AP Physics (rotational motion question)

Question

The drum shown in the figure has a radius of .4 meters and a moment of inertia of 2.3 kgm^2 about an axis perpendicular to it through its center. The frictional torque at the drum axle is 3 Nm. A 14 m length of rope is wound around the rim. The drum is initially at rest. A constant force is applied to the free end of the rope until the rope is completely unwound and slips off. At that instant, the angular speed of the drum si 23 rad/s. The drum then slows down at a constant rate and comes to a halt. In this situation what was the magnitude of the constant force applied to the rope.

 

(I dont know how to attach the picture, but the picture shows a God's eye view of a circular/cylindrical object with a tangential force vector from the top pointing eastwards, labeled constant force)

Answer 1

Hey, 

      A quick answer: you can calculate the kinetic energy of the drum after the rope is unwound 1/2Iω², both I and ω are given. 

 

      That energy comes from the work done by the torque x no of radians needed to unroll the 14 m of rope and the torque is equal to .4*F where F is the force you are looking for. 

 

Hope this helps let me know if you need more details. I didn't have much time so I just talked through the answer.

Jim