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 890 J of work on the skier as the skier moves a distance of 8.9 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 8.9 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

(a) In both cases, the rope does work on skier against gravity. In neither case does the skiers kinetic energy (speed) change. Hence, the work done by the rope, WT is done against gravity Wg = mgh

i.e WT = Wg = 890 J

(b) v =1 m/s, d = 8.9 m

t = d/v = 8.9

P =W/t = 890/8.9 = 100 W

(c) v =2 m/s

t = 8.9/2 =4.45 s

P = 890/4.45 = 200 W

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