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

Question

A skier pulled by a tow rope 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 870 J of work on the skier as the skier moves a distance of 9.0 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 9.0 m up the incline? J

(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? W

(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? W

Explanation / Answer

Work does not depend upon time so the rope does the same amount of work = 870 J

b) Power = F*v = W/d*v = 870J/9.0m*1.0 m/s = 96.67 W

c) Power = F*v = W/d*v = 870J/9.0m*2.0 m/s = 48.33 W

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