A 80 kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 25 degree hill. The skier is pulled a distance x = 230m along the incline and it takes 2.3 min to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is mu_k = 0.15, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?

Answer 1

Since the skier is pulled at a constant speed, the pulling force (for one skier)is given by:

F = m*g[sin theta + mu_k*cos theta]
= 80*10[sin25+0.15*cos25]
= 446.8N (along the incline upwards)

Work done by F in moving distance of 230m:
W=F*x = 446.8*230 =102,776 Joules
Power reqd for this work:
P= W/time = 102,776J/138s = 745 watts = 1HP(approx.)
So for 30 skiers, engine power required = 30HP