Acceleration on a hill (both up and down)

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The discussion revolves around calculating the maximum acceleration of a sports car on a 16° hill, considering static friction with a coefficient of 0.87. To find the maximum acceleration while going uphill, the net force must be determined using Newton's second law, factoring in gravitational force and friction. The user is advised to treat mass as a variable "m" to simplify calculations and derive symbolic expressions for acceleration. There is confusion regarding the application of the equations, particularly in calculating the net forces acting on the car in both uphill and downhill scenarios. The conversation emphasizes the importance of breaking down the problem step by step to identify where the calculations may be going wrong.
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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?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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