Question

A skier is 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 900 J of work on the skier as the skier moves a distance of 8.0 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 8.0 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) 1.0 m/s and (c) 2.0 m/s?

Answer 1

Answer

given,

angle with horizontal = 12°

constant speed with the slope = 1 m/s

Work on the skier to move 8 m = 900 J

a) Rope moved with constant speed

change in kinetic energy is equal to zero

 work done by the force of the rope = 900 J

rate of force of the rope when skier move with

b) v = 1 m/s   total time t = 8 s

            Power =$\dfrac{work\ done}{time}$

                       =$\dfrac{900}{8}$

                       = 112.5 W

c) v = 2 m/s   total time t = 8/2 = 4 s

            Power =$\dfrac{work\ done}{time}$

                       =$\dfrac{900}{4}$

                       = 225 W