# Homework Help: Co-efficient of friction HELP

1. Aug 11, 2011

### COBRA1185

Co-efficient of friction HELP!!

1. The problem statement, all variables and given/known data

Hello Im new to physics forums, im looking for some help with my Year 11 Extended Experimental investigation. My investigation is looking at how different surfaces and different ramp heights (inclined planes) affect the stopping distance of a toy car. Im having difficulty finding out what the coefficient of friction is for the different surfaces are. Please Help.
Note: The ramp is sheet metal and rolls down onto different surfaces eg. carpet, concrete etc..

2. Relevant equations

3. The attempt at a solution

2. Aug 11, 2011

### PeterO

Re: Co-efficient of friction HELP!!

Is this car rolling? If it is, I suspect the only friction you have is the friction in the "bearings"
of the wheels - so will be indepenent of the surface - unless you had a surface "soft" enough for the wheels to sink in.

3. Aug 11, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Yes it is rolling, it is just a toy car. What im really trying to determine is the coefficient of friction on the different surfaces which the car is rolling off the ramp onto.

4. Aug 11, 2011

### PeterO

Re: Co-efficient of friction HELP!!

Good Luck!

5. Aug 11, 2011

### Harrisonized

Re: Co-efficient of friction HELP!!

If you're doing this experimentally on a level surface (not an inclined plane), determining the coefficient of rolling friction is exactly the same as determining any coefficient of friction. (Friction coefficients are approximations anyway.)

The three numbers you need are:
1. the velocity at which the car begins free motion
2. the time that it takes the car to stop
3. the distance of travel (only after release)

From these three numbers, you should be able to deduce the friction coefficient.

vf = 0 = vi - at
F = μ ma
W = F d
E = 1/2 mvi2
W = E

From the above:
1/2 mvi2 = F d
1/2 mvi2 = (μ ma) * d
a = vi /t

Therefore:
μ = 1/2 vi t / d
(for level surfaces)

Try to take measurements using faster initial velocities, since this will make time and distance measurements more accurate.

Also, make sure you understand how to find the velocity of the car after it leaves the inclined plane and onto the surface that you're testing. Make sure that you use a ramp that provides as much friction as possible, so the car's wheels roll without slipping. Then you can find the final velocity of the car at the bottom of the ramp via the time that it takes the car to roll down the ramp.

For the ramp:

vf = vi + at, where vi = 0
a = g sin θ, where θ is the angle that the ramp makes with the level surface

Therefore:
vf = g sin θ t

Instead of timing the car moving down the ramp, however, it's much more accurate instead to measure the distance the car travels down the ramp.

d = 1/2 at2
d = 1/2 g sin θ * t2
2d / (g sin θ) = t2
t = √ (2d / (g sin θ))

Therefore:
vf = g sin θ √ (2d / (g sin θ))
vf = √ (2d g sin θ)

Notice that this vf is equal to the vi of the level surface mentioned above.

By the way, you should mention as an experimental error that the bottom of the ramp will cause deviation from experimental results. The car will lose momentum from the impact of of the front wheel with the level surface, and the car's angle will continuously change from the time the front wheels hit the level surface to the time that the car is totally off the ramp.

Last edited: Aug 11, 2011
6. Aug 11, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Thanks everyone for the responses, removed some stress from my life.
Harrisonized could you please tell me what vi, vf and W stand for.. Thanks in advance

7. Aug 11, 2011

### Harrisonized

Re: Co-efficient of friction HELP!!

vi = initial velocity
vf = final velocity
W = work

... doh.

Last edited: Aug 11, 2011
8. Aug 11, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Thanks thought that was it, just wanted to clarify

9. Aug 11, 2011

### Darth Frodo

Re: Co-efficient of friction HELP!!

The Coefficient of friction is Tan A where A is the angle at which the car just begins to roll.

Last edited by a moderator: Sep 25, 2014
10. Aug 11, 2011

### Harrisonized

Re: Co-efficient of friction HELP!!

It's actually very difficult to obtain accurate measurements of the coefficient of rolling friction using the angle of inclination, because the angle required is hilariously small.

11. Aug 14, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

If the incline increases should the time of the toy car going over a surface increase or decrease?

12. Aug 14, 2011

### PeterO

Re: Co-efficient of friction HELP!!

You could expect it to increase. However, if you had a sharp angle between the ramp and the floor, the nose of the car might dig in and then it is difficult to work out what will happen. The steeper the slope [is sharper the change in surface angle], the more like it is that the nose digs in.

13. Aug 14, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Thanks for the quick reply, but if the speed the car is going at on the level surface is very fast shouldnt it take a smaller time to stop regardless of the distance travelled?

14. Aug 14, 2011

### PeterO

Re: Co-efficient of friction HELP!!

Suppose the car reached the level surface at 2 m/s. It would take a certain time to stop.

Suppose the car reached the level surface at 3 m/s. It would take a bit of time to slow to 2 m/s, then presumably just as long, as the example above, to stop from the "new" 2 m/s. That means the time would be longer to stop from the higher speed.

What do you think?

15. Aug 14, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Yes that is what I thought as well but when I tried to find out the time using:

t= distance travelled/ average velocity
it gave me a lesser time when the average velocity and distance travelled was bigger

16. Aug 14, 2011

### PeterO

Re: Co-efficient of friction HELP!!

So you say - but you are only saying. Let's see some data and calculations.

17. Aug 14, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

Ok

if the toy car was travelling at 1.31m/s and took 50.28cm to come to a complete stop then
s=(u+v)xt/2
0.5028=0.655 x t
t= 0.77 seconds

then if the same car was travelling at 1.83m/s and took 56.52cm to stop
then
0.5652= 1.83/2 x t
t= 0.617

see what i mean isnt it supposed to be longer, i agree with what you are saying, but why am i getting this????

18. Aug 14, 2011

### PeterO

Re: Co-efficient of friction HELP!!

These calculations are assuming constant acceleration - presumably it isn't.

Constant acceleration would result if there was a constant friction force - which would mean a constant co-efficient of friction. That is a problem for you.

How did you know the car was travelling at those speeds? I hope you were not just assuming a perfect transformation of energy as the car went down the hill.

19. Aug 14, 2011

### fleem

Re: Co-efficient of friction HELP!!

Hope this isn't too pedantic but just so its clear to the OP: Technically these values are not the "coefficient of friction for a given surface" as stated in the first post. They are the "coefficient of friction between that particular car rolling on a given surface". A wood block without wheels would, of course, exhibit far different coefficients of friction on those same surfaces.

20. Aug 14, 2011

### COBRA1185

Re: Co-efficient of friction HELP!!

We are trying to determine how different surfaces affect the stopping distance of toy cars.
Therefore we will be assuming that they all should hit at the same time and at the same velocity, if so the formulas state that it should stop quicker, do you agree? but in real life it doesnt due to friction etc...

Any ideas ?