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16 June, 22:14

Calculate the translational speed of a cylinder when it reaches the foot of an incline 7.35 m high. assume it starts from rest and rolls without slipping.

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  1. 17 June, 00:51
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    The total kinetic energy will be equivalent to the potential energy;

    The total kinetic energy is given by the sum of transitional kinetic energy and the rotational kinetic energy.

    Rotational kinetic energy

    I = 1/2mR², but rotational energy = 1/2 I w²

    Thus rotational energy is equal to 1/4 mR²w², which is equivalent to

    = 1/4 mv² since v = wR

    Thus;

    Total kinetic energy = 1/2 mv² + 1/4 mv²

    hence;

    Mgh = 3/4 mv²

    gh = 3/4 v² (assuming g = 9.81 m/s²)

    72.1035 = 3/4 v²

    v = 9.805

    = 9.805 m/s
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