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 14° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.1 m/s. The force of the rope does 990 J of work on the skier as the skier moves a distance of 5.5 m up the incline. (a) If the rope moved with a constant speed of 2.7 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 5.5 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) 1.1 m/s and (c) 2.7 m/s?

Explanation / Answer

a) work done in pulling a skier by same distance = work done as before ( since force and displacement are same)

= 990 J.

b)the rate of work done = work done*speed / distance = 990*1.1/5.5 = 198 W

c)the rate of work done = work done*speed / distance = 990*2.7/5.5 = 486 W

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