Rotation Problem/Total Kinetic Energy

[mburt3]

Homework Statement

A spool of mass 8.67kg and radius 4.58m is unwound by a constant force 48.1N pulling on the massless rope wrapped around it. Assume the moment of inertia of the spool about O is 3/4mr^2 and it rolls w/o slipping. When the center of the spool has moved a distance d, find the total kinetic energy (In terms of F and d).

Homework Equations

Work= ke(final)- ke(initial)
I=3/4mr^2
torque=Fr=I(alpha)

The Attempt at a Solution

I'm feeling pretty lost, but I was thinking that if I just added the rotational energy + translational kinetic energy that that would give me the answer. Obviously it is not this easy and I have no idea how to put it in terms of force and distance.
T

 

[bsodmike]

The most I can get is as follows, the angular velocity, as the force of the massless string is exerted on the circumference of the spool,

F=ma=\dfrac{48.1\;N}{8.67\;kg}=a=5.55\;ms^{-2}

From the definition, \tau=I\cdot\alpha,
\tau=\dfrac{3}{4}mr^{2}\times5.55=757\;Nm = Fr

Also note that from the definition of Nm, 757 Nm = 757 Joules.

Kinetic energy is,
F\cdot d=\dfrac{1}{2}mv^2

The circumference of the wheel is 2\pi r, this needs to be factored into Fr to relate the rotation angle to the ultimate displacement of the center, O?

Hope you can make some progress from this...