Rolling Without Slipping Down a Slope

AI Thread Summary
A hollow spherical shell with a mass of 1.85 kg rolls down a slope at an angle of 32.0 degrees, prompting a discussion on how to calculate its acceleration, friction force, and coefficient of friction. The initial approach involves using a free body diagram and Newton's Second Law, but the lack of specific measurements for the ramp's height and the shell's radius complicates the calculations. Participants suggest introducing variables for unknowns, as they often cancel out in the equations. While it's acknowledged that the coefficient of friction cannot be determined with the given information, a lower bound can be established. The conversation emphasizes the importance of understanding the relationship between torque, friction, and rolling motion.
ZachChaos
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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


atan= rα
τ=rFsinΘ
I=matan

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 Fs-mgsinΘ=max. 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.
 
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ZachChaos said:
the shape is a hollow sphere, the moment of impulse is I=mr2
Check that.
ZachChaos said:
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.
 
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