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 13° 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 570 J of work on the skier as the skier moves a distance of 6.8 m up the incline. (a) If the rope moved with a constant speed of 2.2 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 6.8 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) 2.2 m/s?

Explanation / Answer

a) the work done at a speed of 2.2 m/s is also 570 J

if the force is equal, the work is equal, regardless of what the velocity is.

b) it needs 6.18 s to move the skier up the 6.8 m. The rate of the work done is 570J/6.18 s = 92.23 W

c) it needs 3.09 s to move the skier the 6.8 m. Rate of work = 570/3.09 = 184.5 W

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