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 12° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.2 m/s. The force of the rope does 800 J of work on the skier as the skier moves a distance of 7.5 m up the incline. (a) If the rope moved with a constant speed of 2.9 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 7.5 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) 1.2 m/s and (c) 2.9 m/s?

Explanation / Answer

a) Total Work done is dependent on initial and final position and not on the speed

Hence the work done in this case =800 J

b) Time req to cover the distance = Distance /Speed

=7.5/1.2

=6.25 s

Rate of Work done = 800/6.25

=128 J/s

c)

Time req to cover the distance = Distance /Speed

=7.5/2.9

=2.586 s

Rate of Work done = 800/2.586

=309.33 J/s

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