2011 F = ma Contest Question # 25

[clesling]

Homework Statement

A hollow cylinder with a very thin wall (like a toilet paper tube) and a block are placed at rest at the top of a plane with inclination  above the horizontal. The cylinder rolls down the plane without slipping and the block slides down the plane; it is found that both objects reach the bottom of the plane simultaneously. What is the coefficient of kinetic friction between the block and the plane?

Homework Equations

K = (1/2)MV^2 + (1/2)IW^2 for I = MR^2 and W = V/R

The Attempt at a Solution

Answer is: (1/2)tan(theta)
I have tried many different approaches: F = ma as well as assuming the same mass and/or velocity at the end of the ramp, but have had no success. Thanks for your time and consideration!

 

[Doc Al]

Start by finding the acceleration of the rolling cylinder.

 

[clesling]

Hey, thanks for the response! That really helped and I was able to figure this one out finally.