(8) Is there still an advantage to using a hill instead of lifting the box vertically?
The man is still exerting less force than if he were to lift the box vertically, but he exerts more force than he would if the hill were frictionless. Some of his work is spent in overcoming friction. The loss of energy to friction decreases the efficiency of the system.
(9) How much energy is lost to friction?
The conservation of energy states that change in an energy must equal the work done by the non-conservative forces. The only non-conservative force in this problem is friction. Friction, acting over a distance of 10m, has a magnitude of
The work done by friction, and thus the energy lost to friction, is therefore given by
