I ONLY NEED HELP WITH PART B BUT THE ANSWER AND QUESTION FOR PART A ARE NEEDED F

Question

I ONLY NEED HELP WITH PART B BUT THE ANSWER AND QUESTION FOR PART A ARE NEEDED FOR PART B SO IT IS INCLUDED.

We wrap a light, flexible cable around a thin-walled, hollow cylinder with mass M and radius R. The cylinder is attached to the axle by spokes of a negligible moment of inertia.The cylinder rotates with negligible friction about a stationary horizontal axis. We tie the free end of the cable to a block of mass m and release the object with no initial velocity at a distance h above the floor. As the block falls, the cable unwinds without stretching or slipping, turning the cylinder.

A)

Find the speed of the hanging mass m just as it strikes the floor.

ANSWER:

v = sqrt(2mgh/M+m)

B)Use energy concepts to explain why the answer to part A is different from the speed found in case of solid cylinder,which is v=sqrt(2gh/(1+M/2m))

v = sqrt(2mgh/M+m)

B)Use energy concepts to explain why the answer to part A is different from the speed found in case of solid cylinder,which is v=sqrt(2gh/(1+M/2m))

Explanation / Answer

1)

for hollow cylinder:

mgh = 1/2*m*V^2+ 1/2*M*V^2,

1/2*m*V^2 being the kinetic energy of m

1/2*M*V^2 being the kinetic energy of M.

V being the same for both m and M since they're attached to each other.

this shall give us the v=sqrt 2mgh/(m+M)

2)

for solid one, i think it's necessary to apply integral along the radius R to get the kinetic energy for the body

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