A skier pulled by a towrope up a frictionless ski slope that makes an angle of 1

Question

A skier pulled by a towrope up a frictionless ski slope that makes an angle of 12° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.0 m/s. The force of the rope does 945 J of work on the skier as the skier moves a distance of 7.9 m up the incline.

(a) If the rope moved with a constant speed of 2.0 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 7.9 m up the incline?

(b) At what rate is the force of the rope doing work on the skier when the rope moves with a speed of 1.0 m/s?

(c) At what rate is the force of the rope doing work on the skier when the rope moves with a speed of 2.0 m/s?

Explanation / Answer

The speed is constant in this situation. So the change in kinetic energy is zero. so

dK=0

Then,

W=-Wg

= 945 J

,................ ........... ............   

Power P = energy /time = 945/ (7.9/1) =119.62 W

............... ........... ................

Power = energy / time = 945/(7.9/2) = 239.24 W

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