# Calculating the coefficient of friction of a car going down a ramp

1. Sep 21, 2008

### rhufeo

I designed this lab for my physics class where we roll a hot wheels car down a length of wood that measured 1 m long. we did this process three times at varying angles and we want to investigate how changing the angle affects the coefficient of friction. The problem is, the times that we recorded end up giving us negative coefficients of friction! Whats our problem?!

For example. we recorded that at 20 degrees, the car took 0.75 seconds to travel the 1 m of wood. Using the calculations we get this:

1 m = 1/2(acceleration)(0.75 seconds)^2
a = 3.56 m/s^2

coefficient of friction = (((9.8 m/s^2)(sin20))-3.56 m/s^2) / ((9.8)(cos 20))
coefficient of friction = -0.0226

2. Sep 21, 2008

### cepheid

Staff Emeritus
Well, we have a problem here. The predicted acceleration in the absence of friction is indeed 9.8sin20 = 3.35 m/s^2, which is LESS than the empirically obtained acceleration which occurred in the presence of friction.

3. Sep 21, 2008

### rhufeo

So how should i fix this? The lab is supposed to investigate the properties of friction.

4. Sep 21, 2008

### cepheid

Staff Emeritus
I could be way off here, because it's been a while since I looked at "rolling without slipping", but that's probably what's occurring here (look it up). So, maybe you really need to re-evaluate your experiment. Is friction even opposing the motion of the cars? I would say no, because two surfaces are NOT sliding relative to each other. On the contrary, there is enough friction to prevent any sliding between the wheels and the ramp (hence "without slipping" -- the wheels maintain traction). Instead, at every instant, the wheel "pivots" around the point on its circumference that can be can be considered to be in contact with the ramp, and that propels it forward. So there is in fact a forward pointing friction force in this situation. I hope somebody else who has a better handle on rolling without slipping can comment and explain the situation more clearly. If what I'm thinking is true, then using rolling cars is not a good choice for an experiment that's designed to use sliding objects on a ramp to calculate coefficients of friction.

5. Sep 22, 2008

### atyy

Which angle are you specifying- relative to the horizontal or the vertical?

6. Sep 23, 2008

### schroder

For rolling objects downhill, the acceleration works out to be ~ g times tan theta (for small angles). For an angle of 20 degres that will be 9.8 x .36397 = 3.56 which is exactly what you recorded. As cepheid has already pointed out, the setup you are using is not very useful for measuring coefficients of kinetic friction. What you might do is change the name of your project, and demonstrate rolling acceleration, or you might consider using some sort of ski-like object to slide down the incline.