A skier is pulled by a tow rope up a frictionless ski slope that makes an angle

Question

A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 16° with the horizontal. The rope moves parallel to the slope with a constant speed of 0.79 m/s. The force of the rope does 830 J of work on the skier as the skier moves a distance of 3.2 m up the incline. (a) If the rope moved with a constant speed of 2.4 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 3.2 m up the incline? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.79 m/s and (c) 2.4 m/s?

Explanation / Answer

a) In both cases skier is moving with constant speed. So there is no change in kinetic energy of skier as he moves up. By work energy theorem, work done on skier in both cases is zero.
There are two force acting on skier.
Force of gravity and force of rope.

Work done by gravity depends upon initial and final position or increase in height of Skier. That is same in both cases. Hence work done by rope must be same in both cases. Hence work done by rope is 830 j, as skier moves distance of 3.2 m.

b) Rate of work done by rope = work done / time taken
time = distance / speed
rate of work done = work done * speed / distance
= 830*0.79/3.2 = 204.9 W at speed of 0.79 m/s
= 830*2.4/3.2 = 622.5 W

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