Measuring Static Friction – an Extreme Example

Once you study physics, you are forever its willing prisoner. One of my favorite and most used tags for posts is Can’t Help Thinking About Physics. Here we go again.


Static Friction

While sitting on a leather sofa, visiting with my daughter, we noticed that her phone (in its rubbery case) wasn’t sliding down the cushion. She placed the phone at a steeper and steeper angle until finally it did slide.

We use this method, tilting a surface until an object slides, to measure the coefficient of static friction in our introductory physics class. I had never seen anything tilt this far before sliding. So, of course, I snapped a couple pictures so we could calculate mu.

Angle Measurement

I tried to hold the camera as nearly horizontal as possible, using the arm of the sofa as reference. I used the “selection cursor” of the computer’s own preview software to measure rise and run of the slope. It gave me the pixel dimensions (51×116) of the selected area and using the tangent function, I calculated the angle.

tan calc

Because I chose the angle where the phone JUST began to slide, the component of the gravitational force parallel to the surface (Fp) is equal to the force of friction (Ff). At any angle less than this, Ff would be larger than Fp and the phone would not slide. At any angle greater than this, Fp is greater than Ff and the phone would slide and accelerate. As Goldilocks would say, this angle is “just right.”

If you haven’t seen the math, here is a diagram. I usually have my students work through the calculation of Fp, Ff, and Fn. They just have to realize that IN THIS CASE, Fp is equal to Ff. They are usually amazed that mu = tan theta until they have had some time to think it through.

scans 001

I have attached a copy of a student lab in case anyone wants to use it. It certainly falls into the category of “Cheap Labs” but is still very rich. In the student lab, they first calculate the coefficients (starting and sliding) for a physics book. I guess you really do need physics books. They also calculate mu for their shoe. It is amazing the range of values that shoes yield.


Still, this phone with a static friction mu of 2.27 really surprised me. I was thinking that maybe adhesion was playing a roll. While friction prevents surfaces from sliding past each other, adhesion can be investigated by determining how much force it takes to pull surfaces apart. We did a crude test by placing the case on the floor and trying to pick it up with the cushion. It did not stick so I guess adhesion was a small factor and mu really is very high.

I think that a modified version of this activity would make a pretty good science fair project for elementary school. You wouldn’t really have to do all the math, just recognize that relative friction can be measured by how high you have to raise the end of an incline to get an object to slide. Perhaps various shoes could be measured, or toy vehicles, or flooring types.

As always, your helpful comments are welcome!

Dividing Up the Budget

It’s that time of year again. Departments get a budget and order supplies for next year. At the school I am working at, the budget is for the entire department. So I decided to create a spreadsheet that would allow each teacher in the department to get an idea of how much they could spend.

We started out by acknowledging that some courses cost more to teach than others. It’s not that everyone couldn’t spend money if they wanted to, but traditionally chemistry has more consumables that physics. So we sat down as a department and decided how much of the budget should be allocated to each course. We assigned the courses a “factor” between 1 and 7 based on their “costliness”.

After that, it was easy to build a sheet that counted sections and “factors” and divided the budget. There are a couple little tricks build into this one. For instance, no section gets less that $100 no matter how many sections of the other, more expensive courses there are.

budget SS pic

The numbers don’t add up to the budget exactly due to some rounding.

When each teacher gets their schedule, they put in the number of sections of each course they are to teach and it returns their personal spending amount.

Of course, no one is required to spend all their money and some teachers pool their resources. But it is a good starting point and a way to start a conversation about budget issues.

Here is a link to the actual spread sheet. Try it out and modify it in any way you like. It has worked well for us.

Budget Spreadsheet

Factors Affecting Resistance Lab – Free Lesson Plan


If you are teaching about electricity and you don’t have any lesson plans for today or you have to be absent sometime soon and don’t have plans for the sub, this post is for you!

We study electricity using CASTLE, a program for teaching conceptually about electric circuits. It is well supported by research that students who experience this program are more likely to give up commonly held misconceptions about circuits. My students are able to learn the “formulas” in a very short time after our work with CASTLE. I am, as you know, a big fan.

The concept of resistance is clearly demonstrated in CASTLE using carbon resistors and bulbs with different amounts of resistance. But I like to add this lab to our post-CASTLE unit because resistance is so interesting and measurable.

The format of the lab is also one I like to use. If every student is doing the same thing, you need a complete “class set” of materials. But if you set the lab up in stations, the students move around and you can take advantage of objects that you may only have one of. This lab started out with just four stations and I used it to illustrate the factors that affect the resistance of a wire (length, diameter, temperature, and material).

But it was easy to add stations as I learned something interesting or acquired a unique piece of material. When the electrician came to my room to fix the thermostat, he replaced the thermistor just in case it was bad.


It was not defective, so now I have the exact device that measures the temperature of my classroom for the students to play with in lab. I went to the hardware store and picked up interesting switches and dimmers that rely on resistance and made them into stations.

So here is what you will find in the folder if you follow the link:

1. A copy of the student lab paper.
2. A copy of the instruction sheet that I use at each station (and a necessary table for station 9)
3. A short video of each station that can be used with the student material to collect data.

I like having the videos, because then if a student misses lab, they can see the videos and still collect data from them and answer the questions. You can use the videos in that way for your whole class, or better yet, use them as a guide to set up the actual lab in class.

Click on the links below:

Student Lab Sheet

Station 1 – Length of the Wire           Instructions     Video
Station 2 – Diameter of the Wire        Instructions     Video
Station 3 – Type of Material               Instructions     Video
Station 4 – Temperature                      Instructions     Video
Station 5 – Color Code                       Instructions     Video
Station 6 – Variable Resistors             Instructions     Video
Station 7 – Photocells                         Instructions     Video
Station 8 – Thermistors                       Instructions     Video
Station 9 – Resistivity                         Instructions     Table      Video

I would really love to hear from anyone who uses the material. Let me know if it is useful, how you use it, how I could be more helpful.

Sources of Continuous Voltage – Demonstration Videos

I recently posted some videos of the activities in the CASTLE curriculum program for teaching students about electric circuits.

As a supplement to those activities I do a demonstration showing ways that a continuous voltage (and therefore current) can be maintained.

I have posted 6 short videos that show these demonstrations. Try them yourself with your students! Ask the students what they know about their utilities; gas, water, electricity. Some have no idea where these things come from, where the power plant and water towers are. They will be interested!

Continuous Voltage Demos
Electromagnetic Induction Part 1
Electromagnetic Induction Part 2
Chemical Cell
Solar Cell
Piezoelectric Cell 


If you have read my posts before, you know that I like the CASTLE program for teaching about electric circuits. The students work their way through several sections of material that address common misconceptions held by high school students about electricity. The program asks them to rebuild their mental model based on the evidence they see as they build circuits. An important part of this learning is the inclusion of a 25,000 microfarad capacitor in some circuits.

Students work in pairs, often consulting the other pair of students at their table. The teacher leads the class in model building at intervals. Students learn to color code circuits to help understand what is happening.

I have created some videos of the actual lab activities associated with the first 6 sections. I did so for several reasons:
1. To help students who are absent catch up.
2. To help teachers who are using CASTLE for the first time see what to expect and check their results.
3. To allow students who have completed lab work to review what happened while they are studying or completing homework.

The videos are not intended to replace the actual lab work done by students in class. Though, if a person were studying physics and had no access to lab equipment, the videos could be used to help them work through the CASTLE materials.

The videos have relatively low production quality (I have no crew) but hopefully good usefulness. My own students report that they use them to keep up when they are absent (25%), review (75%), check to see if they “did it right” (50%), work ahead (5%).

Let me know if you think they are useful! Your helpful comments are always welcome.

Section One

Investigation One Part 1
Investigation One Part 2
Investigation Two Part 1
Investigation Two Part 2
Investigation Three Activity 1.8
Investigation Three Activity 1.9 Large Bulb
Investigation Three Activity 1.9 Small Bulb
Investigation Three Activity 1.10

Section Two

Activity 2.1
Activity 2.2
Activity 2.5
Activity 2.8
Activity 2.9
Activity 2.12
Section Three

Activity 3.5 step1 (0.025 farad capacitor)
Activity 3.5 step3 (0.025 farad capacitor)
Activity 3.5 step5  (0.100 farad capacitor)
Activity 3.7
Activity 3.13 with Old Used Batteries

Section Four

Section 4.1

Section Five

Activity 5.1
Activity 5.2
Activity 5.3
Activity 5.5
Activity 5.7
Activity 5.10
Activity 5.12
Activity 5.13
Activity 5.15

Section Six

Close Up Photo of Digital Multimeter
How to Use a Voltmeter
How to Use an Ammeter
Activity 6.4a
Activity 6.4b
Activity 6.4cActivity 6.5
Activity 6.6 part1
Activity 6.6 part2
Activity 6.7 a-c
Activity 6.7 d-f
Activity 6.9
Activity 6.10
Activity 6.12
Activity 6.16
Activity 6.19
Activity 6.20 c

Tips for Doing Well in Physics

Most teachers have a list of suggestions that help students do well in their class. Here is mine. I post it on my web site and show it to parents at open house and conferences. I especially like the table at the end.

Suggestions for Doing Well in Physics

1. Do all the homework! Becoming a good problem solver takes practice. Don’t just do the easy problems and skip the hard ones. Remember, if you get stuck on a problem there are steps you can take to get yourself unstuck!

Draw a diagram with as much info as possible. Indicate +/- directions.
Make a list of values given in the problem and label them. Ex: t=2 minutes=120 seconds
Think about what physics ideas apply. What are we studying?
Consider what equation might be useful, you can only solve for one variable at a time.
Carry out the calculations. Keep an extra digit as you round.
Think carefully about the results. Do they make sense?
Keep track of the units. Having the units correct does not guarantee a correct answer, but the answer cannot be right if the units are not right.

2. Work independently. Working in a group is easier than working on your own, but you may learn less. It is easy to watch someone else solve a problem and then think you understand it. It is much harder to come up with the entire solution on your own (as you will be expected to do on the test). Practice solving problems on your own. If you “compare” your answer to someone else’s, always discuss any differences with them to see why you disagree

3. Consider looking at the material ahead of time. Check the calendar (online and in the room) and see what we will be discussing in class. Read those pages and look at the example before the class discussion. Print out the class notes if they are available. In this way, you will know which parts of the discussion are harder to understand and you can use the class discussion time to ask good questions.

4. Review the examples in the text. You can often find an example that is very similar to the problem you are trying to do.

5. Remember the online resources that are linked to the teacher’s web site. They often explain the same concepts we are covering but may use different words or examples that would be make more sense to you. Everyone thinks a little differently and has different experiences on which to draw.

6. Consider staying for resource period to do your homework. That way you can ask questions.

7. Think about how the labs are related to the physics problems. Labs are not separate and different from the material we are studying. They are often exactly like one of the problems, but instead of giving you the numbers, you measure them in an actual example.

8. Think ahead about what might be on the test. Ask questions to help focus your study time on the important concepts.

Do MORE of this

Do LESS of this

Begin assignments as soon as you get them. This leaves time to ask questions about the more difficult concepts.

Do assignments in the moments before class begins or during other classes that you have in the morning before physics.

Do your own work. If you “compare answers” with another student, discuss any differences so that each can learn from the other.

Copy another person’s homework so you get “points”.

If you don’t know how to do a problem, think about it for a while. Try different approaches to see if they lead you anywhere. Read the strategies for doing well in physics.

If you don’t know how to do a problem, ask the teacher what the answer is after one nanosecond of thought. Then, act disgusted when she asks you to try harder.

Read the assigned material BEFORE class discussion. Assignments are available on the web site for several days in advance.

Scan the text material quickly, for the first time, right before the test. If the teacher asks you if you have read the book, say “sort of”.

Do all the problems.

Do the easy problems and skip the hard ones.

Think about how the lab activities relate to the concepts you have been learning. Practice all calculations and when answering lab questions, carefully consider the implications of your lab results.

Sit around and watch the other people in your lab group do the work while you entertain them with interesting stories. During passing time on the day the labs are due, copy what they have written. Act indignant and say “we worked together” when the teachers asks what you are doing.

When you miss a homework problem, ask about the process, not just the answer. Retry the problem from scratch with your new understanding.

Ask to “see the solution”, as though looking at someone else’s work is as good as doing the work yourself.

Jumping on the Force Plate – A Net Force Activity

It is always fun to think up new activities for my second year AP Physics students. We do 55 labs in the first year course, so the second year is spent mostly solving problems.

Today, I told them to jump off the force plate, find the impulse the plate exerted on them, calculate how long they should spend in the air, and compare this calculated time with the measured value. I told them that they could have one person jump or they could all jump themselves or some combination.

I was pleased with this activity for many reasons.

  • I told the students what to do, but not how to do it.
  • The students immediately began discussing it AMONG THEMSELVES!
  • I was able to sit back and listen to their conversation and look for opportunities to ask probing and irritating questions to check their understanding.

After their first attempt, the students calculated a 35% relative error. They actually asked me if that was “good enough”. High school students can be so amusing. I withheld comment except to challenge them to do better.

Here are some things that we learned.

1. The force that the force plate exerts upon you is not the critical value, but rather the net force. The force sensor can be “zeroed” with nothing on it or with the person standing on it. At first, the students tried to subtract the effect of gravity from the calculations. On the second try, they zeroed the scale with the person standing on it to get the force plate to read net force (no subtraction necessary).


2. Jumping is a complex motion. You lower yourself by bending your knees and then jump into the air by straightening your legs. The graph below shows what happens if the students begin collecting data before they lower themselves for the jump. There is an additional section of the graph that dips below the x-axis (near 0.6 seconds in this example). This is confusing to students and introduces the possibility that the rebound of the scale will affect the reading.

Data showing up and down motion of the jump.

Data showing up and down motion of the jump.

Once they had some good data, zeroed the force plate while standing on it, and lowered themselves before collecting data, this is the analysis.

First, determine the impulse by highlighting the time interval and selecting the INTEGRAL button.

Determining the Impulse

Determine the weight of the person from the graph and calculate their mass.

weight graph


Use these values to calculate the launch velocity.


Determine the calculated “time of flight”.


Compare the calculated time with the time from the graph.

Determining Time of Flight

Determining Time of Flight

Deciding exactly where to place the brackets for this time interval led to an interesting discussion. We decided to place them as the force value passed through zero. This led to very good results but I am not sure this was the best choice. There seems to be some “rebound” action going on with the sensor. My force plate is quite old. You can see from the graph that had we placed the brackets as they reached the -603 N mark, our measured time would have been shorter. We read the time interval from the delta t in parentheses in the lower left corner of the graph.

The value of t=0.40 matched our predicted time of flight very well.

The activity led to lots of good discussion and was reasonably good in terms of error. What else could you wish from a physics lab?

As always, your helpful comments are always welcome.