One-fourth of length L is hanging down over the edge of a frictionless, table. The rope has an uniform, linear density (mass per unit length), lambda, and the end already on the table is held by a person. a) How much work does the person do when she pulls on the rope to raise the rope and from this the work done. Note that this force is variable because at different times, different amounts of rope are hanging over the edge. b) Suppose the segment of the rope initially hanging over the edge of the table has all of its mass concentrated at its center of mass. Find the work necessary to raise this to table height. You probably find this approach simpler than that of part a). How do the answers compare and why is this so?

Question

One-fourth of length L is hanging down over the edge of a frictionless, table.  The rope has an uniform, linear density (mass per unit length), lambda, and the end already on the table is held by a person. a) How much work does the person do when she pulls on the rope to raise the rope and from this the work done.  Note that this force is variable because at different times, different amounts of rope are hanging over the edge.  b)  Suppose the segment of the rope initially hanging over the edge of the table has all of its mass concentrated at its center of mass.  Find the work necessary to raise this to table height.  You probably find this approach simpler than that of part a).  How do the answers compare and why is this so?

Leshawn · Answer

I am not certain how to approach this. Sure a) asks for Work = F*x, so I take the integral of F*x with F= T-mg? b) Takes center of mass, but how do you get the center of mass of something that is constantly changing its position?

nick · Answer

idk help