Consider a uniform rope of length l and mass m. one fourth of the rope hangs over the edge of a frictionless table. a force is applied to the end on the table to hold the rope in place. now, the force slowly pulls the rope so that its hanging end rises onto the tabletop. a) find the force necessary to do this as the rope rises to the table. then find the work done by the force. b) instead, consider the mass of the hanging portion to be concentrated at its center of mass, and calculate the work necessary to raise the quarter rope to the tabletop. c) compare the results.

Asteel tube (k=50 w/mk) of inner and outer diameter di = 20mm and do=26mm, respectively, is used to transfer heat from hot gases flowing over the tube (h-hot = 200w/m2k) to cold water flowing through the tube (h-cold = 8000 w/m2k). what is the cold-side overall heat transfer coefficient uc? to enhance heat transfer 16 straight fins of rectangular profile are installed longitudinally along the outer surface of the tube. the fins are equally spaced around the circumference of the tube, each having a thickness of 2mm and a length of 15mm. what is the corresponding overall heat transfer coefficient uc? *solve for uc in both cases*