A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 7.1° 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 600 J of work on the skier as the skier moves a distance of 4.6 m up the incline. (a) If the rope moved with a constant speed of 2.8 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 4.6 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) 0.60 m/s and (c) 2.8 m/s?

Question

Physics

Regan Gonzales

6 June, 09:25

A skier is pulled by a tow rope up a frictionless ski slope that makes an angle of 7.1° 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 600 J of work on the skier as the skier moves a distance of 4.6 m up the incline. (a) If the rope moved with a constant speed of 2.8 m/s, how much work would the force of the rope do on the skier as the skier moved a distance of 4.6 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) 0.60 m/s and (c) 2.8 m/s?

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Answers (1)

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Wade Logan · Answer 1

W = 600 J

Explanation:

Let's use the work equation to find the force

W = f d

F = W / d

F = 600 / 4.6

F = 130.4 N

a) The expression for power is

P = W / t = f. v

W = f v t

We need to calculate the rise time, which can be found by kinematics

v = x / t

t = x / v

t = 4.6 / 2.8

t = 1.64 s

We calculate

W = 130.4 2.8 1.64

W = 600 J

b) we repeat the calculations changing the speed to v = 0.60m/s

t = 4.6/0.6

t = 7.67 s

W = 130.4 0.6 7.67

W = 600 J

You can see that work is always the same what changes is the power