# Friction question

1. Dec 2, 2003

### Chapin

A Corvette can brake to a stop from 60 mi/hr (26.82 m/s) in 123 ft (37.49 m) on a flat surface. What is his stopping distance on a roadway sloping downward 10 degrees?

--This question is in our Forces of Friction section, and we can find the acceleration and the coefficient of friction. What equations do we use to get the stopping distance on the 10 deg slope?

2. Dec 2, 2003

### Staff: Mentor

First find the coefficient of friction using the data for a flat surface. Then, for the sloping case, consider all the forces acting on the car when the brakes are applied. Find the net force, and thus the acceleration. Then you can calculate the new stopping distance.

3. Dec 2, 2003

### Chapin

OK, I have the deceleration to be -9.59 m/s^2 and the coeffiecent of friction to be .978 on the flat surface.

I am having a problem finding the net force on the slope because mass is not given.

I guess I need to derive an equation to do this but it is kicking my butt.

Does this look right?
$$\sum F_x=mgsin(10)-.978\\\sum F_y=mgcos(10)$$

Last edited: Dec 2, 2003
4. Dec 2, 2003

### Staff: Mentor

Just call it "m" for now; it will drop out.
Partly. There are two forces acting on the car along the plane:
- the weight, which is mgsin&theta; (acting down)
- the friction, which is &mu;N (acting up; where N is the normal force)
The normal force, N, equals mgcos&theta; so, Ffriction = &mu; mgcos&theta;.

Thus, Fnet= mgsin&theta; - &mu; mgcos&theta; = ma

Solve for a.

5. Dec 2, 2003

### Chapin

Thank you

Thank you, thank you and thank you.