Finding force P to pull rope wrapped around rotating hollow cylinder

[totalmajor]

Homework Statement

A light, flexible rope is wrapped several times around a hollow cylinder with a weight of 55.0 N and a radius of 0.25 m, that rotates without friction about a fixed horizontal axis. The cylinder is attached to the axle by spokes of a negligible moment of inertia. The cylinder is initially at rest. The free end of the rope is pulled with a constant force P for a distance of 3.00 m, at which point the end of the rope is moving at 4.00 m/s. If the rope does not slip on the cylinder, what is the value of P?

Homework Equations

v=$$\omega$$r
$$\alpha$$=$$\tau$$/I
I=MR^2

The Attempt at a Solution

Alright, I honestly don't know where to start with this problem. It's review we're doing and I know the basics of inertia but nothing past that!

Can anybody help me start?

Thanks a lot,
Peter

 

[andrevdh]

work done by P on the cylinder = change in kinetic energy of the cylinder