# Find friction from stopping distance and initial speed.

1. Feb 27, 2013

### Sneakatone

According to test performed by the manufactures, an automobile with an initial speed of 75 km/h has a stopping distance of 25 m on a level road. assuming that no skidding occurs during breaking, what is the value of μ , between the wheels and the road required to achieve the stopping distance?

I dont know how to apporach this

2. Feb 27, 2013

### voko

Assume that the force of friction is constant and depends only on the weight. What is the equation for this force?

Then, what is the acceleration due to this force?

3. Feb 27, 2013

### Sneakatone

Mg=F?

4. Feb 27, 2013

### voko

Have you heard about the coefficient of friction? What is μ in the problem?

5. Feb 27, 2013

### Sneakatone

Do you mean F=-kx?

6. Feb 27, 2013

### voko

That is not the force of friction.

7. Feb 27, 2013

### lep11

Just use the work-energy theorem.

8. Feb 27, 2013

### Sneakatone

you mean KE=1/2mv^2?
but im not given a mass only velocity n stopping distance

9. Feb 27, 2013

### voko

Just assume the mass is some m. It will, as usual, drop out eventually.

What you really need to do is recall what the force of friction is.

10. Feb 27, 2013

### Sneakatone

force of friction is unknown

11. Feb 27, 2013

### rcgldr

As Voko implied, assume that the acceleration is constant (and negative since it slows down the car). What is the equation for constant acceleration?

12. Feb 27, 2013

### voko

It is unknown. But you have to assume it is known and it related to the weight. Recall how the force of friction depends on the weight.

13. Feb 27, 2013

### Sneakatone

F=ma

14. Feb 27, 2013

### rcgldr

For this problem, F, m, and a are constant. What is the equation for distance with constant acceleration and some initial velocity?

15. Feb 27, 2013

### voko

You are guessing, and this is not good. It looks like you need to review the force of friction.

16. Feb 27, 2013

### Sneakatone

17. Feb 27, 2013

### rcgldr

This equation should have been given to you in your class or textbook. It relates distance to initial velocity and constant acceleration, using x to represent the final position, and x0 to represent the initial position. (The total distance traveled = x - x0). You can assume that x0 is zero for this problem.

x = x0 + v0 t + 1/2 a t2

18. Feb 27, 2013

### voko

What you have here is the force of rolling friction (no skidding occurs). It is also known as rolling resistance. The force is $F_r = \mu N$, where $\mu$ is the coefficient of friction that you are supposed to find, and $N$ is the normal force.

19. Feb 27, 2013

### Sneakatone

I thought about that equation but what should be the inputs for acceleration and time.
im guessing to get time you can do d/v=t

20. Feb 27, 2013

### rcgldr

Those aren't inputs. You're given distance and the initial velocity, and the fact that the final velocity is zero. You'll need to solve for acceleration and time. You need a second equation for velocity versus time, where you know that the final velocity v is zero and v0 is the initial velocity (75 km/h):

v = v0 + a t

for distance (which you are told is 25 m):

d = v0 t + 1/2 a t2

These equations should have been given to you in your class or textbook.

Last edited: Feb 27, 2013