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 11° with the horizontal. The rope moves parallel to the slope with a constant speed of 1.4 m/s. The force of the rope does 630 J of work on the skier as the skier moves a distance of 5.2 m up the incline. (a) If the rope moved with a constant speed of 3.0 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 5.2 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) 1.4 m/s and (c) 3.0 m/s?

Explanation / Answer

A) The expression for work is

W = F .d

as the distance and force are parallel to the plane the = 0

W = F d

we must know the strength, for this we use the data given

F = W /d F = 630/ 5.2

F = 121.15 N

The work changes if changes the force, from the second law of Newton

F – Wx = m a a =0 F = Wx

as the force is constant regardless of the speed, we see that it has not changed so the work is equal

W = 630 J

We calculate the power

P = W /t = F v

b ) v = 1.4 m/s

P = 121.15 1.4

P1= 169.61 W

c) v = 3 m/s

P2 = 121.15 3.0

P2 = 363.45 W

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