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## Homework Statement

A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 49.0 N and a radius of 0.27 m. The cylinder is attached by spokes of a negligible moment of inertia to a fixed horizontal axle coincident with the axis of the cylinder; the cylinder is free to rotate without friction about this axle. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 4.95 m, at which point the end of the rope is moving at 6.25 m/s; the rope does not slip on the cylinder.

A)What is the change in kinetic energy of the hollow cylinder as a result of the rope having been pulled?

B) For the situation as described in the introduction, what is the value of P?

## Homework Equations

v=rw

k = 1/2mv

^{2}+ 1/2Iw

^{2}

w = omega

k

_{i}+ u

_{i}+ Work = k

_{f}+ u

_{f}

## The Attempt at a Solution

i didnt know how to do part a so i just skipped to part B)

W = FD ----> W = P(4.95m)

W = k

_{f}

P(4.95m) = 1/2(5kg)(6.25

^{2}) + 1/2(1/2(5kg)(.27m)

^{2}(6.25/.27)

^{2})

P = 29.59 N

This is wrong though and i am not sure why. Also if i could get some help on part A that would be great.

Thank you :)