Question

A 73- kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23 ∘ hill. The skier is pulled a distance x = 280 m along the incline and it takes 2.0 min to reach the top of the hill. Part A If the coefficient of kinetic friction between the snow and skis is μ k = 0.10, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?

Answer 1

Total mass of 30 skiers,

m = 73*30 = 2190 kg

Normal force on skiers,

N = mgcos

Friction force, f = u_kN = u_k mgcos (parallel to lincline)

Force of gravity on skiers, Fg = mgsin (parallel to incline)

Let, pulling force on skiers = F

Net force along horizontal = 0

F - Fg - f = 0

F - mgsin - u_k mgcos = 0

F = mg (sin + u_kcos)

Work done by engine,

W = F*x

W = mg (sin + u_kcos) * x

W = 2190*9.8 (sin23 + 0.10*cos23) * 280

W = 2.90*10^6 J

Power of engine,

P = W / t

P =  2.90*10^6 / 2*60

P = 24176.73 W

P = 24176.73 / 746 hp

P = 32.4 hp