Physically Incorrect

Level of Difficulty: Undergraduate

Okay, enough of these party problems. It’s back to physics!

A rope of uniform mass (say, x kg/meter) lies coiled on a smooth surface. You start pulling it up at a constant speed v (say, with your hand). What force will you have to apply? Hint: the force is a function of the length of rope that’s already up in the air. You may assume there is so much rope it never stops comin’!

Having answered that, calculate the work you put in, and compare that to the change in mechanical energy of the rope. Is there a discrepancy? If there is, can you explain it?

ADDED 28/June/2009: A detailed solution has been added here.