP Physics C Electricity and Magnetism course is on Electric Potential. With the digital multimeter, a couple of electrodes made out of wire, and a couple of batteries, students can map the electric field lines created. Penn State has placed a nicely written lab on Electric Potential and Field Mapping on the Internet.

The second chapter in my course is on electric potential, thus static electricity labs would seem a natural. I've not had much luck getting the static electricity labs to give decent results. Thus I skip doing a lab in this chapter, and instead have them do two labs in the third chapter in my course on Ohm's law and Electric Circuits.

The first lab we do in the third chapter is a simple lab on DC electrical circuits. Cerritos College in California has a web site that hosts a nice introductory lab on DC Circuits that includes an explanation of how to use the DMM.

The second lab we do in the third chapter is on Ohm's Law. Cerritos College also has on their web site a nice Ohm's Law lab that would be similar to what my students do. Or you might find pages 1 though 8 at the Southern Australian Science Teachers Association web site to be a suitable lab for your students on Ohm's Law and basic DC circuits.

The fourth lab I have my students do with the DMM is looking at charging and discharging a capacitor in a DC circuit. For suitable versions of this lab activity, you might check out the following:

a) Pages 10 and 11 of Capacitor Changing and Discharging Circuits at the Southern Australian Science Teachers Association web site.

b) This site hosted by North Carolina University deals with charging and discharging a capacitor through an LED. While they use a proprietor program called Data Studio, with a little bit of effort you should be able to work around that. When they talk about using a Signal Generator, notice that they also tell the students to set its output to DC; I call that combination "a battery".

c) The lab Mr. White posted at this site, gives students work with the time constant in an RC circuit.

d) I like the way they use the calculus to lay the foundation for the study of the voltages in an RC circuit at this lab hosted by Harvard.

As exploratory material, since LEDs usually aren't talked about in our textbooks, here is a site that has a very nice background and explanation of LEDs and how they are hooked into a circuit.

Content related to this blog posting can be found at HippoCampus under Electric Field Lines, Potential & Electric Field, Resistance, Multiloop Circuits, Capacitor & Resistor Circuits, and Flashing Light - Simulation.

Getting and Using a Digital MultiMeter in Physics

2009-03-29T08:00:00.000-07:00

Last week's blog was on the need to give physics student exposure to the basics of measuring volts, ohms, and amps in a real circuit using a digital volt-ohm meter. This week, I'll talk about purchasing such a meter and finding appropriate lab material to use with it.

I now teach virtually, and while I depend on the physical school my students attend to supply the basic lab materials, I'm finding many of these schools apparently don't have a volt-ohm meter (DMM - Digital MultiMeter) in the science department. I suspect the custodial staff has access to one the school owns, but not the physics teacher. While a good DMM used to run in excess of $100 in the 1980s, like most electronic equipment the price has dropped appreciably since then.

In the past couple of weeks, as my students were working on the Ohm's law chapter, I came across two adds in the newspaper for what I would consider adequate DMMs to carry out basic circuit labs corresponding to what they are studying. The advertisement in Figure 1 is from a Farm and Fleet store, many of which populate the Midwest.

Figure 1

Figure 2 is from a Sears store. (Clicking on a picture will enlarge it.)

I find it interesting that a DMM now costs a dollar less than a decent set of screw drivers. Come on folks, let's put some DMMs in the classroom! Given these prices for a DMM, I simply asked my online students to purchase one if their school doesn't have one. It doesn't make sense to ask Illinois Virtual High School to package, pay the postage and ship a $10 item out at the start of the course, and then repeat the process for getting it shipped back at the end of the course.

I went ahead and bought myself a third DMM, the one in the Sears add. That way I have one in the house, one in the garage, and now one in the car. Here is a cleaner picture of the Sears $9.99 special, and a scan of it's features.

For the spring semester AP Physics Course on Electricity and Magnetism, I then go to Radio Shack and for a rather minimal cost I purchase some resistors, a capacitor, an LED, some magnet wire, and some regular wire. I can put these in a standard business size envelope and mail it to my students using a standard 42 cent stamp. This is a picture of my single envelope "lab-pack" that, using the DMM and a 1.5 volt battery, my students have four labs they are responsible for with this equipment.

I package the capacitor, LED, and resistors with their leads stuck into the corrugation openings of pieces of corrugated cardboard cut from the flap of a corrugated box.

Next week I'll link to some web sites that can be used as jumping off points for some labs you might choose from to have your students do with this equipment.

Content related to this blog posting can be found at HippoCampus under Resistors & Batteries in Series and Measuring Current & Voltage.

Ohm's Law Lab - Using a DMM

2009-03-21T08:33:00.000-07:00

For most physics instructors, electricity is covered in the spring of the year. While I've considered all of the physics I've taken valuable and interesting, maybe not quantum mechanics, I've always enjoyed electricity and electronics the most. I'm fascinated by what I will call "action a distance". I remember in about third grade thinking it was so neat to be able to plug the motor from the Erector Set in to the end of an extension cord, and then even though the motor was ten feet away from me, I could turn the motor on and off by plugging in or unplugging the extension cord from the wall. Nothing seemed to be moving in the extension cord, it wasn't like I was pulling on a string. I did this one action here, and then another action some place else happened.

When we started studying electromagnetic waves, I started to get an understanding of the electricity and magnetism behind how somebody in a radio station in New Orleans could make the speaker in my radio in Iowa vibrate. Of course now we control satellites beyond the solar system, and robots on other planets with the same principles. Oh Marconi, what a wonderful invention your 1895 radio waves were!

All too often, it seems to me that science teachers short change electricity. I remember my wife, a grade school librarian, telling about the day the seventh grade science teacher brought a 1.5 volt battery, some wire, and a light bulb down to the library looking for additional information. The demonstration the science book wanted her to do was to use a battery, a light bulb and some wire to demonstrate how a flashlight works, and they hadn't supplied enough detail for her to be able to create that circuit and get it to work. All too often I think science teachers "just skip that part", fortunately this teacher wasn't. Yet apparently the teachers of this teacher had skipped this topic, or taught Ohm's law only as a mathematics equation that you plugged two knowns into and got out the unknown.

Teaching my physics course online, I rely on the brick and mortar schools my students attend to supply them with the lab equipment they need for my AP Physics C course. I try to keep the required equipment to a minimum, spring scales, pulleys, weights, etc., and in the spring a volt-ohm meter to take some measurements with. When I get ready to do a couple of Ohm's law labs in the spring I find that many, actually the majority, of the science departments at their schools do NOT have a volt-ohm meter. Given that decent volt-ohm meters can now be bought for $10 or less, it seems such a shame that they aren't part of the equipment found in a typical high school science supply room. An understanding of the basics of electricity and the basics of using a volt-ohm meter to take measurements would seem to me to be one of the most practical aspects of what we are teaching in physics at the high school and AP Physics B and C level. Many technical careers depend on a basic understanding of electricity.

In next weeks blog, I will give examples of where you can pick up a decent volt-ohm meter locally in the $10 price range, give links to some web sites about how to use them, links to some web sites that host Ohm's law labs, and also a web site that supplies a virtual volt-ohm meter and a virtual circuit construction kit.

Content related to this blog posting can be found at HippoCampus under Resistance and Single Loop Circuits.

Video Capture and Posting using Jing

2009-03-15T12:52:00.001-07:00

Two weeks ago I talked about and demonstrated the free program CamStudio that you can use to make video screen captures with sound. The quality of those videos is quite good and there was not a lot of messing to produce the video. You ran the CamStudio program to capture the action on your screen, you then converted the file to a ".mov" or ".swf" file to get the file size down, and then you uploaded the needed files to the server you have space on. If you don't have server space on a convenient server, you don't want to do the file conversion, you don't want to work out the URL for the file on your server, you are a beginner to video capture, or any combination of these, you might be interested in starting with Jing.

Jing is a free video capture program that also gives you access to a companion web hosting site screencast.com. Jing skips the process of having you convert the file to compress it, then it automates the upload process to the Screencast site. After the file is uploaded, you are sent a link you can click on to view your file that is now hosted on the Screencast site. If you then capture the URL for that link, you can email the link to your students and they will be able to view the lesson you created as a video capture.

I've made a two minute video of how Jing works. Because I have to use a different program to capture what Jing is doing, I used Camtasia to do that, and that is why my video resides at the mtl.math.uiuc.edu site, not at screencast.com. The short video that was created in Paint, after I started Jing, that you then saw get automatically loaded up to screencast.com and then the URL sent back, as shown in the video clip, can be view by clicking here.

My recollection of the way you get your screencast account, is that I followed a set of directions they gave me when I downloaded the program Jing. At the end of that process, I believe they prompted me to set up my Screencast account. Sorry, but I've stopped removing working programs from my own computer, just to find out how they got there the first time I installed them.

Are there any downsides to Jing? Yes, you don't have the editing capability that you do with CamStudio or Camtasia. I edit my CamStudio files using Microsoft's Window Movie Maker which is part of Service Pack 2 for Windows XP. Camtasia has its own built in editor. You also have a limited amount of space on the Screencast site, if you run out of your free space they charge for additional space. Because the Jing file is strictly a ".swf" file, with no associated HTML code that would be produced by a program like Camtasia, it is not convenient to post the file created by Jing to your own server. A ".swf" file run in what I'll call the "raw" format without an associated HTML loader, is very jerky. Jing overcomes that when posted to the Screencast site, because Screencast automatically supplies the HTML code when posting at Screencast. Jing is capable of saving the file as an mpeg4, but they make you pay a yearly fee to have that add on. A positive is that Jing is produced by TechSmith, the same company that produces Camtasia.

Gauss's Law - a Video Explanation

2009-03-08T12:13:00.000-07:00

This week I had one of my online students indicate they were having trouble understanding Gauss's Law. I spent some time and worked up eight pages of notes with examples and then used a screen share session with the class to go over what Gauss's Law says. Then we looked at a number of examples where we can apply Gauss's Law to find the electric field strength in the vicinity of charged item.

Having my previous blog be about using video capture, I thought the above work might be a good way to demonstrate how you can use video capture to help explain some of the more difficult concepts in physics. Teachers in face-to-face classrooms have both the textbook and their presentation to help explain these topics. In the case where you are working with the student online, usually because its the only way the student can get the course due to geography, school size, school staffing, schedules etc., we can use the textbook and we also have accompanying professional explanations as you find in HippoCampus. Here is a link to the treatment of Gauss's Law in HippoCampus.

But if that isn't enough, and you are teaching online, or you are teaching face-to-face and the student has been absent a lot, then a "homemade" video clip might be just the thing. The video clip I am linking to below was made with Camtasia, but you could also make it with the free CamStudio that I talked about in the previous blog. The ".avi" file for my ten minute recording came in at 39 Meg, but after it was converted to a Windows Media Video (".wmv") the file size came in at 9.6 Meg. To put this in perspective, many $100 digital cameras will take pictures that are 8 Meg for a single picture. So if you are sending a picture as an email attachment, or posting it on the web without shrinking it, one of those pictures is about the same size as my ten minutes of video. I have a cable modem, I find it takes about 20 seconds for the video clip to load and start playing.

Video clip explaining the basics of Gauss's Law.

Please understand that the video is "homemade". I'm not interested in spending three days typesetting it, followed by a couple days of editing as you would for a professionally done clip like I linked to above at HippoCampus. This clip is to help students who are still having trouble after they watched the professional version and read the textbook.

As I had mentioned previously, I put together eight pages of notes. However I have only posted a discussion of the first two pages of those notes in the above video clip. I hope the video clip gives you a feeling for how you might use screen capture software in your teaching, how it works, and the file sizes involved.

Next week I'll pick back up on creating and posting a video with Jing.

Content related to this blog posting can be found at HippoCampus under Flux, Electric Flux, and Gauss's Law.

Doing Video Capture

2009-02-22T13:56:00.001-08:00

This past weekend the Illinois Virtual HS that I teach for held their professional development day for the spring semester. All of the teachers for IVHS gather in Bloomington, IL for the day and we have a variety of sessions we attend. This year two other people and myself were asked to present on using video capture software and incorporating it into our course. I thought this topic might be of interest to other physics teachers, both online teachers and face-to-face teachers.

In our presentation we talked about three different methods of doing video capture. The first was Camtasia, a product with an educational purchase price of $179. On their web page they have free tutorials and they offer a free trial of the program. I'm mentioning Camtasia in this blog, the video capture program I actually use, but I'm going to focus on a free alternative in this blog. I suspect most teachers interested in getting started with video capture would rather begin with a free program than an initial layout of $179. In our presentation, after talking about Camtasia, we also talked about two free programs that do video capture of your computer screen.

CamStudio is a free open source program that does screen video capture. If you have been in education long, you are familiar with the phrase "Free is Good!" When a screen video capture program does the initial capture it creates a file with a relatively high quality video. The purpose of keeping high quality at this stage is to make it easier to edit your original capture. Every time you edit a video, you usually loose some quality. The high quality file format that CamStudio (and Camtasia) uses is called an "avi" file. By starting with high quality we can still end with good quality after editing.

A two minute capture of a relatively small screen area, like the one that I will show below, ends up being about 35 Meg in size. This is much to big for effectively posting on the web or emailing. So the next thing we want to do is to compress that file. By converting the "avi" file to a Flash "swf" file, the file size drops from 35 Meg to about 7 Meg. We can do the file conversion directly in CamStudio. The conversion to "swf" creates two files, one that ends in "html" that I will call the loader file, and one that ends in "swf". The "swf" file contains the actual video. The "html" file calls and controls the "swf" file.

Click on this link to view a two minute video that I created with CamStudio, converted in CamStudio to an "swf" file and the "html" loader, and then uploaded to the web server that Math Teacher Link at the University of Illinois gives me space on. Next week I'll talk about the second free screen video capture program we demonstrated at the workshop. With that program you do not have to have a web hosting service like the one I have at Math Teacher Link.

How Christmas Tree Lights are Wired

2009-02-08T13:35:00.001-08:00

One would expect Christmas tree light strings to be wired in series as shown in Figure 1 below, because that situation would account for why when one bulb goes out they all go out, or so it used to be.

Figure 1

Last week, we posed two observations about Christmas tree light strings that seem to be problematic if the lights are indeed wired in series.

1) In some strings, a bulb can burn out but the rest of the string remains lit. Yet if you pull a bulb out of the string, the entire string will go out. It would seem that a burnt out filament and a bulb removed from the string would break a series circuit in the same manner, and both should cause all of the other lights to go out.

2) In some strings of lights you can have exactly half the string out and half the string lit. If they are truly wired in series, then they should either all be out or all be lit.

The only thing that makes sense as a solution to item 1) is that there must be a second filament in the bulb, with the two filaments wired in parallel as shown in Figure 2. The filaments F1 and F2 having different electrical characteristics.

Figure 2

If this were the case F1 could burn out but we would still have continuity from point A through the bulb via filament F2 and over to B. What they do is to make the backup filament F2 out of a material that won't heat up and glow like tungsten does, thus filament F2 isn't going to be prone to also burning out like F1 which was made of tungsten. When F1 burns out, the light doesn't light, but the circuit path isn't completely broken since F2 is still in place. The proper name for F2 would be a shunt; filaments glow, shunts simply provide an alternate path for the electricity. If the entire bulb is taken out of the string, then neither filament F1 or F2 can provide a path for the electricity passing through the series circuit and the entire string will go out. What often happens is that a bulb will become loose in its socket, or twisted in its socket, which is effectively the same as the bulb being out of the socket; in this case the whole string of lights will be out. Item 1) above is thus satisfactorily explained as a result of the shunt F2 that is built into each of the bulbs.

The most recent puzzling string I came across was case 2, with half the string out and half the string lit. I happened to notice that for most of the sockets there were two wires going in an out of the socket, but in a few cases there were three wires going in and out of a socket. There were only two wires leaving from the plug end and two wires arriving at the socket end where you would plug the next string in. Yet for most of the length of the string there were three wires. When I finally traced wires and laid the geometry out in a symmetrical way, I found what is in Figure 3 to be the case.

Figure 3

What is happening if you trace various paths in the above circuit is that the "hot" wire can come in through point A, travel to E, pass through the first set of bulbs just to the right of point E making it to F, from F to J, and from J to B, thus completing the circuit and lighting the string of bulbs to the left of point F. I'll summarize this circuit path as A - E - F - J - B.

To light the bulbs between points F and G the circuit path is A - E - H - I - G - F - J - B. Thus if all bulbs are in their sockets both halves of the string will be lit. If one bulb is out of its socket between E and F, then all the bulbs between E and F will be out, but the bulbs between F and G will be lit. Similarly a bulb out of its socket between F and G would cause all the bulbs between F and G to be out, but the bulbs between E and F would remain lit.

We do have one more condition that the circuit must meet, it must transmit the electricity at the plug point A to the socket point C, and from plug point B to socket point D, if another string of lights plugged into socket CD is going to light. The path from A to B exists because of path A - E - H - I - G - C and the path from B to D is B - J - D.

Also notice that points E, F, G, and J account for why we are seeing some sockets with three wires going into them, but the others only have two wires going into them.

It is interesting to fold the right half of Figure 3 over the symmetry line FJ, resulting in Figure 4.

Figure 4

This makes it pretty clear that we effectively have nothing more than a slight modification on two separate strings of lights that have been joined at points I and J to make the string physically twice as long as a single string.

I do want to share with you, Figure 5, the sketch I made of this circuit when I was only making it for my own records. I was making this sketch so that I wouldn't have to figure it out again when the lights needed fixing the next time.

Figure 5

In the process of writing this blog, I wanted to see if other people had written about this topic. I found a very detailed analysis at this site.

I think it would make for a great physics lab to invite your students to bring in strings of Christmas tree light from home that aren't working correctly, then let them use a volt-ohm meter to try to fix the string. While trouble shooting the lights should not be plugged in and they should be using the ohm meter setting on the meter, exploring continuity in the string. Don't let them work on the string while it is plugged into 110 volts. I'd even consider putting duct tape over any 110 volt outlet in the lab that is in the vicinity of where the students are working. When they think they have the string fixed have them call you over, and after you look it over then you supply the 110 volts. Using an extension cord with a switch in the extension cord would be a good way to handle this.

If they have used the ohm meter well, they should have been able to fix the string. If when you plug the string in to 110 V it lights - an A. If it blows the circuit breaker - an F? These strings usually do have fuses in the plug that goes into the wall, so it is not likely you will kick a circuit breaker when you plug the string in, but you can worry them - hey you're the teacher.

Content related to this blog posting can be found at HippoCampus under Single Loop Circuits and Multiloop Circuits.

Fixing Christmas Tree Lights

2009-02-07T10:23:00.001-08:00

We are there, it's time to talk about how Christmas tree light strings are wired and why they work the way they do.

Over the years, how Christmas tree light strings are wired has been changing. When my folks got their first string of Christmas tree lights, the lights were all wired in series. This easily accounted for why if one bulb burnt out, the other bulbs also went out. To get the string to light again you had to go through the string bulb by bulb swapping in a new bulb until you located the bulb that burnt out. Once you replaced the bulb that had burnt out with a good bulb the entire string would come back to life. Over the years, a couple of things changed in how strings were wired and the effect of those changes made you have to ask, "Are these really wired in series?"

1) A bulb could burn out, but the rest of the string would remain lit. Yet if you pulled a bulb out of the string, the entire string would go out. It would seem that a burnt out filament and a bulb removed from the string would break a series circuit in the same manner, and both should cause all of the other lights to go out.

2) In some strings of lights you would see exactly half the string out and half the string lit. If they are truly wired in series, then they should either all be out or all be lit.

Before going further, due to my age, I was first introduced to Christmas tree lights when they were truly wired in series with no additional gimmicks. The first string of lights I can remember in our house were bubble lights. Figure 1 below is a picture of a string of "new bubble lights", the kind you can buy today.

Figure 1

Figure 2 below is a picture of one of the bubble lights from the 1950 string we had. In 1950 bubble lights there seemed to be an oil being used for the liquid in the tube and some sand particles in the base of the tube. This caused very small beautiful little bubbles rising slowly through the tube. In new bubble lights, it looks like the fluid is colored water, you get a "gulp" of a bubble leaving the bottom and it rises rapidly to the top.

Figure 2

The old lights were much nicer! In my initial search for a picture, I went to eBay and I did find an add for one of these bubble lights, Figure 3. This is just ONE light, and they are asking $50.00! I expect that in 1950 the entire string probably sold for under $5.00. No, I didn't copy their picture and superimpose it on a picture of a pine tree. Photography is also one of my hobbies, and I had photographed this bubble light several years back. If you look close you will see that the bulb in the base of mine is not as bright as the bulb in the base of the one on eBay, more on that later.

Figure 3

One of my first experiences with series circuits was this bubble light string. I always liked taking things apart to see how they worked. That include mechanical pencils, the first retractable pens, ... it did not endear me to my grade school teachers when during English class I would be disassembling and reassembling my pens and pencils.

In figuring out how a flashlight worked, also while in grade school, I came up with my first circuit tester. Using the batteries from the flashlight, a piece of wire, and the bulb from the flashlight I created my first circuit tester, Figure 4.

Figure 4

I could get away with doing this because when I was done with the circuit tester I would reassemble the flashlight, so it wasn't like I was destroying things around the farm. A few years back my parents had come across the "circuit tester" in the attic and remembered what it was. They returned it to me.

Using the above circuit tester I could identify which bulb in the string of bubble lights was bad. Since we were out of spare bulbs, I would then clip the bad bulb out of the circuit, bare the ends of the remaining string where I had created the gap, twist them together, tape them up with electrical tape, and wonder of wonders when I plugged the string back in the entire string would light up.

But what was unfortunate, is that after doing this fix two or three times, I discovered that just as soon as I plugged the string back in another bulb would burn out immediately. At that time, I had no idea why this was happening. Fortunately, I put the remaining string back in the box, and the box back in the attic. Later in high school, we studied Ohm's law, and then it was clear to me why this was happening. The original string was evenly dividing the 110 volts to each bulb among all seven bulbs, giving each bulb 16 volts of electricity. After I had burnt out two bulbs and removed them from the circuit, now the 110 volts was being divided among five bulbs and each bulb was seeing 22 volts. They couldn't handle 22 volts, since they had been designed for 16 volts, and they would immediately burn out.

It wasn't until I was away at college and we studied AC electricity that I hit upon a solution. I now had access to a "better" circuit tester that went by the name of a "Volt-Ohm Meter" and a variable voltage power supply. I hooked up one bulb and gradually brought the voltage across one bulb up until the bulb would just start to bubble, this resulted in a voltage that was less than the original string was providing. For example, while the original string was supplying 16 volts, I found the bulb would light and start to bubble at around 12 volts. [I don't recall the exact numbers and I don't have these bubble lights at the location where I live now, so I'm having to use "reasonable numbers" to illustrate my points.]

Since 12 volts was a typical voltage that you would find in other common circuits, I decided to buy a 12.6 volt transformer (Figure 5), thus step the voltage down to 12.6 volts and wire the bulbs in parallel as shown in Figure 6.

Figure 5

Figure 6

By stepping the voltage from 16 volts down to the 12.6 volts, the bulbs have much less of a chance of burning out. In addition, with them being in parallel, if one bulb did "go" the rest would stay lit.

Since I try to hold these blogs to 300-500 words, and this one is already over 1,000 words the answers to the opening two circuit questions are going to have to wait until next week.

(Note: I have intentionally removed the current rating, model number, and catalog number from the above add. You need to measure the voltages and current draws to determine the appropriate values, and I don't have one of the bulbs here to do that, so I can only supply concepts and estimates.)

Content related to this blog posting can be found at HippoCampus under Electric Current, Resistance, Resistors & Batteries in Series, and Multiloop Circuits.

Wiring Three Way Switches and Christmas Tree Lights

2009-01-30T16:34:00.001-08:00

Last week we were exploring how to wire a light in a hall way so that one switch would turn the light on as you entered the hall way (from the left below) and a second switch would turn the light off as you exited the hall way (on the right below).

Above is schematic of how this is done. The 110 volts comes into the circuit at point A on the left. Terminals C, D, and E make up switch 1. As the switch is shown terminals C and E are connected. If the switch is flipped, then terminals C and D will be connected and C and E disconnected. Likewise terminals F, G, and H make up switch 2. As shown above terminals F and H are connected. If the switch is flipped, then terminals G and H will be connected and F and H will be disconnected.

As the switches are positioned above the electricity has no complete path to leave from A, flow through the bulb, and get back to B, thus the light is NOT lit at this time. If the person entering from the left flips switch 1 to the up position, then the electricity can take the path A - C - D - F - H - I - J - K - B and the light will be on as they walk down the hall. When they get to switch 2, then they flip switch 2 down, and this breaks the circuits path from A to B and the bulb goes out.

The key to understanding this is that no matter what the position switch 2 was left in, by flipping switch 1 you can choose to have the light either on or off. Switch 2 will always be connected to either the red or the black wire, and by flipping switch 1 to the matching wire the light will be on. By flipping switch 1 to the red or black wire that switch 2 is not connected to will turn the light off. For example if after exiting the hall to the right, the last person left switch 2 in the down position, then by flipping switch 1 down the light will come on, by flipping switch 1 up the light will go off. And you can do the same from switch 2, no matter what the position of switch 1, alternating switch 2 between up and down will alternately turn the light on and off. So from either end of the hall the light can be turned on or off.

The practicality of now stringing this circuit in your house takes on a bit of its own geometry. We don't want to run three completely separate wires from one end of the hall to the other end of the hall. The next diagram brings in the actual geometry of how this is wired.

Here the light blue boxes represent actual electrical boxes in the wall. On the left, coming into switch box 1, circled in pink, is a two conductor piece of cable containing two wires, usually called 12-2 AWG; the 12 refers to how heavy the wire is and the -2 that it has two conductors in the single sheath of wire cable. In a 12-2 AWG electrical cable the conductors are black and white, with the idea being that the black wire is "hot" at 110V, while the white wire is "neutral" at zero volts. In my diagram I had to make the white wire yellow, otherwise you wouldn't be able to see it. (Note: It isn't always true that the white wire won't end up with 110 V on it, and our white wire above from point H to I will at times have 110 V on it when the light is on. In the diagram below, you will see the end of this white (yellow) wire wrapped with black tape to signal this white wire will be hot at times.)

Leaving the switch 1 box and traveling to the right you see a red, black, and white (yellow) wire. I've circled these three wires with an orange circle to indicate that they are all part of one sheath (cable) of wire that would be called a 12-3 AWG wire, meaning the single sheath of wire cable has three individual wires running inside. After the 12-3 electrical cable leaves switch 1, it passes up through the electrical box on the ceiling that the bulb is attached to. Then there is another piece of 12-3 electrical cable that leaves the electrical box where the bulb is and runs on to the electrical box that switch 2 is in.

The way the electrician wiring the house would see this wiring project is depicted in the next diagram. If you click on the picture you will get an enlarged view. In the picture I've added lettering and arrows to correspond to the labels in the two previous schematics. The green wires you see in the picture below are common grounds that run through the entire electrical system of a house for safety; I neglected those in my drawing above to make the circuit switching easier to understand.

I need to give credit to the web site that did this drawing . There they talk more about the physical electrical wiring in a house, the drawing above is based on their Option 3.

So how do you use this in physics class? I was a big believer in using real equipment in my classroom, equipment that I bought at the local lumber yard, at other places in town, or brought in from home. If I used switches from the science supply house, students may not make the connection to everyday life. If I used switches from the lumber yard, they would view the lesson as something practical and see how science connects to their everyday life. Even though the switches came from the lumber yard, I would power it all with two 1.5 volt batteries, using battery holders and 3 volt flashlight bulbs that you can pick up at Radio Shack, as well as lighter wire from Radio Shack that is easier to work with. You can buy the wire in assorted colors, red, black, and white would be good. You don't want the students working with 110V coming from the outlets in your classroom, your insurance isn't that good!

The Christmas tree light wiring is going to have to wait until next time, this week's blog is already longer than I want it to be.

Content related to this blog posting can be found at HippoCampus under Multiloop Circuits.

Electrical Circuits in Physics are Practical

2009-01-25T11:19:00.001-08:00

Growing up on the farm had some advantages when it came to studying physics. My first recollection of thinking science, and in particular physics, might be something I would be interested in occurred in junior high school when we hit the chapter on "Simple Machines". The six simple machines talked about were the pulley, the lever, the wedge, the wheel, the inclined plane, and the screw. I had used all of these extensively growing up on the farm; even from the perspective of a junior high student this course had some relevance to everyday life!

Another advantage of growing up on the farm was that there were no zoning codes. When we needed to add an extra outlet or an extra light bulb someplace, if we thought we knew how to do it, we were free to do it. It seemed like we were always tearing one building down as we built the next one, and my late Dad being of the depression era, never threw things like light bulb sockets, outlet sockets, or electrical wire away; he also never let us go to the store and buy new electrical supplies (that last part is almost true).

I remember my Dad talking about having the farm wired in anticipation of the power lines that were being run by the rural electric cooperative being energized. He talked about coming in from the field one evening and seeing the lights on. Electricity had arrived on the farm! While my Dad had clearly been a good student while in school, he could still recite Edgar Allen's Poe "The Raven" by heart, clearly electricity was new enough that it had not been a subject in his science classes.

On multiple occasions, when I would come home from college, Dad would have done some new wiring on the farm (with old materials), and the circuits would work in unpredictable ways. On one trip home he showed me the two new lights he had installed in the basement; when you turned the switch on, the bulbs had this pale orange glow. They just barely lit up. Having had a couple of physics courses by this point, it was obvious to me what had gone wrong. But it was going to be a lot easier to fix it than to explain to Dad how to fix it. Here's a crude schematic of Dad's circuit.

Figure 1

Because the bulbs were in series, they were sharing the 110 volts, each getting 55 volts. The way it needed to be wired was to wire the bulbs in parallel, as shown in Figure 2.

Figure 2

In this configuration both bulbs see the full 110 volts.

The point of this weeks blog is to emphasize that when teaching physics, we should be tying it to the world around us. Physics shouldn't be taught as a theoretical abstraction if you want to keep the student's interested.

As we get into the spring semester, electricity is often one of the topics in physics class. I think a great question to ask after students have learned about serial and parallel circuits, is to have them draw a schematic similar to the one above of a three-way light switch arrangement. By a three-way light switch arrangement, I mean the kind you encounter where you can use one switch to turn on the light in a hallway as you enter from one door way, and then turn the light off using a different switch as you leave exiting the other end of the hallway. Something we all encounter everyday!

Stating it more precisely, try to modify the above circuit in Figure 2 by adding or rearranging wires where needed and an additional switch located to the right of the existing bulbs, so that the two bulbs can be turned on or off by using either switch. We are simulating a hallway with two bulbs, wired so that you can flip the left switch when you enter, have both bulbs light, and then flip the right switch when you leave and have both bulbs go out.

Unfortunately, I don't believe you can add pictures in a comment posted to this blog, so it probably isn't possible to send in a drawing. Perhaps some people may be interested in trying to describe the circuit needed in words.

Next week, I'll provide a solution, and I'll also talk about how Christmas tree lights are wired.

Content related to this blog posting can be found at HippoCampus under Single Loop Circuits, Multiloop Circuits, and Measuring Current & Voltage.

Making Sense of Data, Graphs, and Equations - Doing Labs

2009-01-12T12:44:00.001-08:00

I'm not convinced that students associate what they are learning in Algebra class with what is going on in the world around them. My experience has been that when they later take Physics, the main (and almost only) application they see for the Algebra is symbol manipulation.

In the previous week's blog, I gave an example of a case where the data, the graph, and the equation didn't seem to relate to each other for the student whose work I used in the example.

There are a limited number of relationships of how one thing changes with respect to another in the physical world. Some of the earliest and most important ones we study for a student's understanding of physics (and math), are:

1) Item A varies linearly as item B.
Velocity under constant acceleration with respect to time:
The force needed to stretch a spring:

2) Item A varies as the square of item B.
Distance traveled under constant acceleration vs. time:
Centripetal force vs. velocity:

3) Item A varies inversely as the square of item B.
Gravitational force with respect to distance:
Electrostatic force with respect to distance:

Yes, I'm leaving inversely, exponentially, and trigonometrically out for now. The above three examples will be sufficient to make the rest of this coherent.

When I taught Algebra and Algebra II to students, after we had worked with one of the above relationships algebraically and graphically, I would always try to find a lab to do in Algebra class that modeled this relationship. Yes, I mean "a lab" in Algebra class.

Underlined materials on this web-page contain links to the items being talked about.

One of my best sources for those labs was the Explorations^TM Series books from Texas Instruments. When I was doing these labs in the 80's and 90's, prior to retiring from face-to-face teaching, we used to see these books at the conventions, and then place an order from Texas Instruments. The books cost us about $30 each. The material in these books is now available for FREE at the TI Web site.

While I personally own several of these books, the one I found most useful for Algebra and Physics was the one called "Real World Math Made Easy". It has labs where you collect and analyze real-world data. From that one book I was able to use actual hands on data to illustrate and give them practical experience with most of the relationships in physics. For the three relationships I've sited above, the labs I would use were:

1) Item A varies linearly as item B, I would use Activity 9 Stretch It to The Limit: The Linear Force Relation for a Rubber Band

2) Item A varies as the square of item B, I would use Activity 10: What Goes Up: Position and Time for a Cart on a Ramp

3) Item A varies inversely as the square of item B, I would use Activity 16: Light at a Distance: Distance and Light Intensity

Of these three my favorite was Light at a Distance. I would move all of the chairs to the side of the room, and when the students would walk into the room, sitting in the middle of the room on the floor was a single light bulb. That got their attention. We would then use a TI Light Probe that cost about $13.00, attach it to our TI-CBL2 that cost about $165 for collecting the data. I had four sets of equipment and had the students work in groups. After they had their groups, equipment, and handouts we would darken the room so that the only light was the one in the middle of the room. It looked like they were sitting around a campfire. I learned a lot about what they understood and didn't understand as they gathered the data, graphed it, and processed it to get a best fit equation in this lab.

Content related to this blog posting can be found at HippoCampus under Inclines and Mass-Spring System.

Connecting Data, Graphs, and Equations

2009-01-11T19:18:00.001-08:00

Each year, when I work with my new collection of students in physics, I'm usually surprised to find that I have a significant portion of the students in the room that seem to have learned the topics of data, graphs, and equations in isolation from each other. A description of a traditional lab to measure centripetal acceleration using a string and cork stopper can be found at http://campus.pc.edu/~rarts/cf-trad.pdf . Figure 1 below is an accurately drawn graph of the data one of my students collected in the situation where the hanging mass and the mass of the cork stopper have been held constant.

Question Asked: The question asked in my version of the lab for this data was "What is the relationship between the radius and the velocity of the rotating object?"

Student's Answer: "The radius shouldn't play a part in velocity because it would always need to keep up the same velocity to keep the system in equilibrium."

Teacher's Concern: Does the student not see in the top graph that as the velocity has increased the radius has been decreasing?

The student that did this is an excellent student, one of my best. The student, from other homework problems that I have graded, knows that the proper equation for centripetal force is:

It is also clear to me that this student would have no trouble manipulating this equation into the form:

But this is were the disconnect seems to happen, the student doesn't seem to see that this is the equivalent of

and then have an understanding of what that relationship is telling him. He doesn't take this and make a statement like "r is proportional to v-square ", or I would even settle for "as v increases r increases". Since he doesn't comment on it, he also apparently doesn't recognize the contradiction that the data in the graph was saying the radius goes down as the velocity goes up, but the equation is saying the radius should go up as the velocity goes up. I really wrestle with why this student would say "The radius shouldn't play a part in the velocity". Granted his data looks lousy, but I'm far more concerned with the lack of ability to understand what the data and equations are saying. If others reading this blog have insight as to why this happens, I'd love to hear from you.

I'm going to suggest that we teach mathematics and science in too much isolation from each other. In the next blog, I'm going to go to some "Exploration Series " books at the Texas Instrument's web site that I feel have activities in them that ought to be done in the math classroom when students are learning to connect the ideas of data, graphs, and equations. I make the previous statement without intending it to be an attack on math teachers, since I'm both a math teacher and a physics teacher. The goal here is to get students to relate data, graphs, and equations with each other and with objects in the world around them. The TI site has some valuable content for helping to forge those connections.

Content related to this blog posting can be found at HippoCampus under Centripetal Acceleration.

Measuring Motion with a Calculator Based Ranger (CBR)

2009-01-02T20:42:00.001-08:00

One of my favorite activities to do with students is based on a "lab" designed by Texas Instruments. Students are given a time vs distance graph, of which two examples are shown below.

Figure 1

Figure 2

Then using a motion detector, known as a Calculator Based Ranger (CBR), the student walks in front of the motion detector and tries to walk a path that will match the graph they were given. An example of a very good job of walking for the first graph above is shown below in Figure 3.

Figure 3

The equipment needed is relatively minimal if you are willing to structure your work in such a way that you use a calculator overhead panel to project what is on your own calculator. Most math teachers (or at least the school) already have a TI graphing calculator and an overhead panel that it hooks into. Beyond that, the only other piece of equipment you need is the CBR . A CBR can be purchased for under $100.

Initially, I start this activity without passing out any additional paper work. I first want to get the students engaged, then later we will work on the equations that model this data. While I have used this activity in various forms with different classes, my most memorable use was on a trip where I spent one day doing a workshop at King American HS, one of our US Department of Defense high school in Sasebo, Japan.

I had the equipment hooked up, and without much explanation other than explaining that the CBR measured how far you were from it, we separated the chairs to make room for a walkway, and I had it draw the graph in Figure 1. I then asked for a student volunteer to walk the graph. I try to pick a student that looks like they would be comfortable doing this and also that looks like they would be successful. As the student that volunteered was positioning himself, I saw a very small student who happened to be seated close to the walk way, tugging on the walkers pant leg and telling him he needed to back up further for the starting position. I let the first couple of student volunteers watch their path build on the projected image as they walk, we count down "3, 2, 1, go" and they start walking and make the needed corrections. It comes out pretty good.

After one student does it, then there are numerous volunteers who are sure they could do better, and they do. After having seen the small student help position the first walker, I knew he was seeing more in the graph than the typical student. I asked the small student in the room to walk one of the randomly drawn paths, but this time I turned the projector off so he had to walk it "blind". After his walk we turned the projector on, and his walk had been nearly perfect.

That small student was a seventh grader who had come up to the high school to take Algebra II along with the high school students. When he had first looked at the graph, he had noticed that the vertical scale was marked in meters and the horizontal scale was marked in seconds. So using Figure 2 above as an example, before the first volunteer had walked, he already realized they needed to start 2 meters away from the detector, walk away from the detector a distance of 2 meters in four seconds, stand still for two seconds, and then walk 3 meters towards the detector in the next four seconds.

At the end of the hour, the high school students were giving the 7th grader hugs, he fit right in with that group. A couple of weeks after I got back to the states, the teacher emailed me and said "The students are still talking about that activity".

When you are ready to tie the equations and the mathematics in more formally, such as in a Physics class or in an Algebra II class, I would suggest you use the hand-out ModelingMotion_HS_CBR_Act07.pdf from the Texas Instrument Calculator site. If you are using this equipment to explore motion and graphing with beginning science students, or beginning Algebra I students as you introduce them to slope, then I would suggest using the hand-out MathScienceMotion_MS_Act02_Match Me.pdf or EasyData_Act05.pdf , again both are from the Texas Instrument web site.

Content related to this blog posting can be found at HippoCampus under Equations of Motion.

Memorable Moments in Teaching

2008-12-29T06:43:00.001-08:00

Winter break is always a nice time to reminisce about the years gone bye. Being semi-retired from thirty-two years of teaching in the face-to-face classroom, and now having taught part-time an additional eight years online, I have both the history and the time to reminisce about that teaching. About once a year I will have a former student, a student from many years ago, come up to me when I'm out in public and say "hi". It can happen in the barber shop, in a restaurant, in a store a hundred miles away from home. It can be a student I may have had twenty-five or thirty years ago. What I find most interesting is what they remember about the class they took after that length of time.

Almost without exception the memories will center on the unconventional things that had been done in the class. The most recent student remembered going out on the roof of the school to take measurements at noon time of the shadow cast by the sun. The force tables in the physics lab had a pin located in the center of the force table to hold the three attached weights running over the edges centered while you made your adjustments to the weights. I had replaced that pin with a longer dowel that would cast a shadow of an appropriate length. Not far from the physics room was a door out onto a flat roof area above the physics room, and we set the force table out there. Over a period of several weeks we took measurements of the sun's shadow to measure our latitude and by using a watch also got our longitude. I was a very young teacher at the time; as an older teacher I question the wisdom of taking the students out on the roof. But hey, I never lost a force table, nobody every repositioned the force table on me, and I also never had a student fall off the roof.

Students remembered the thermodynamics experiment we did around Christmas time when we made home-made ice cream in the room and plotted the temperature of the salt brine solution.

Other student memories centered on the few days we took in the spring of the year to build Estes rockets, and go out to the football field to launch them. One student from the 1970's reported still having his rocket. He's not alone-I kept a couple of mine, and continue to have them set out as memories in the room in my house where I do my online teaching.

My memories as a teacher often center on using some technology with the students, using it in a way that pertained to what we were studying, but upsetting the student's mental balance just enough that this was no longer a textbook example, and they had to think through what was actually happening. A convenient source for that technology was the Texas Instruments calculators and the attachments that would fit them. In the next blog, I'll talk about one of my favorite days in a classroom in Japan where I used that equipment to explore motion with the students.

Content related to this blog posting can be found at HippoCampus under Projectile Motion.

A Look at OpenOffice Calc as a Free Alternative to Excel

2008-12-22T08:07:00.001-08:00

As a teacher, because of the educational discount to teachers and schools, I personally use Microsoft Office to do my work in. While many of my high school students have computers at home, it is not uncommon for them to not have purchased Microsoft Office to put on that computer. As I've mentioned in previous blogs, I do consider it important that we have our students work with contemporary technology in our classes. It no longer is sufficient to teach your classes, allowing students to only use paper and pencil technology. A free alternative to Microsoft Office is available for downloading from the Internet, and it goes by the name Open Office .

For my purposes as a science and math teacher the components my students will find useful will be the spreadsheet known as OpenOffice.org Calc and the word processor known as OpenOffice.org Writer.

In this blog I'm going to focus on OpenOffice Calc, the spreadsheet, and use it to work up the lab data I had gathered in the December 1 blog, and presented in Excel and Google Docs in the December 15 blog. The first image below is the data worked up in Excel.

[Double clicking on any of these images will give you an enlarged view.]

The image below this it the data worked up in OpenOffice Calc.

As you can see the OpenOffice Calc workup is almost identical match to what I had worked up in Excel! Here are the aspects that I want to point out that I was able to do in OpenOffice Calc that I wasn't able to do in Google Docs

I got control of the number of decimals places I wanted to show in each of the numbers!
I was able to add a trend line to the data.
I was able to have it show the equation of the best fit trend line directly on the graph.

For the purposes of mathematical understanding, just as in Excel and in Google Docs

I was able to use an = SLOPE(E5:E8; D5:D8) command to get the slope showing in cell H6.
I was able to use an = INTERCEPT(E5:E8; D5:D8) command to get the y-intercept showing in cell H7.

The commands in OpenOffice Calc were almost identical to the commands that I used to accomplish the comparable task in Excel. A student learning to use OpenOffice Calc will not be wasting time when they later transition to Excel in the workplace or at college. Likewise a student using Excel at school will not find a new learning curve to use OpenOffice Calc at home. I consider this a VERY IMPORTANT factor in software decisions we as teachers make for our students.

In the process of taking material back and forth between the two platforms, I found the spreadsheet done in Excel to open perfectly in OpenOffice. Below is a screen shot of the Excel file opened in OpenOffice.

OpenOffice does provide you the opportunity to save in the Excel (.xls) format, as shown in the screen shot below.
However, when I opened the OpenOffice document then in Excel, I did see some degradation, but nothing I couldn't live with. OpenOffice seems to support Excel better than Excel supports OpenOffice.

I can strongly endorse having students use OpenOffice if costs prevent them from installing Microsoft Office on their home computer!

(Yes, I worked this blog up in Microsoft Office. The educational discount is such that I would be crazy not to use Microsoft Office on my own computer.)

Google Docs vs. Excel

2008-12-15T06:25:00.000-08:00

While Excel, as part of the Microsoft Office package, is available to schools and teachers for a terrific educational discount, it is not available to students to put on their home computer for the same kind of pricing. For example, because of my faculty status I recently bought Microsoft Office Enterprise 2007 for $66 and that included shipping and handling. A search of the web showed the price on that same product from Dell without the educational discount to be $589 not including S&H charges.

Schools, faculty, and students on college campuses would be foolish to not take advantage of this excellent software, but we can’t expect parents to pay retail and be placing it on their home machines for their students to use after school hours. There are simpler and less expensive packages available from Microsoft, but some students will still not be able to afford them for their home computers.

While I strongly recommend students process their data at school where they have access to Microsoft Office, I’m going to explore in this blog an online alternative known as Google Docs, and see how it stacks up as a substitute.

[You can click on above image to enlarge it, and then the back button on your browser to return to the blog.]

In the above image, I’ve worked up the data for the Changes in Potential Energy Lab from the previous blogs in Excel. Because most of the measurements were taken to three digits of accuracy, I used the Format feature in Excel to express, round, and display all of the resulting computations to three decimal places; with the exception of the slope and y-intercept in cells H6 and H7 where I needed to use four decimal places to get an appropriately displayed value. I then plotted a graph of the force in cells D5:D8 vs. the extension in cells E5:E8.

To get the best fit line and its equation in the chart I clicked directly on the data series in the graph and choose Add Trendline, then as an option I choose Display Equation on chart. Of course, based on the physics and data involved, I choose to fit it with a linear fit.

This process of getting the best fit straight line seemed to me to bypass more of the mathematics than I would like, so in cell H6 I also asked Excel to calculate the slope of a line that would best fit the data in the graph using the statistical function =LINEST(E5:E8,D5:D8,TRUE,) . Here they describe the function as “Returns a statistic that describes a linear trend matching known data points, by fitting a straight line using the least squares method.” Under Help on this function, Excel shows the summation formula that it uses for a “best fit”. Your students may need additional help from you to understand that formula, but at least the slope of the line isn’t just appearing by magic with no explanation given. Likewise, in cell H7, I’ve used the statistical function =INTERCEPT(E5:E8,D5:D8) to determine the y-intercept. Cells H6 and H7 reinforce what is going on when you add a trendline to the data in the graph.

[You can click on above image to enlarge it, and then the back button on your browser to return to the blog.]

In the above image, I used the spreadsheet in Google Docs, and tried to replicate what I had done in Excel. Google Docs is freely available to students; they simply need to create a Google email account to access it. The Google email account is free, and many students already have one.

I did like the fact that Google Docs provides for multiple students to be able to work on the same document, so if you have two or three students working together on the lab, they can all access the spreadsheet in Google Docs and work with it. However, I also found two very big negatives in Google Docs. Google Docs would only let me choose to format the data to two decimal places, there was no provision for showing three decimal places, which is essential to the physics going on in this problem. For example in cell B7 I want to write 0.100 to show that I know the mass to the nearest gram. Google Docs would allow me to format it as 0.10, or use the default that didn’t display the trailing zeros, thus rendering the display as 0.1. Neither of these is acceptable to me as a physics instructor.

The second major draw back I faced was that I was not able to add a trendline to the graph, thus I was not able to give a visual representation of what our best estimate of the meaning of the data was. It was possible to calculate the slope and the y-intercept in cells H6 and H7 and the commands for doing so were not appreciably different than the command in Excel. The representation of the numbers for the values in H6 and H7 were horrendous, the data we collected doesn’t warrant suggesting we have done the calculations to 15 digits of accuracy, and there is no way (that I could find) to get control of that representation, displaying 3 or 4 digits of accuracy.

While it is a good free alternative, I would not be a big fan of sending your students to Google Docs to write up a lab where they need to process data that involves fitting equations to data. Next week we will look at the spreadsheet in Open Office, and see how it stacks up.

Spreadsheets vs. Graphing Calculators

2008-12-07T18:16:00.001-08:00

When I teach my students the content of a course, the content needed is often determined outside my classroom by combinations of what the title of the course is, what the AP College Board expects to be in the course, and what the instructor following me will be assuming the student knows if his transcript says he has had such a course.

When it comes to "how" I teach my course, I have more discretion in what I choose to do. But on the "how" front, an idea I try to pay attention to is that when possible I should have my students working with the content in the course using techniques that a person working in the field would be using.

While we in education will never have the financial resources at our disposal that people working in the private sector often do, we still have choices we can make. In the previous two blogs, I talked about and gave examples of lab reports for a lab on "Changes in Potential Energy" that I have my students do. In the first of those two blogs, I included the write up I had received from two students at the Northside College Prep school in Chicago, a well equipped magnet school. The following week, I talked about processing the data for the lab using a TI-83 Plus calculator, that the majority of math and science teachers use with their students. In this blog, I'm going to argue that we shouldn't be stopping with the use of the TI graphing calculator for processing data in our classrooms.

Since I retired from full time teaching, I've had more flexibility in how I schedule my day, my time, and my activities. During my thirty two years in the classroom, my school allowed me to attend one national convention. During my last year of face-to-face teaching I had to take a personal day to attend the state convention. Since I retired from full time teaching, for the last eight years I have attended EVERY national math convention (NCTM) , and each spring I look forward to doing that. You might say it is my vacation of choice. This additional flexibility in what I do now is also part of why I took early retirement and switched over to teaching online.

On the flight to the NCTM convention in Anaheim, California, I had the window seat, the middle seat next to me was occupied by a high school senior from Kentucky, his mother had the aisle seat. The high school student had a TI 83 Plus calculator along, he had his cell phone, he had his MP3 player, he had a wrist watch with more dials than I imagined you could get on a wrist watch. During the first half of the flight, I quietly sat back and watched him entertain himself with all of this technology. Meanwhile his mother had been working with an Excel spreadsheet on her laptop. Part way through the flight the mother asked her son "Do you know how to create a formula in a spreadsheet?" When the student answered "no", mother said "Here, let me show you." I thought to myself, "How sad!"

I didn't express those feelings to the student, but also having my TI 83 Plus calculator along since it would be used in many of the presentations I attended at NCTM, I pulled out the TI 83 and used it as a starting point to engage the student in conversation. I wanted to find out more about how a senior in high school, who by all reasonable expectations would be considered proficient in technology, had arrived in his senior year with apparently no experience in using a spreadsheet like Excel.

As we talked, I discovered the student, based on the Kentucky state testing, was from the top performing high school in Kentucky. The student was very proud of this. The student would also be attending college next year and intended to major in engineering. The student had taken a normal compliment of math, science, and computer classes while in high school, and he had been on the honor role every semester.

As I reflected on this, I had remembered seeing one TV show in my life where I saw a person working in a lab in industry that had a TI graphing calculator sitting on the lab table, and I also remembered how odd that had seemed when I saw it. I do have to point out that probably 90% of my TV viewing is PBS programming, and no I don't believe that TV is the best source available to make educational decisions regarding career planning. What's important here is that if you watch working people in the workplace, people in the airport, people on the airplane, people in the coffee shops, they are using laptops and spreadsheets, they aren't using TI calculators to do their work.

Yes, TI calculators have a place in our classrooms, and I'm extremely pleased with the support Texas Instruments has given the educational community. I personally own a TI-73, two TI-83s, a TI-83 Plus Silver Edition, a TI-85, a TI-89, and a TI-Inspire CAS. And yes, I teach my students how to use the TI calculator and I do workshops with teachers on how to use the TI graphing calculators, but we can't stop there. We also need to teach students how to use spreadsheets.

Having come from a classroom background, I can tell you that it was the business department in my high school that got all of the technology. They had two computer labs, while the math and science department had none. The school added a third more general purpose computer lab, but in the end that was a real misnomer; they staffed it with a full time person from the business department that was certified to teach business classes. They should have called it the "Word Processing Lab", there was precious little "computing" (as we use the term in science and math) that was going on in that third lab. The only computing that was going on was to use the "Count Words" feature in Word to see how many words they had in the essay they were typing up for their English class.

In my next few blogs, I'm going to examine several spreadsheets that are available to students. I'm going to look at processing the data that was found in the previous two blogs pertaining to the lab on "Changes in Potential Energy" and see how some commonly used spreadsheets fare. We will process that lab data in Excel, in Google Docs, and in Open Office, and devote the blogs to talking about the pros and cons of these three different spreadsheets.

“Changes in Potential Energy” lab done as a Simulation.

2008-12-01T09:07:00.000-08:00

In last week's blog I showed you the work from two of my students on a potential energy lab, where the lab was done as a hands on lab in a well equipped school. This week we will look at the Changes in Potential Energy Lab done as a simulation using the PhET website .

Once you open the Changes in Potential Energy Lab, find Lab Procedure, Prepare the spring. To do the lab virtually students would simply click on "Run Now" on the above simulation at the PhET website. I would recommend having students use the default settings at the website to start.

Under the lab directions Measure spring extension students are asked to add weights to the spring and measure its extension and record that data in the table "DATA SHEET 1". What I get when using the simulation is the following, where I’ve left the meter stick positioned so that the rest position with no weight attached is at 31 cm, as it is when the simulation is first started. My data for Data Sheet 1 came in as:

If my students were completely new to data fitting I would have them plot these four points by hand on graph paper and then estimate a line of best fit. Hopefully you, a previous science or math teacher, have fit a straight line to data with the students prior to this in which case you could either use a graphing calculator or Excel to get a best fit line. Since I’m often working with students who will be writing the lab up at home, where they may not have Excel but likely would have a graphing calculator, I’ll continue this blog explaining how a student might continue with getting the best fit line with a TI-84 calculator.

On a TI graphing calculator you can fit a line to data by placing the data in lists L1 and L2. If this is new to your students, you might direct them to the tutorials on using the TI-84 calculator on the Math Teacher Link Website.

The lab directions say to “make a plot of force vs. extension”, so that implies we should plot force on the x-axis (L1) and extension on the y-axis (L2). We use the Stat, Edit feature to enter the data as shown below. L1 contains the force and L2 the length of the resulting spring extension.

Doing a Stat, Calc, 4: LinReg(ax + b) L1, L2 gives the linear best fit equation to be

y = 0.0961 x – 0.00180.

We can then enter the equation y = 0.0961 x – 0.00180 into Y1 and set the StatPlot feature so Plot1 plots L1, L2 and combining the two plots we visually see both the data and the best fit line.
The learning moves up a notch as students work up their answer to question 2 in the Lab Report / Analysis Questions. Most students will recall that Hooke’s Law says the spring extension formula is F = - k x. They will then claim that k is the slope of the line and thus conclude that k = 0.0961 N/m, but they would be wrong. Because we graphed force on the x-axis and extension on the y-axis, the slope of the graph represents extension/force, not force/extension as k would be when F = - k x is solved for –k = F/x. After some thinking, they should be able to conclude that they need to take the reciprocal of the slope to get their value for k, so k = 10.4 N/m. Students will also struggle with the negative sign, because clearly the slope of our graph is positive.

To fill out Data Sheet 2, it will be helpful to slide the ruler down the page. In the data I’m posting below, I slid the ruler far enough down so that the resting position of the empty spring was at the 10 cm mark on the ruler. Then I added the 250 g weight, and found the oscillation was too rapid for me to get a good measurement of the maximum spring extension. To compensate for this, I used the feature that allowed me to set the speed of the simulation to 1/16 real time.

Under the table for Data Sheet 3, I show the calculation for the change in energy. The gain in elastic potential energy comes in at 1.05 J and the loss in gravitational potential energy comes in at 1.10 J.
Let’s examine now what was lost by doing a simulation rather than a hands on (wet) lab.
1) The students lost the tactile sense of how heavy the 50 g, 100 g, and 250 g weights are.
2) The students may not fully appreciate how difficult it is in real time to measure the maximum extension of the dropped weight.
3) The students may lose some of the sense that what they are measuring is related to the real world around them.

But there are other features the simulation adds:
1) The lab gets done by a student who is in a school where time or equipment constraints would not allow them to have performed the lab at all otherwise.
2) The student put more of their time into thinking about the physics concepts and less time getting out and putting away equipment.
3) By being able to slow the simulation down, the student may gather better data, and inherently become more convinced that the energy was conserved. Is this any different than photographing a hands on experiment and playing it back at a slower speed to get more accurate measurements?

The discrepancy between the 1.05 J gained by the spring and the 1.10 J in gravitational potential energy may be where the most learning in this lab takes place. What happened to the other 0.05 J? Some students may speculate it went into heat, others may argue it was simply error in the measurements. Is the discrepancy between the two energies in the right direction for some additional energy to have gone into heat? Is the amount of error commensurate with the accuracy with which we were taking measurements? Did the person designing the simulation inadvertently design a flawed simulation?

This is where I feel the simulation ADDS value. If the students decide that it probably was energy lost to heat, in the simulation they can adjust the friction slider to equal zero and repeat the experiment, then no energy should be lost to heat. When they re-run the experiment, they will experience the difference between damped oscillations and non-damped oscillations. When the friction is set to zero, does the maximum spring extension become larger, thus increasing the value we get for the potential energy stored in the spring?

I would like to argue that the ability to more easily manipulate a good simulation like this one probably offsets the losses incurred by this not being a wet lab. I especially argue this from the standpoint that when a student is first learning the concepts, the closer the experiment comes to the theoretical values, the better the initial learning environment. When we assign homework problems to students, we don’t build error into the numbers that are being supplied to the student. Having exact values in homework problems makes it easier for the student to see if he/she is actually dealing with the physics concepts correctly.

I think the bottom line is that there is both room and a need in a physics class to do some of the labs both ways, some of them as simulations and some of them as hands on labs.

Feel free to add comments if you agree or disagree with my feeling regarding the value of the virtual approach to this lab.

Content related to this blog posting can be found at HippoCampus under Kinetic Energy, Kinetic Energy & Gravity, Potential Energy, Mass-Spring System, and Energy Harmonic Motion.

Virtual Labs in Physics

2008-11-22T12:29:00.000-08:00

When I submitted my AP syllabus to AP central for approval, they did not like the fact that my course used a number of virtual labs. In this and the next blog I want to take a look at a lab done in a "traditional" manner and a similar lab done virtually, then compare how equivalent these two approaches might or might not be.

As an online AP Physics teacher, my online students predominately come from either rural schools that do not have the enrollment or the resources to offer AP Physics, or suburban schools where the individual student is involved in so many things that although attending a school that offers AP Physics the student can’t work AP Physics into their schedule. In either of these situations it can be very difficult for students to get access to the equipment needed to do a “traditional” lab.

While Illinois Virtual High School, the organization I teach online for, has reached out to students like those I’ve described above, it still remain problematic to do traditional labs in an online course. One issue is equipment access; the other issue is teacher liability in having the student work with equipment while the teacher isn't physically present. The particular lab I will use for this blog is one called “Changes in Potential Energy”. In this lab students study the conservation of energy in a mass hanging from a spring.

The lab is part of the original design in the AP Physics C course I teach that comes from NROC, and because the lab can be accessed on line through HippoCampus I don't break any copyright laws when I let you see a copy of it. You can access the lab built into the NROC course by going to the AP Physics C1 course at the HippoCampus site, selecting the Course View, going to Chapter 3, and selecting "Lab1". Or as a shortcut directly to the lab you can just click here. To follow along with what the students submitted, it would be best to print the above lab.

At the end of this blog post is the lab write up I got from the students at Northside College Prep in Chicago. Northside College Prep is a well equipped Math/Science magnet school in Chicago. Clearly these students have learned to use Word, Excel, the Internet, had access to the science equipment they needed, and understood the physics being presented in the lab. Since they were last year's students I can now also say one is attending Harvard and the other Dartmouth. NO, not all the lab write ups I get from my students look like this.

Can we provide similar experiences to students in small rural schools by taking advantage of the Internet? Next week I'll take you to the University of Boulder Colorado PhET Interactive Simulation Site, and we'll see if a student in a small rural school could reasonably gather the data virtually from the PhET site, complete the lab at home, and have an equivalent learning experience to the two students from Northside College Prep.

You can click on the individual pages below to enlarge what the students wrote.

Content related to this blog posting can be found at HippoCampus under Mass-Spring System .

Preparing Students for the AP Exam – Part II

2008-11-11T09:42:00.000-08:00

When I first started teaching the AP Physics C course, I had visited the CollegeBoard’s Website and looked at their sample Multiple Choice questions. I have to say that I was a bit disappointed with the Multiple Choice questions I was able to see as samples, there were only 20 of them and they were all from AP Physics B and I was teaching AP Physics C. Contrast that with the FRQ sample questions discussed in last week's blog where they gave all of the AP FRQ questions from 2002 though 2008 along with the grading rubrics.

I DO NOT at the beginning of my course tell my students about the online resources for the AP Exam. I want to utilize those resources with them in a shared manner, where I reel out various pieces in my classroom in a setting where we can make the best possible use of them. About a month ahead of the actual AP exam, I will direct them to the portion of the CollegeBoard website that is designed for students, and that portion does give them access to the full compliment of the 2002-2008 FRQ questions to use for additional practice.

Fortunately Illinois Virtual High School (IVHS), who I was teaching online for, was willing to cover the costs of letting me attend a week long AP workshop in the summer of 2007. At that workshop, taught by a sanctioned AP workshop provider, we were given two CD’s of AP material and one of the CDs were copies of previously released AP Multiple Choice questions from 1984, 1988, 1993, 1998, and 2004, both for the Mechanics and for the Electricity and Magnetism courses. This constituted a large enough sample of questions that I could draw from them to put together my end of the chapter reviews talked about in last weeks blog.

In addition to a collection of previously released Multiple Choice questions, the CD distributed at the workshop also contained FRQ questions and scoring rubrics from the 1974 through 2006 exams. An opening file on the CD states the terms of use to be, “AP Exam materials are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought from the AP Program.”

During the 2006-2007 school year I also had an opportunity to do an online version of the AP Physics C workshop, and as part of that workshop we were also provided with the above materials to use to help our students prepare for the AP Exam.

If you teach an AP class, I would strongly urge you to attend one of the summer workshops, in addition to some examples of previous test content, you also receive what is referred to as the “Acorn” books which are very helpful in knowing what content will be tested, approximate timelines for various topics, and also additional examples of previous exams and student work. You can view one of the Acorn books that is posted at the College Board’s website. At the College Board website, you can also order up print copies of a number of the previous released exams. Here is a link to the website for ordering the 1998 Released Exams.

At the top of this page is a link to “Store”, you can use it to explore more of the materials that are available to you from the AP site.

The listing of upcoming AP workshops can also be accessed at the College Board's website.

I believe that as an AP instructor, you do have an obligation to familiarize yourself with the resources mentioned in these past two blogs. It would be extremely unfair to have your students take the AP exam without you or them having had exposure to these resources, thereby on that exam your students would be competing with students who have had these resources available to them.

Preparing Students for the AP Exam

2008-11-11T07:49:00.000-08:00

While I had taught high school in a traditional face-to-face setting for thirty-two years, teaching a combination of mathematics and physics, I was new to teaching the AP style courses until I semi-retired from the traditional classroom and started teaching part time online. I’m in my seventh year of teaching online and in my third year of teaching AP Physics online for Illinois Virtual High School (IVHS). I’m going to use this week’s blog to share my trials and tribulations of converting from teaching traditional physics to teaching AP Physics C.

Fortunately IVHS didn’t ask me to also write the AP Physics C from scratch, but rather subcontracted with the National Repository of Online Courses (NROC) for the course content. All of their media and most of their course content can be viewed at HippoCampus. I would consider HippoCampus to be a source you can use to bring supplemental materials into your traditional physics course. For teaching a full blown version of AP Physics online I would strongly recommend using the NROC site itself, because they provide additional support as well as additional content.

As with ANY course you teach, you will find that there are adaptations you make that you feel will make the course more suitable for your situation. As an experienced teacher, one of the most valuable things for me when teaching a new course is to see some previous tests so that I can get a feel for the exact level of the questions that will be asked. In the case of teaching AP Physics, that means seeing some old AP exams to get a sense of the level of difficulty in the questions and also to get a sense of where the AP folks place their emphasis. If you never get to see an actual previous exam, it’s pretty hard to prepare your students for that type of an exam.

For those of you new to AP Physics teaching, the AP exam for Physics consists of two parts, the multiple choice questions (MC) and the free response questions (FRQ). At the CollegeBoard website you can download copies of the FRQ questions asked from the 2002 through the 2008 exams. In addition, the above link also let’s you download the scoring rubrics used by the AP graders for those FRQ questions. Imagine the disadvantage you place your students at if you have not utilized this tool!

The way I now utilize these back AP questions in my course is that at the end of every chapter I put together a collection of about fifteen old multiple choice problems and an FRQ question from previous AP exams. I ask the students to work through these old questions on their own, and then in an online screen share session we discuss the problems. I don’t collect these as a graded assignment, because at the beginning of the course students still need to build up to how best to attack this level of a question. When we get to the midterm exam in my course, I use both an in class component that is supplied by the NROC course I teach, and I also then use a set of old AP questions as a take home component. Allowing the old AP questions, which are usually a bit harder than the NROC questions, to be done as a take home test gives the students time to go back and dig through previous materials they may not have learned as well as they should have on the first pass.

When we get to the end of the semester, then I utilize an old AP exam for my final exam and I have them take it in the same time frame as the actual AP exam. Of course the scoring needs to be scaled to convert their AP percentage to the traditional percentage scale used in a high school. For example, a student getting 65% right on an AP exam, which would likely give him a 5 on the AP, does not deserve a D in your class because he scored in the middle of the 60%-70% range that is often used in a high school for establishing what is D level work.

In next week’s blog I will talk about how to get copies of old AP multiple choice questions and more details on how I convert the raw percentage on the AP exam to my high school equivalent grade.

Newton's Second Law - Using an Atwood's Machine -

2008-10-27T06:41:00.000-07:00

Last week's blog introduced students to an Atwood's Machine by using an online simulation. That activity allowed students to develop an understanding of the formula for acceleration that measures the acceleration occurring in an Atwood's Machine. It also allowed them to take some online measurements, apply those measurements using the formula developed, and clarify that their thinking about what was happening was correct.

This week's blog builds on that by asking the students to apply the same concepts in a hands on wet lab. I have to give credit for this lab to Martin Kirby who introduced me to it at an AP workshop he was conducting in Colorado during the summer of 2007.

Because the previous virtual lab gave a good background of the concepts, the directions for this lab are intentionally written to be more open ended, forcing the student to think about what they need to measure in the lab, how to do the calculations, and how to write up their lab report. Following between the row of asterisks is exactly all the information I give my students.

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Chapter 2 Lab - Weighing a key by the use of an Atwood’s machine.

This lab we are going to do hands on, because the materials needed are very simple. It will take an ordinary key, a light pulley, some thread, a stopwatch, a ruler, and a 5 or 10 gram weight. You should be able to locate the light pulley, the stopwatch and the weights at your school and if needed borrow them overnight to do the lab at home.

You are going to suspend as light and as frictionless of a pulley as you can find from a ring stand, or hang it from the ceiling, whichever is easier. Run a very light cord over the pulley and from one end hang one of your keys. On the other end attach a 5 or 10 gram weight, the choice as to which weight to use is yours.

Either the key or the suspended weight will be heavier than the other one and the pulley will rotate, letting the heavier item fall. By measuring the time and distance of that falling and then doing some calculations, you should be able to come up with the mass of your key.

Then I want you to weigh the key on a balance and compute your percent of error. Write up your lab in a way that another reader would be able to tell what you did, would be able to repeat your experiment, and would be able to understand your calculations and results. Fax the written lab to me at the fax number given under Course Home, Teacher Information.

The name of this device is an Atwood’s machine; search the Internet if you would like to learn more about it.

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Below is an example of what I got back from a student, I feel it demonstrates the advantage of periodically using an open format, thus requiring the student to decide how to best write their work up. The image as shown below is at the maximum size I can post in the blog; I have found that in my Internet Explorer browser I can click on the image below and it will open in a much larger format in a new window, becoming very readable.

Content related to this blog posting can be found at HippoCampus under Newton’s Second Law and Atwood’s Machine - Simulation.

Atwood Machine Lab – Blending Virtual and Wet Labs

2008-10-20T06:12:00.000-07:00

Measuring the acceleration in an Atwood machine is one of the classic labs to have student do when they are studying Newton’s laws of motion. As an instructor a challenge you often face is to find a balance in how much detail you supply the students for labs. If you give the students to prescriptive a lab, where they simply do things step by step, plug in numbers, and write a simple conclusion at the end, they can end the lab not even having thought about the physics. If you aren’t prescriptive enough, you will find the students moving so slowly during the lab period that they end the period with no data taken.

Using a blended approach, where you first have the students do a simulation activity on the topic, followed by a modified “wet” lab over the same topic can work better.

In this week’s blog, I’m going to illustrate this with a blended lab using an Atwood machine to measure the acceleration of two masses suspended from a pulley. This week we will look at the online lab component, then next week the “wet” lab component for an Atwood machine.

Have your students go to the Rutgers website and there they will find a Quick Time movie of an Atwood machine in operation.

As with many things I find on the Internet, I feel I need to make modifications for my classroom. On this activity, I didn’t feel the questions were adequate for the students to get the full benefit of what was going on. Here are the tasks I would ask the students to do as a homework assignment using this site:

1) Draw a free body diagram for the object on the left, labeling the mass on the left at m1.

2) Write the force equations using Newton’s second law for the motion of the object on the left when the object on the left is released.

3) Draw a free body diagram for the object on the right, labeling the mass on the right as m2.

4) Write the force equations using Newton’s second law for the motion of the object on the right when the object on the left is released.

5) Using your force equations, show why the motion of the system should be governed by the equation

6) Notice that the movie plays at one frame every 30th of a second. You start the movie by clicking on the red “HERE” link.

7) After the movie plays, use the control bar at the bottom of the screen to back the movie up. Using the single step button, play the move one frame at a time, counting how many frames you have gone through. Taking length measurements from your first frame and your last frame, and time measurements from how many 1/30 of a seconds steps occurred between your first frame and your last frame, calculate the acceleration of this Atwood machine.

8) Using the masses given for m1 and m2, and the formula from step 5, validate that your measured acceleration measure in step 7 are in agreement.

The reason I have included an equation in step 5) is that if a student has done something wrong in steps 1 through 4, they will then know that, and hopefully go back and make the needed corrections.

The reason question 8 is asked is that some students will not take or apply the numbers from the movie correctly. If they don’t get the same answer that the equation in step 5 gives, this should serve as a clue that they need to go back and resolve the difference. If you can build in some self-checks for the students along the way, such as in step 5 and 8, you will improve the chances that they will resolve what it is they are doing wrong, and that is where some of the best learning takes place.

Next week we will look at the “wet” lab that can build on the above simulation.

Content related to this blog posting can be found at HippoCampus under Newton’s Second Law and Atwood’s Machine - Simulation.

Teaching Vector Components

2008-10-10T09:08:00.000-07:00

I have found that my physics students frequently have trouble going into a diagram on a physics problem and correctly breaking out the x and the y components of the forces involved. They understand that they need to get the x and y components, but they mess up on the trigonometry/geometry involved. Here is a student’s work on an old AP question regarding the forces on a block resting on an inclined plane. This student is currently taking Calculus III, so there is no shortage of math in their background. I can’t be critical of his math teacher, because the math teacher for Calc I and II was me.

I have added the angle labels A, B, and C in blue to the triangle in the question, and D, E, F to the student’s work to make the diagram easier to talk about.

From the student’s work it is clear that he considers vector ED to be the downward force of 50 N due to the weight of the block. But now he needs to break out the x-component acting down the ramp and the y-component acting perpendicular to the ramp. You can see that he decided the x-component is 40 N and the y-component is 30 N and offered supporting work, but it turns out his values are wrong. What has gone wrong is that he has placed the angle he called theta at the wrong location in his vector diagram for the weight of the block, having assumed that angles A and D are the corresponding angles between the two diagrams. This is a very common mistake, and you can see that the AP writers provided an incorrect answer of 49 N just for the students that make this mistake, while the correct answer turns out to be 42 N.

My experience has been that most students try to set the angles in the diagram by going back to what they were first taught in high school geometry about similar triangles. As a student I also used to do that until I got tired of making mistakes with it and using up precious time on a timed test trying to be careful not to make exactly the mistake above.

I now approach working up the components in a diagram in a different way with my students. I feel my new approach saves time, is more often done correctly, and better illustrates the physics going on in the problem.

I now ask the students to think about the possible range of answers for the x-component of the weight based on angle A in the original diagram changing through a range of 0 degrees to 90 degrees. It isn’t hard for a student to understand that when angle A is 0 degrees the x-component of the weight will be zero, none of it acting down the plane. When angle A is 90 degrees the x-component of the weight will be all of the weight because in this case the plane is vertical and the weight is acting straight down along the plane. Thus the possible answers for the x-component will vary from 0 to all the weight of the block, and we will use 1 to represent “the whole thing - all the weight”. We also know the function needs to be one of the circular trigonometric functions because we are smoothly moving an angle through 90 degrees as we lift the ramp from 0 degrees to 90 degrees. The students seem to realize that they usually will be choosing Sin or Cos, the issue is which of the two.

Based on the physics of the situation in the previous paragraph, if we consider 1 to represent the whole weight of the block, then to get the x-component of the weight we are looking for a trig function that varies from 0 to 1 and has a value of 0 when angle A is 0 degrees. Again, this is because there is no component of the weight acting down the plane when angle A is 0 degrees. The Sin function has the characteristic of having a value of 0 when angle A is 0, while the Cos function does not because the Cos of zero degrees is 1, not 0. By using this type of reasoning, even without drawing the additional weight triangle the student drew above, they could conclude from the physics in the problem that the x-component of the force caused by the weight acting down the plane should be Fx = W * Sin(A) = 50 Sin(A) = 50*(3/5) = 30 N. Once that is in place, then by the process of elimination the y–component of the weight will need to be Fy= W*Cos(A) = 50 Cos(A) = 50 (4/5) = 40 N.

At this point the vectors are resolved and we are done, but to give another concise example in this blog, let’s this time use the same analysis with respect to the normal force between the plane and the block. When angle A is zero, the normal force should be the full weight of the block, what we will call “1” for the whole thing. When angle A is 90 degrees, the normal force needs to be zero. The trig function with this characteristic is the Cos function, thus Fy = W Cos(A), and no additional vector diagram was needed to get the component of the vector that is acting perpendicular to the plane.

With the correct trig functions used, the student's work on the left would then give the force of friction as f = 0.30*40 = 12 N and the component of the weight down the plane being 30 N for a total force of 42 N, answer C.

A link to an explanation of vectors that might be of help to your students can be found on the HippoCampus site.

Content related to this blog posting can be found at HippoCampus under Vectors, Forces in Two Dimensions, and Forces in Balance - Simulation.

My Mystery Site for Good Physics Lab Simulations

2008-10-01T12:29:00.000-07:00

I spent what would normally be called my "full teaching career" teaching in a face-to-face classroom. When I reached the magic age for retirement, the Internet was well under way and I transitioned to part-time online teaching. One of the challenges in teaching science online has been to handle the lab component of the course, a component I consider very valuable. The majority of my students are taking AP Physics online because they are from small high schools that doesn't offer AP Physics, and almost by definition the students aren't going to have access to high quality or expensive physics equipment that you would find in a first year college physics class that the AP experience is designed to replicate.

Given that lack of equipment, yet firmly believing in the value of labs, I spent many hours my first year of teaching physics online looking for good simulations that I felt could help fill this void. For my online content, I was using the Monterey Institute's AP Physics course, for which the media is also posted at the HippoCampus site, but I needed a solution to this lab issue.

During those many hours I came across what I call my "Mystery Site for Good Simulations". The site is at the University of Calgary and it has THE SINGLE BEST simulation I have ever found online. I'm only speculating now, but it looks to me like there must have been a grant a few years back to develop quality online labs using simulations, but before the process was completed the funding ran out. I find some of their simulations to be very complete, ready to use with my students. I find others that look like they are still in the prototyping stage among collaborating authors. I also find the site to be somewhat intermittent with respect to when it is available.

In an effort to learn more about this site, when I would see something in a lab that would allow me to identify an individual's name that worked on the project, I would search the Internet and in a few instances found an email address or a phone number. I would email and phone the person, but I never was able to get an answer back. I would like to know more and give more credit to the people that wrote these. If any of the readers of this blog can help me out, please do!

The lab is a simulation of Fletcher's Trolley. It demonstrates and allows measurements related to Newton's Second Law of Motion, F = ma. Here is a screen shot of the opening screen you will see for the lab. Below the picture, the label "Fletcher’s Trolley" is hyperlinked to the simulation itself.

Fletcher’s Trolley

I liked this site right away because it is highly configurable with respect to what we need to investigate for the physics, it allows measurements to be taken, and with no additional prompting the site was simple enough to operate in a matter of seconds. By doing pause and play, I could get data out of the site, and that is an important aspect of what I want my students to deal with in labs.

But now the issue is "what do I want them to do with the site and the data", beyond just playing with it. I, like other teachers, don’t have time each week to generate my own set of lab directions for what I want investigated with the simulation. It turns out this site already has a Lab Handout available. When you are at the above site:
1) Click on Help, and choose Applet Help.
2) Then click on Lesson and up comes a lab handout you can give your students for their investigation of Newton's Second Law using the simulation.
3) Right click in the Applet Help window and you can print out a copy.

Now a word of caution and why I suspect the funding for this project ran out. Another lab called Projectile Motion: OneBall is an applet that I wanted to use in the chapter on motion. If you go out under the Applet Help this time, you will still find the lab handout, but this time it also contains the answers. Obviously you could cut the answer out before giving a printed copy to your students. I recommend you never tell the students about going out to the Applet Help, and hope they don't discover that some of the lab handouts for the simulations already have the answers in them. Now how many students do you know that will click on Help when they are having trouble, even though we try to train them to do that? You will also find some of the Calgary Applets to not have anything completed under the Applet Help button and thus the suspicion that the funding ran out.

Content related to this blog posting can be found at HippoCampus under Newton’s Second Law and Atwood’s Machine - Simulation.

Having Students Type Mathematics

2008-09-22T12:56:00.000-07:00

When you look at science and mathematics textbooks, you see mathematics typed in notation that parallels how you write mathematics by hand. For example in the screen shot below taken from the free online Physics materials at HippoCampus, these equations look "good", they look like what you would write by hand or see in a textbook.

Few people would disagree that part of a K-12 curriculum should include teaching students how to use a word processor like Word from Microsoft. I'm going to argue that learning how to use a word processor should also include learning the basics of typing mathematical expressions in a word processor.

While there are a lot of word processors out there, including WordPad and Notepad which come with the Microsoft operating system, Word itself is virtually an industry standard. It would be strange to find word processing being taught in a school that wasn't being taught by using the Microsoft Word product. I strongly believe that while we can find shareware and freeware alternatives to software, the time invested in learning software is significant and we do not do our students a favor by having them learn some off brand product only to have them then need to relearn the mainstream products when they go off to college or join the workforce.
We teach word processing on Word because Word is the product most often used in the workplace. Following that same line of thinking, when teaching students how to word process documents that contain mathematical notation, we should also be training them using mainstream products. My experience has been that there are three categories of products out there for typing mathematics, they are the Equation Editor built into Word, MathType that is made by DesignScience as an extension of the Equation Editor, and programs that are specifically designed as math software like Mathematica and Maple.

If I'm predominately typing a document that has a few equations in it I use MathType. If I'm typing a document that is predominately mathematics, where it includes equations, graphs, and the results of calculations, then I will use Mathematica. In schools, cost is a factor. A single copy of the academic version of Mathematica to use on a school computer would currently cost $270. A single copy of the academic version of MathType currently sells for $57. Equation Editor is free if you already have a copy of Word, which most school do have on their computers.

As you introduce your students to typing documents containing equations, Equation Editor will be quite satisfactory and not add to the school's cost to incorporate learning to type some mathematics into their word processing classes. An added benefit is that Equation Editor is made by DesignScience, the same people who make MathType, so the interface and thus the transition later to MathType does not result in wasted learning time on the part of the student.

Getting Started with Equation Editor

While Equation Editor is part of Word, it isn't part of the automatic installation process, so you may well find that the installations of Word on the computers in your school are not currently configured to allow you to use the Equation Editor. If that is the case, the directions for installing it can be found under step 3 at the Microsoft website.

As a first introduction to your students on using the Equation Editor I would suggest the "Tutorial from the University of Rhode Island".

The University of Waterloo also has a Video Based Tutorial .

For more in depth work with Equation Editor, take a look at Design Science's "Equation Editor Tips and Tricks" article.

Students should also be taught to look things up by using the Help command in the equation editor window, because when you aren't there this is one of the first techniques they should use.

A good equation for your students to practice with is the quadratic formula that they learn in second semester of Algebra I.

Or even better, using Word for the text and inserting the equation using the Equation Editor you would have:

Media and Simulations Relating to the Study of Motion

2008-09-22T06:21:00.000-07:00

Most physics courses start out covering the equations of motion in one dimension, and then apply those equations to freely falling objects. Next comes motion in two dimensions, and the extension of freely falling objects turning into a discussion of projectile motion. This week’s blog is going to be about material available on the Internet that can be used to enhance this opening chapter.

Quality media lessons for most first year physics topics are currently available on the Internet. You may find these resources valuable for direct use in your class as you instruct students on these topics. Even if you are a very traditional teacher and work from the textbook and your own notes when presenting topic, you may find the media lesson on the Internet helpful supplemental material for those students that didn’t understand the concepts as thoroughly as they should have when they were covered in class.

How do these websites come to be? The website I’m going to link to below for the media is known as the National Repository of Online Courses, abbreviated as NROC. Part of the funding it receives to develop its courses, stipulates that the media needs to be made freely available to students. Those freely available online media lessons are then made available at the HippoCampus site. The William and Flora Hewlett Foundation is one of their main sponsors.

Take the time, approximately 10 minutes, to look at the following four media lessons that would tie to the chapter on motion in any first year physics textbook.

Each of the items in the list below are hyperlinks to the topic listed:
Equations of Motion
Freefall
Motion in Two Dimensions
Projectile Motion

Another useful aid for the teaching of physics that has come of age on the Internet in the last five years is simulations related to various topics. Teachers and educators are well aware of the advantage of making their lessons interactive, and that is the most important component that these simulations can bring to your class. I find that students can often do well with finding solutions to written problems by applying the proper equations. But give them the same activity in a lab setting, or in a simulation, and it can seem like they are back at square one. For me that argues in favor of needing to expose them to the same topic in a setting that isn’t just paper and pencil.

Below are three of my favorite websites due to the quality and quantity of the simulations they have. In each case the first hyperlink will bring you to the opening page of the sponsoring site. The second hyperlink will bring you to the specific simulation. The specific simulation being show was selected as an example of a simulation that could be used in a chapter on motion.

1) HippoCampus
They have a simulation at the end of each of their lessons; the lessons typically consist of about 10 to 15 minutes of media, as you saw with the above links.

Projectile Motion: Cannonball

2) PhET, Physics Education Technology
The site is developed and hosted by the University of Colorado at Boulder. Again you will see that one of the principle sponsors is the William and Flora Hewlett Foundation.

Projectile Motion: Hit the Target

3) University of Calgary Physlets
These simulations were developed by Wolfgang Christian at Davidson College. This simulation shows visually how we can analyze a more complex 2-dimensional motion by breaking it down into separate 1-dimensional motions, which are easier to analyze. These seem to be unique in that they are very focused on a particular topic and students can take measurements off of the screen. They are nice setups for an in-class discussion or an investigation you might ask your student to do.
Projectile Motion: Horizontal and Vertical Components done Visually
Projectile Motion: Numerical Values Assigned to the x and y positions

Hopefully you will be able to see how simulations like these can help explain concepts and also make the topic you are studying interactive for your students. I invite you to use the comment area of the blog to suggest other simulations you have found on the Internet that you find helpful in teaching about motion.

Content related to this blog posting can be found at HippoCampus under 1D Equations of Motion, Freefall, Ball Toss - Simulation, 2D Equations of Motion, Projectile Motion, and Cannon Ball - Simulation.

Showing Work on the AP Exam

2008-09-10T13:00:00.000-07:00

In last week’s blog we talked about having students write and work with units when they are doing homework. What you write for units on homework when time is not an issue can be considerably different than what you write for units on a timed test. This week we will explore the amount of work you might accept from your students when they take a timed test.

While a blog is often an expression of personal opinion, and part of this blog will be that, I like to make my suggestion based on more than just opinions. So for this discussion regarding how much to write on a test, I’m going to make extensive use of looking at writing samples from the College Board for the AP Physics test. By looking at samples from an actual AP Physics test, we will be viewing what a group of veteran physics teachers consider to be appropriate.

I need to acknowledge that the College Board and AP are registered trademarks; this is a link to the main page on their AP Physics C-Mechanics website. Below I will be pasting in some samples of student writing from their website, invoking “fair use” for educational purposes. My examples come from the 2007:Free-Response Questions Scoring Guidelines and Sample Responses Q2.

Here are three sample solutions of student work for question M2.

Click here for an enlarged image of the above solution.

Notice that the student writing in M2A1 used exactly the style of writing we talked about in last week’s blog, the style we would ask students to use on their homework. Units have been supplied in every step.
Click here for an enlarged image of the above solution.

In M2B1 the only place this student used units was on the answer. The student doesn’t show the numerical values that were substituted for T and v.
Click here for an enlarged image of the above solution.

In M2C1 the student uses incorrect units of “m” where he substitutes for the velocity as 3.41 x 10³ m”. Correct units for velocity would have been “m/s”.

When these three problems were graded, you may be surprised to learn that “Full credit was awarded” for all three of these solutions. You can verify that by clicking on this link to the AP Website and looking at the last page.

So what would you advise a student to write down when taking the AP exam?

I’m telling my students to:

1) Write down your formula and solve for the variable of interest while you are still using variables, they take less time to write out than the numbers.

2) Show the numbers you are substituting for the variables, that way if you make a mistake in the substitution or in the arithmetic, the grader will know that you had the physics right and the arithmetic wrong.

3) If you already know the proper units for the answer, you don’t need the units yourself to help you keep track of things in the intermediate steps, and you are not involved in an intermediate unit conversion, save time and just show the units on your answer.

If I have a VERY STRONG student, one who always has extra time at the end of an exam, I would make an exception and encourage that student to write like the student in example M2A1. Below is that student’s response to all parts of question M2A1,. Isn't it a thing of beauty!

Physics Problems - Show Your Work !

2008-09-04T14:27:00.000-07:00

How much work do you expect your students to show when they are solving a physics problem? I'm not going to pretend that I have the only answer to this, and I strongly invite your comments. I'll start by sharing my thoughts.

I find that for my students, a good understanding of units enhances their ability to remember formulas and vice-versa. When working problems, including the units helps them tell if they are making a mistake as they work toward a solution. Writing out the units helps them learn the basic MKS units that comprise the more complicated units used in physics.

I don't want students to simply memorize that energy is measured in Joules, and that is the unit you put after your number at the end of the problem. I want the student to think that work is done by a force acting through a distance (W = F d), a force is mass times acceleration (F = m a), so a Joule breaks down to being a ((kg)(m/s²))(m) = kg (m/s)². When they do their homework, I want to see units being treated just like other algebraic variables.

While it's an over simplistic example, let's say a student is having trouble remembering if KE = (1/2) m v² or if KE = (1/2) m v. A student knowing that energy and work are equivalent, would use the reasoning in the above paragraph to know that energy would be measured in W =m*a*d= (kg) (m/s²)(m) = (kg)(m²/s²) and therefore KE = (1/2) m v².

When my students do homework, I expect to see units. I require that they

Show the formula they are using.

Supply units when they substitute a value into the equation.

Track the units through the the solution, so that they arrive at the correct units in the answer.

Let's look at a specific problem to see what would be expected.

Question: If you wish to throw a baseball straight up into the air so that it reaches a height of 15 meters, how fast must it be going when it leaves your hand?

I'm not big on having students memorize lots of formulas, I'd rather have them memorize basic formulas, understand the physics involved, and arrive at their solution in that manner. Yes I know that:

and when we are doing that chapter in my course we use this formula. But I find this particular formula a lot harder to remember than what I call the three main formulas about acceleration, velocity, and position. Because my students are expected to have or be taking calculus, I do expect them to know that:

These three equations can be achieved by only understanding that a = g, and knowing the basics of calculus. I would expect they would be able to write down these three formulas years after they have taken the course.

If the student recognizes the symmetry of the physics in the above question, i.e. that the velocity-distance relationship while rising is the same as the velocity-distance relationship while falling, they can pretend instead that the ball was dropped, and simply determine its speed when it hits the ground. Then x_o and v₀ become zero, and the solution simplifies to:

Above is the amount of writing I would like my students to show on homework, along with a short comment about switching the problem from throwing the ball up to dropping the ball down being equivalent items. This would also be the typical amount of writing found in a worked example in a textbook, or in an online electronic textbook like http://www.hippocampus.org/ . The screen shot below is from the AP Physics C1 - Equations of Motion topic on the HippoCampus website.

However, I don't believe their is only one answer to how much work students should show. On the AP exam, where the test is timed, I don't believe the students time would be well spent working the problems as I have shown above, where they write the units in every line of their work.

In next week's blog I will share my thoughts on how much I think students should write when taking the AP Physics exam.

Content related to this blog posting can be found at HippoCampus under Equations of Motion.