# Acceleration on a hill (both up and down)

1. May 1, 2009

1. The problem statement, all variables and given/known data
A sports car is accelerating up a hill that rises 16.0° above the horizontal. The coefficient of static friction between the wheels and the road is µs = 0.87. It is the static frictional force that propels the car forward.
(a) What is the magnitude of the maximum acceleration that the car can have?
(b) What is the magnitude of the maximum acceleration if the car is being driven down the hill?

2. Relevant equations
FN=ma=mgcos$$\theta$$
fs=FN$$\mu$$s

3. The attempt at a solution

Attached is the pic I've been using to figure this out. I'm somewhat lost at how to proceed though.

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2. May 1, 2009

### Staff: Mentor

Find the net force acting on the car. Apply Newton's 2nd law.

3. May 1, 2009

I've been trying to do that. I know I'm trying to find acceleration, thus the equations I'm working with should be the ones I gave. However, I need the mass for both of those and I'm not given it (at least that's where my line of thought is).

4. May 1, 2009

### Staff: Mentor

Maybe you do, maybe you don't. Just call the mass "m" and keep going.

Hint: Solve for the acceleration symbolically before plugging in any numbers.

5. May 1, 2009

The way I've figured it, it'd be:

9.8cos16/8.7=a=10.82 m/s2

I put the answer in the system and it doesn't work out. Where am I going wrong?

6. May 1, 2009

### Staff: Mentor

Do it step by step. What's the force acting up the hill? Down the hill? What's the net force?