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 5.1° with the horizontal. The rope moves parallel to the slope with a constant speed of 0.99 m/s. The force of the rope does 810 J of work on the skier as the skier moves a distance of 4.1 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 4.1 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) 0.99 m/s and (c) 2.4 m/s?

Explanation / Answer

The power IS different.

The force doing the work is

F = 810J /4.1m = 197.56097 N

The power

at 1.0 m/s is P = F v = 197.56097 N *0.99 m / s = 195.5853603 W

and

at 2.4 m/s is P = F v = 197.56097N * 2.4m / s = 474.146328 W

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