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.
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.
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.
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.
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!