A wheel with a weight of 387 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating a

Question

A wheel with a weight of 387 N comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at an angular velocity of 26.5 rad/s . The radius of the wheel is 0.622 m and its moment of inertia about its rotation axis is 0.800 MR2. Friction does work on the wheel as it rolls up the hill to a stop, at a height of h above the bottom of the hill; this work has a magnitude of 3506 J.

Required:
Calculate h.

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Cherry 5 years 2021-08-29T17:12:34+00:00 1 Answers 23 views 0

Answers ( )

  1. Nem
    0
    2021-08-29T17:13:59+00:00
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    Answer:

    h = 15.6 m

    Explanation:

    The kinetic energy, minus the work of friction, will convert to potential energy.

    v = ωR = 26.5(0.622) = 16.483 m/s

    m = 387/9.81 = 39.45 kg

    ½Mv² + ½Iω² – Wf = Mgh

    ½Mv² + ½(0.800MR²)(v/R)² – Wf = Mgh

    0.9Mv²  – Wf = Mgh

    h = (0.9(39.45)(16.483²) – 3605) / 387 = 15.6103…

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