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 19° with the horizontal. The rope moves parallel to the slope with a constant speed of 0.83 m/s. The force of the rope does 820 J of work on the skier as the skier moves a distance of 8.8 m up the incline. (a) If the rope moved with a constant speed of 2.3 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 8.8 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) 0.83 m/s and (c) 2.3 m/s?

Explanation / Answer

a) change in KE = work done by gravity + work done by the force in pulling the skier

0 ( since the body is moving with constant Velocity) = work done by gravity + 820 J

work done by gravity = - 820 J

therefore work done will remain same

b) time = d/ speed = 8.8 / 0.83= 10.6 seconds apprx

P = 820 / 10.6 =77.358 watts

t2= 8.8/ 2.3= 3.826 seconds apprx

P = 820/ 3.826=214.323 watts

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