Rolling Without Slipping Down a Slope

[ZachChaos]

Homework Statement

A hollow, spherical shell with mass 1.85kg rolls without slipping down a slope angled at 32.0∘. Find the acceleration, friction force, and coefficient of friction.

Homework Equations

a_tan= rα
τ=rFsinΘ
I=ma_tan

The Attempt at a Solution

I'm not quite sure where to begin. I started by making a FBD and using Newton's Second Law to determine F_s-mgsinΘ=ma_x. Since the shape is a hollow sphere, the moment of impulse is I=mr². I know the frictional force is causing the torque. Without the height of the ramp or the radius of the shell, I'm not quite sure how the proceed, but once I can solve for the acceleration, I should be able to solve for the frictional force and coefficient of friction quickly. This seems like a simple problem, but I'm at a loss with regards to how to approach it.

 

[haruspex]

the shape is a hollow sphere, the moment of impulse is I=mr2

Check that.

Without the height of the ramp or the radius of the shell, I'm not quite sure how the proceed

Never be afraid to throw in symbols for such unknowns. Generally you will find they cancel out later.

There's not enough information to find the coefficient of friction, but you can find a lower bound for it.