Against the Wind



This morning I went for a bike ride. The weather forecast said that it would be breezy but there was little chance of rain. Here in the midwest, our weather and prevailing winds generally arrive out of the west. I learned long ago that when there is wind, always ride into it on the way out and you will be rewarded on the way home.

In the past, I have made comments to the effect that my 20 mile ride takes longer on windy days like today, only to be met with skepticism. The comments often go something like “well, whatever you lose on the way out you gain on the way back, so it all comes out even.”

Students often found the idea of averaging speeds counter-intuitive. They did not distinguish between situations where two speeds were undertaken for equal distances or equal amounts of time.

Warning: If you are going to use these examples with students, fix the significant digits.

The classic problem goes something like this:

If I drive halfway to the state capitol at 50 mph, how fast will my sister have to drive the rest of the way so that we average 75 mph? Most students will wonder briefly why they are getting such an easy problem and quickly write 100 mph. Some will have trouble with the concept even after it is explained and demonstrated with real numbers.

Imagine that the trip length is 150 miles. Making up an example is another thing that students often fail to try. In this example, I ask them “do you think the trip length actually affects the answer?” I point out that if it did, then it would have needed to be supplied in the problem or there would be no way to calculate the answer. Since the problem did not specify the length of the trip, it must not matter and we are free to make up an example to simplify the problem conceptually. In the end, if we want to check to see if our assumption that trip length did not matter was valid, we could make up a second example with a different trip length and see if we got the same answer. Of course, you could use x and 2x for the distances and in the end the x’s will disappear, but for some students numbers are easier.

This problem actually appears in our 7th grade algebra book. I keep trying to explain to the math teachers that it is conceptually more complicated than they think because students do not always have a firm grasp of the motion concept and will therefore have a difficult time applying the algebra. Here is a table of values that are either supplied in the problem or made up for my first example.


Using the formula for average speed the other values can be calculated. Rather than moving at 100 mph (as some students predict), my sister must actually drive 150 mph if we are to average 75. The lesson is that speeds can only be averaged if they two drivers drive for equal amounts of TIME, not if they drive equal DISTANCES.

table 1

To check the original assumption that trip length did not matter, a second example with a trip length of 300 miles yields an identical answer, 150 mph.

table 2

Back to the bike ride. How does wind affect my speed. Assuming I give a constant effort, the wind will decrease my speed on the way out when I am riding into the wind and increase my speed on the way back when I am riding with the wind. In the simplest example, the speed with be increased and decreased an equal amount.

I usually ride 12 mph and my normal ride is 20 miles. This means when there is no wind, I complete the ride in 100 minutes (1.67 hours).

10 miles / 12 mph = 0.833 hours out

10 miles / 12 mph = 0.833 hours back

 total time = 1.67 hours

If I assume that the wind can increase and decrease my speed by 3 mph then:

10 miles / 9 mph = 1.11 hours out

10 miles / 15 mph = 0.67 hours back

total time = 1.78 hours

The total time of the ride with wind is longer than the time riding without the wind. This is because the speed were changed for equal DISTANCES, not equal amounts of TIME, therefore cannot be simply averaged. The wind did not “make up” on the way back what it took on the way out in terms of time.

If I assume that the wind was even more severe, robbing and returning 6 mph, the calculations are even more extreme.

10 miles / 6 mph = 1.67 hours out (actually the original total!!!!)

10 miles / 18 mph = 0.55 hours back

 total time = 2.23 hours

This is a full 0.56 hours (34 minutes) (33%) increase in time over the ride calculated with no wind. No wonder I hate wind. Even the numbers fail to convince some students. One student suggested that if I rode the other direction first, perhaps I would benefit and complete the ride in less time rather than more. Oh, physics. You are a harsh mistress.

Of course, this is not really how wind affects speed. Instead, wind contributes to the total resistance that I encounter when I ride. And that resistance is a function of the speed. That discussion would be much more complex but still fun.

As always, your polite and helpful comments are welcome.


Melting the Frost

Frosty Mornings – Can’t Help Thinking About Physics

Our unseasonably warm spell is continuing. The mornings are frosty and icy as the temperatures that overnight fell below freezing rise into the mid 40s by noon. Its hard not to think about physics when I’m out walking or biking. I snapped a few interesting pictures, took some data with my iPhone and decided to come home and read about frost.

The amount of water vapor that can be held by the air depends on the temperature. At higher temperatures the air can hold lots of water. At lower temperatures it can hold less. Water vapor (gaseous water) has more energy than liquid water which has more than solid water (ice or frost). As the temperature of the air cools, the water vapor can undergo a change of state to liquid or solid.

The temperature at which this change occurs depends on how much vapor is in the air. If the air is quite full of water vapor, even a small drop in temperature can lead to the formation of dew. When the air is dryer, with less water vapor, the temperature must fall further before dew begins to form. So the term “dew point” refers to the temperature to which the air must fall before the formation of liquid water (dew) begins. In some ways, dew point can be thought of as a measure of the water vapor load of the air.

We used to measure the dew point in the 9th grade science class by cooling a beaker of water with ice until condensation started to be seen on the outside of the container. (An ordinary glass would have worked just as well but somehow it all seemed more official and scientific if we used a beaker.) One year I heard the teacher in the room next door having trouble with the lab. I stepped in to see what was the matter. Finally it dawned on us that following a restructuring of the course, the lab moved from August to January. The difference being that in August the air is very juicy and the dew points can easily be as high as 60 or 70 F. In January the air is very dry and the dew point actually falls below freezing. We were never going to get the temperature of the water in the beaker low enough to form condensation using just ordinary ice from the freezer. It was one of those head-slap moments that sometimes leads to more learning than a lab that goes according to plans. The teacher took a few moments with the class to explain what was going on and they all brainstormed ways to actually measure such a low dew point. Using dry ice was a common suggestion. The students thought that by adding frozen CO2 to water you could lower its temperature below freezing. Clearly they needed some additional time and experience with these concepts.

So what actually does happen when the dew point falls below freezing? Instead of dew forming in the grass the water vapor moves from it gaseous state straight to a solid on the blades of grass. Instead of forming dew, it forms frost in a process called sublimation.


My interest was piqued when I noticed that the temperatures were near freezing and the frost in the shade had not melted while the sunny spots were nearly clear of ice. There was a very narrow strip of frost that had newly been exposed, but not yet melted, as the shadows moved.


I collected some data related to the position of the sun and the weather conditions. The time was about 9:35 CST on December 5.

I wondered how quickly the sun would be able to provide enough energy to melt the frost. Solar energy calculations are pretty straight forward. The sun sends out energy at a fairly constant and well known rate. How much power falls on each point depends also upon the angle of the suns rays. The easiest way to find the angle is to compare the height of an object to the length of its shadow. Objects used in this ways are referred to as gnomons. This sign acted as a fine gnomon. I don’t need to know its actual height, only the relative lengths of the object and the shadow.


Not everything has to be high tech. The easiest way to get this ratio was to make the picture full screen and then use a ruler to measure the two distances. Sadly, all I could find was this old school ruler. For measuring ratios, one unit is as good as another.


Here are the measurements and angle calculation.


Its always fun to check the Navy or Nasa websites to see how close your measured valued are to the official tables.

correct table


This would indicate that my measurements were pretty far off. Disappointing. Too late to run back and set up a better gnomon, one that is more perfectly vertical and on a surface that is more perfectly horizontal. And then take a better picture. I think I will trust the Navy Table and call it 19 degrees. Interestingly, the azimuth as measured by pointing my phone at the sun and using the compass agrees with the table pretty well. Too bad that is not the measurement I need.

Here is the way to calculate how much solar energy is falling on each square meter of the grass.

1. The sun produces energy which spread out into the sphere that surrounds it. If you divide the total solar output by the number of square meters on the surface of an imaginary sphere with a radius of 1 AU (a sphere that would touch the earth) you get a value of 1360 Joules of energy passing through each meter of the sphere’s surface each second. That value would be measured at the top of the earth’s atmosphere.

2. Some of that energy is reflected or absorbed by the atmosphere. Variations in the atmosphere will affect how much passes through but the value is generally considered to be near 1000 Joules falling on each square meter each second. This would be true of a spot on the earth directly below the sun, where the sun’s rays would be striking the surface perpendicularly.

3. At all other locations that same amount of sunlight is spread out over a larger effective area making the energy per area less. The lower the sun is in the sky the more spread out the beam becomes. The energy is less by the sine of the angle with the ground, the angle of altitude (or cosine of the angle with perpendicular, called the zenith angle). For 19 degrees the energy available each second on each square meter is a measly 330 Joules. Little wonder it is so cold here this time of year.

I am going to assume that 330 Joules of energy is available each second on each square meter and that it can all melt frost. This will let me calculate the minimum amount of time needed to melt the frost and the actual time will be something more than this.

Well, how much energy is needed? It depends on how much water there is. Each gram of ice requires  about 334 Joules to undergo that phase change from ice to water assuming the frost isn’t too cold. This is a pretty good assumption since the temperature was already 34 F. But how many grams of water are there?

To determine this I weighed a paper towel, took it to a newly melted spot and pressed it into the grassy surface to collect surface water. I then reweighed the towel. Pretty cool! I measured the length and width of the paper towel.

data table

Using this data I estimated that the total mass of frost on one square meter of grass was about 33 grams. If each gram requires 334 Joules of energy to melt, this means 11,000 Joules are required to melt the frost on each square meter. If the sun can supply 330 Joules each second to this square meter then the minimum time required for the sun to melt the frost is….. 33 seconds.

Mass Calculation



Energy Calculation


Time Calculation


No wonder the frost band outside the shadow is so small.

While reading about frost I learned a few interesting things and ran across some useful web sites.

Great explanation of the effect of angle on illumination (with diagrams).

No longer called the “solar constant” since we now know that it varies with the occurrence of sun spot in an 11 year solar cycle. How called total solar irradiance.

About 29 percent of incoming sunlight is reflected back to space by bright particles in the atmosphere or bright ground surfaces, which leaves about 71 percent to be absorbed by the atmosphere (23 percent) and the land (48 percent).

Remember, always use physics for good, not evil!


Winter Biking – It’s OK, I’m a Physics Teacher.

The weather has been unseasonably warm this week. While the temperatures dip below freezing at night, they have been rising into the 40s during the day. While walking early in the morning yesterday, I noticed that the frost was disappearing about 9 am so I planned a bike ride for this morning about that time.

The temperature was a chilly 34 when I left but I knew it would warm up during the 2 hours I planned to be gone. I bundled up with hat and gloves, filled my water bottle, reset the trip meter, and took off. As I reached the fitness trail, which follows a series of parks along the flood plain of a large creek, a runner yelled “Watch out for the ice!” I replied “Thank you!”

Sure enough, the trail was frosty/icy in spots, especially in the shady spots where the sun had not warmed the ground. I was worried that it might be too treacherous. The biggest impediment to my fitness in the last couple of years has been injury. So I was worried about the risk of falling. But, I bolstered my courage and decided if anyone could do it, a physics teacher could. After all, the laws of physics rule everything. I did decide to document my effort with some photos. Here are the results.

I know that my bike and I have a calculable amount of inertia and at any given speed a fixed amount of linear and angular momentum. But this post is more about strategies than numbers.

When the trail is dry, the interaction between the tires and the pavement generates forces that can overcome the effects of air resistance, slow the bike down or speed it up, change the direction of travel, carry me up a hill. Since I have an old touring bike with its original thin rims and no special studded snow/ice tires, the nature of this force is almost entirely frictional.

The guy at the bike store showed me these studded tires and said they were really helpful on ice, but didn’t help in snow or mud. And, they don’t make them for my thin rims.


Although I did not measure the coefficient of starting (hopefully) and sliding (hopefully not) friction of bike tires on dry and icy asphalt, I found them in several tables to be about 0.75 for dry and 0.15 for icy surfaces. The exact numbers matter less than the fact that in icy conditions, there is substantially less frictional force to work with when trying to make the bike do what you want it it do.


Your best course of action when you hit a patch of ice is to stop peddling and try to keep your bike upright without attempting to change the speed or direction of the bike. If the icy patch is small and on a flat straight part of the trail, like the one shown above, you should sail right through.


If the icy patch is on a hill, like the one shown on this bridge, you have to get up enough speed ahead of time to coast up the hill. If the icy hill is too high, you may need to walk your bike up the hill off the trail in the grass.


If the ice is covering a flat curve, think circular motion formula F=mv²/r. Since your mass is fixed, the only variables you can control in the face of reduced centripetal force are your speed and the radius of the curve. Speed is easy, just slow down. Of course this requires that you pay attention and notice the icy patch before you actually find yourself upon it. Generally slowing your ride down on days such as these is a good idea in case any surprises pop up. Since only the hardier folks were out for walks, runs, and rides today, the trail was not very busy and I had the whole width to work with. So I chose a path through the curve with the largest possible radius. Fortunately, there was a sunny spot soon after the bridge where I could straight out and get back on my side of the trail.

There is a another consideration when it comes to curves. Not only do you risk sailing off tangent to the curve, like a car traveling too fast for conditions, but you also risk tipping over. The center of mass of you and the bike is carried above the points of contact with the trail creating an unstable equilibrium. Most riders, when traveling around a curve, lean inward. A frictional force directed sideways is needed to prevent the tires sliding out from under you. Try to stay as upright as possible. Again, slowing down.


You can see in this picture above that on this short patch of frost, all the riders who came before me chose a large radius path through the slippery spot and waited to correct their course until they reached the dry spot. I guess there were more physics teachers out on the trail than I thought.


On this part of the trail, I usually love to see how fast I can get going. It is a long downhill stretch with good visibility. There is an uphill stretch on the other side of the bridge and the added speed makes it easier to climb that hill. But look at the bridge! Bridges are notoriously icy even when the trail (or road) around them is not. So there was no way I was going to risk hitting that bridge at high speed. Of course that meant braking on the way down, wasting all the precious potential energy that I had worked so hard to attain.

As I sadly braked I was reminded of my hybrid car. It captures some of the energy during breaking and stores it in batteries to be used later. I thought perhaps I could add a battery to my bike….. No, that would just be lots of extra weight to carry around. Some generator/light combinations convert the energy to electricity and use it to power a headlight. It was daylight so I didn’t need a light, but quite cold. Maybe I will make a system that converts the energy to heat to keep my hand warm. Hmmmmm.

lexus cut

I love to see the arrow on my car’s display going toward the wheels from the battery, rather than the engine icon . Its even more fun when the arrow points toward the battery during braking.

Now, here’s a quiz. Look at these picture below and think about what you would do.


Since the right side of the trail seemed be dry I slowly rode to a point where I could turn and head across the bridge in a straight line.


This was a tough one. I didn’t want to brake on the icy hill coming off this bridge because there may not be enough friction to prevent sliding (the tangent of the angle of incline may be greater than mu). The bike would start to slide and then control would be lost. But letting the bike gain too much speed would make it difficult to negotiate those curves at the bottom. And you really need to go straight down the hill, not cutting diagonally across the bridge ramp, or you might slip out.  I considered getting off and walking here but that didn’t seem as though it would much better since I could not get off the asphalt surface. Fortunately, the sunny spots were not slippery so I was able to make some quick slight turns there.

When I was at the far end of the trail a walker again yelled out, “Watch out for the ice!”. I was ready this time and replied, “It’s OK, I’m a physics teacher!”





Oh, GoPro! Frame of Reference Issues.

GoProGoPro videos are an exciting way to capture motion events. Since I can’t help thinking about physics, I wondered if it would be possible to analyze the motion to determine speed and acceleration. I wanted to figure it out so that every time I did something fun and recorded it, I would be able to go back and see how fast I was going or how great my acceleration was.

I found that using these videos to analyze motion using LoggerPro creates some problems.

Traditionally, the videos we have used for analysis are recorded with a stationary camera and a moving object. The fixed background provides a reference frame through which an object moves. But with the GoPro, the camera seems stationary while the world flies past.

I took a GoPro video while riding my bike on a sunny day. In this way, I had a second measure for the bike speed. In the shadow, you can see the wheel going around. So I decided to compare the speed of the bike using data from the shadow and data from the video to see if using video analysis was reliable.

Screen Shot 2014-11-10 at 4.57.51 PM

Click Here To View the Video

Speed Calculation – Method 1 – Circumference and Time

The GoPro records 30 frames per second. If you watch the tire stem as it travels around, you discover that it takes 22 frames or 0.733 seconds to complete one rotation. During this time the bike travels forward one circumference.


The diameter of the bike wheel is 65 cm and circumference of 2.042 m.

Screen Shot 2014-11-10 at 4.13.51 PM

This yields a speed of 2.79 m/s using the circumference and time for one rotation.

Speed Calculation – Method 2 – Video Analysis

As with all video analysis, some object of known size is used to determine the scale. A meter-stick serves as a good measure as long as it is placed the same distance from the camera as the moving object. If it is not, errors arise. (See previous post). The camera and the reference meter-stick remain the same distance apart through out the video.

Screen Shot 2014-11-10 at 2.47.37 PM

The GoPro video is different. All objects in the field move relative to the camera. To overcome this aspect of the video, I chose to do the analysis within a small area directly in front of the camera. The GoPro has a fixed focus of 4 ft. In the bike video analyzed here, the area directly in front of the bike wheel was chosen. At the start of the video I found a feature of known length (85 cm) and was perpendicular to path of motion.

Screen Shot 2014-11-10 at 3.38.37 PM

I chose a spot in the road that was moving directly toward me (that I was moving directly toward?) and recorded its position in 8 frames. The data looks fairly straight on the graph, so the slope of the line should represent speed.

Screen Shot 2014-11-10 at 2.50.20 PM

This graph shows the slope of the line if all 8 points are included. The slope, and therefore the speed is 2.451 m/s. That result is a little disappointing. Recall that the speed from method 1 was 2.785 m/s.

After some consideration, I decided that part of the problem was that the farther away from the camera the spot in the road was, the less correct the reference distance was. If that were true, the more points included, the less correct the results would be.

Screen Shot 2014-11-10 at 3.01.25 PM

If I only included the last 4 points in the analysis, the speed was determined to be 2.698 m/s. That was somewhat better!

Screen Shot 2014-11-10 at 3.01.58 PM

If only the last 3 points are used the speed is determined to be 2.791 m/s.

So, the agreement between the two methods improves as fewer points are used, perhaps because the reference distance is more true for these later points (when the spot is the road was nearer to the bike).

I would not usually be in favor of ignoring some data points, but in this case there is a clear reason for doing so. This would be a good conversation to have with students, when would such a decision be legitimate?

I hope this helps you think about some of the issues associated with using video analysis with GoPro videos. This situation was very contrived. The road at least was always a fixed distance from the camera. I imagine that if you jumped off a cliff, nothing would remain constant and the analysis would be even more complex. It does, however, provide another opportunity to talk with students about frame of reference.

Always, your helpful comments are welcome.

Video Analysis – Tips for Making Good Movies

Video analysis provides a great way for students to understand all kinds of motion that is just too darn hard to measure any other way.

In an ecology class in 1975, my lab group and I ran around a flower field, following a bee, sticking a flag in the ground every time the bee landed, timing how long the bee stayed on the flower, shouting out numbers for the recorders to write down, and returning later to measure the positions of the flags. We used slide rules and the “sum of least squares” to see if there was any correlation between the time the bee spent on the flower (as an indicator of food quantity) and the angle and distance the bee flew to the next flower. We thought perhaps that a bee would try to stay in the area (sharper angle, short distance) when it had found a good food source. After a week of work we found the dreaded “no correlation”. Imagine how different that activity would look today. We would place a video camera over the flower field and clickity click click, collect some data. Open some graphing software and the analysis would be done in minutes.

Video is so easy to collect these days that students can record any kind of motion they want and apply newly learned physics rules to understand it. One of my students video-taped herself jumping a barrier on her horse. She discovered that she moved in such a way that she always kept herself over the center of mass of the horse. We had a great discussion about why this might be so.

Sometimes my students get bad results. I have learned a few tricks that increase the likelihood that they will get good data.

We used Vernier’s Logger Pro. It has a great tutorial. That is how I learned how to do video analysis and I use the tutorial to teach my students. Try it, you won’t be sorry.

In Logger Pro choose, File -> Open. Among the folders that contain the science experiments, you will find a folder called Tutorials.


Video Analysis

Select 12 Video Analysis.cmbl. Follow the instructions and don’t skip anything. And tell you students not to skip anything.

The cursor that is used to locate the objects in each video frame is cross-hairs. Students usually think it best to put the center of the cursor on the center of the object. But the cursor obscures the view of the object somewhat and the center of the object is a judgement call. I tell them instead to place the top of the cursor on the top of the object.

Place the top of the cursor on the top of the ball.

Place the top of the cursor on the top of the ball.

Students should enlarge the movie screen as much as possible when locating the object in each frame. Click the movie, grab a corner and stretch the movie. After the locations have been determined, the movie can be made smaller again.

Students need to use an some object in the video of known size to set the scale. In the sample basketball video, there is a two-meter stick on the floor. If the students themselves are in the video, their height can be used.

It is important to place the meterstick the same distance away for the camera as the action. In the sample video, notice that the meterstick and the ball are the same distance.

Some of  my students were having trouble with data, so I decided to see how much difference it would really make if the meterstick were too far or too close. In picture from the video shown here, you can see there are three metersticks. The center one is in the correct position, the others are too close or too far. My hidden associate, Ian, tosses a ball. Click on the link below the picture to watch the video.

Three metersticks placed at various distances from the camera.

Three metersticks placed at various distances from the camera.

Click Here to View the Video

Since we know the acceleration due to gravity is 9.80 m/s/s, we have a way to check our accuracy. The actual analysis screen shots are included at the end of the post. Here is a summary of the results of the analysis:


As you can see, the position of the reference meterstick makes quite a difference. It is an important consideration.

You might be wondering why the data from the correctly positioned meterstick didn’t give us a value for the vertical acceleration that was closer it -9.80 m/s/s. When I used the basketball video from the tutorial I got a value of -9.607 m/s/s. The results were better because the video was better.

The video I used was shot under low light levels. The camera collects light for a longer period of time for each frame when light levels are low and as a result, the image is blurred. This makes it difficult to get really accurate positions. The object in my video is small and hard to see. The basketball is much larger and easier. Sometimes we paint a white or black spot on the object to make it easier to see.

So, here is my list of things to do in order to get good video analysis results:

Screen Shot 2014-09-23 at 4.15.23 PM

I usually have my students arrange the video, data table, and graphs on the screen and take a screen shot. These files are uploaded to a Google folder that is shared with me. This is there way of “turning in their lab” without wasteful printing. If you want more information about how to do this, see the previous posts on video analysis and the NSTA STEM14 tab for information on using Google Drive.

As always, you helpful comments are welcome.

Here are the images of the data analysis in case you would like to see them. Click on the images to see them enlarged.

Acceleration with meterstick in correct position.

Acceleration with meterstick in correct position.

Acceleration with meterstick too far away.

Acceleration with meterstick too far away.

Acceleration with meterstick too close.

Acceleration with meterstick too close.

Horizontal Velocity with meterstick placed correctly.

Horizontal Velocity with meterstick placed correctly.

Horizontal Velocity with meterstick too far.

Horizontal Velocity with meterstick too far.

Horizontal Velocity with meterstick to close.

Horizontal Velocity with meterstick to close.

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