Acceleration on a hill (both up and down)

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SUMMARY

The discussion focuses on calculating the maximum acceleration of a sports car on a 16.0° incline, considering static friction with a coefficient of µs = 0.87. The key equations used are FN = ma = mgcosθ and fs = FNµs. The maximum acceleration when driving up the hill is derived symbolically as a = 9.8cos(16°)/0.87, resulting in approximately 10.82 m/s². The discussion emphasizes the importance of identifying net forces acting on the car to solve for acceleration accurately.

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Homework Statement


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?

Homework Equations


FN=ma=mgcos\theta
fs=FN\mus


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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Find the net force acting on the car. Apply Newton's 2nd law.
 
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).
 
BATBLady said:
However, I need the mass for both of those...
Maybe you do, maybe you don't. :wink: Just call the mass "m" and keep going.

Hint: Solve for the acceleration symbolically before plugging in any numbers.
 
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?
 
Do it step by step. What's the force acting up the hill? Down the hill? What's the net force?
 

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