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?
k = 1/2mv2 + 1/2Iw2
w = omega
ki + ui + Work = kf + uf
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 = kf
P(4.95m) = 1/2(5kg)(6.252) + 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 :)