posted by monic .
A skier of mass 74 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him 90 m up a 30° slope (assumed frictionless) at a constant speed of 3.0 m/s?
(b) What power (expressed in hp) must a motor have to perform this task?
(a) The speed does not matter, since the kinetic energy does not change.
Multiply the weight M*g = 725 N by the vertical rise 90 sin30 = 45 m. You should get 32,630 Joules.
(b) Power = (Work done)/(Time required)
The time required is (90 m)/(3 m/s) = 30 s.
Power = 32,630/30 = 1088 Watts
= 1.45 hp