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12 January, 08:03

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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  1. 12 January, 08:25
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    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
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