Problem 32. The ski slopes at Bluebird Mountain make use of towropes to transpor

Question

Problem 32. The ski slopes at Bluebird Mountain make use of towropes to transport snowboarders and skiers to the summit of the hill. One of the towropes is powered by a 22-kW motor which pulls skiers along an icy incline of 140 at a constant speed. Suppose that 18 skiers with an average mass of 48 kg hold onto the rope and suppose that the motor operates at full power a. Determine the cumulative weight of all these skiers. b. Determine the force required to pull this amount of weight up a 14 incline at a constant speed. c Determine the speed at which the skiers will ascend the hill

Explanation / Answer

Given,

P = 22 kW ; theta = 14 deg ; N = 18 ; m = 48 kg ;

a)The cumulative weight will be:

W = N m g

W = 18 x 48 x 9.81 = 8.5 x 10^3 N

Hence, W = 8.5 x 10^3 N

b)force required will be:

F = W sin(theta)

F = 8.5 x 10^3 x sin14 = 2 x 10^3 N

Hence, F = 2 x 10^3 N

c)We know that

Power = F x v

v = P/F = 22 x 10^3 W/2 x 10^3 N = 11 m/s

Hence, v = 11 m/s

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