A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 17° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.5 m/s. The force of the rope does 950 J of work on the skier as the skier moves a distance of 6.6 m up the incline. (a) If the rope moved with a constant speed of 2.2 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 6.6 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) 1.5 m/s and (c) 2.2 m/s?

(a) 950J

(b) 216 W

(c) 316.67 W

Explanation:

(a) If the skier is moving at a constant speed, then his kinetic energy is unchanged. The work done by the rope is the same for speed at 2.2m/s as it is for 1.5m/s. It is 950J

(b) When the speed is 1.5m/s then the time it would take to move up a distance of 6.6 m is 6.6 / 1.5 = 4.4 s

If the work is 950J over 4.4s then the rate of work is 950 / 4.4 = 216 W

(c) When the speed is 2.2 m/s then the time it would take to move up a distance of 6.6 m is 6.6 / 2.2 = 3 s. If the work is 950J over 3s then the rate of work is 950 / 3 = 316.67 W

(A) The work is still the same as in the first case since the skier is not accelerating but moving at constant velocity. So the force rope exert is still the same and has a value of 950/6.6 =144N. If the skier accelerated in this case the force would not be the same as above and the work done would be different.

(B) P = W/distance × speed = 950/6.6 × 1.5 = 216W

(C) P = W/distance × speed = 317W

Explanation:

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