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 9.5° with the horizontal. The rope moves parallel to the slope with a constant speed of 0.60 m/s. The force of the rope does 510 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 2.1 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? At what rate is the force of the rope doing work on the skier when the rope moves with a speed of (b) 0.60 m/s and (c) 2.1 m/s?

Explanation / Answer

Whether the rope (with the skier) moves at 0.60 or 2.1 m/s, the net force on the skier is zero since the speed is constant. That means the upward force on the rope is equal to the downward force of gravity along the slope. So the work done by the force on the rope =
Force on the rope X distance travelled up the slope
= Force of gravity down the slope X distance travelled up the slope
= Skier's weight X sin 9.5 deg X 8.9 m
Since this is independent of the upward speed,

(a) the work done at a speed of 2.1 m/s is also 900 J.

So the rate of work done per unit time is
(b) 900/14.83 = 60.67 J/s
(c) 900/4.238 = 212.35 J/s

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