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March 29, 2017

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A skier of mass 74 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him 90 m up a 30° slope (assumed frictionless) at a constant speed of 3.0 m/s?
J

(b) What power (expressed in hp) must a motor have to perform this task?
hp

  • physics - ,

    (a) The speed does not matter, since the kinetic energy does not change.
    Multiply the weight M*g = 725 N by the vertical rise 90 sin30 = 45 m. You should get 32,630 Joules.

    (b) Power = (Work done)/(Time required)
    The time required is (90 m)/(3 m/s) = 30 s.

    Power = 32,630/30 = 1088 Watts
    = 1.45 hp

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