A skier of mass 110 kg travels down a frictionless ski trial. a.) If the top of the trail is a height 200m above the bottom, what is the work done by gravity on the skier? b.) Find the velocity of the skier when he reaches the bottom of the ski trail. Assume he starts form rest.

Question

A skier of mass 110 kg travels down a frictionless ski trial. a.) If the top of the trail is a height 200m above the bottom, what is the work done by gravity on the skier? b.) Find the velocity of the skier when he reaches the bottom of the ski trail. Assume he starts form rest.
c.) Suppose the ski trail is NOT frictionless. Find the work done by gravity on the skier in this case.
   I solved part a.) as W=Force times displacement, W=(9.8)(200)=1960 Joules
Part b.) I solved as V= sqrt(2gh), so  sqrt((2)(9.8)(200)),V=62.6 m/s.
I am confused as to part c, becasue I can't figure out what the difference is between work done by gravity on friction vs.  nonfriction. ?

Damon · Accepted Answer

a) m g h = 110 * 9.81 * 200 Joules
(you left the mass out)

b) m g h = (1/2) m v^2

c) The work done by gravity is the same, force of gravity times distance down.
The work done by friction makes the kinetic energy (speed) less at the bottom. It does not change the change in potential from top to bottom.