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31 October, 01:29

A mass of 5kg starts from rest and pulls down vertically on a string wound around a disk-shaped, massive pulley. The mass of the disk is 5kg and its radius is 2 m. What is the linear speed, in m/s, after the mass drops by 0.3 m

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  1. 31 October, 02:29
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    1.98 m/s

    Explanation:

    To solve this, we would be using the law of conservation of energy, i. e total initial energy is equal to total final energy.

    E (i) = E (f)

    mgh = ½Iw² + ½mv²

    Recall, v = wr, thus, w = v/r

    Also, I = ½mr²

    I = 0.5 * 5 * 2²

    I = 10 kgm²

    Remember,

    mgh = ½Iw² + ½mv²

    Substituting w for v/r, we have

    mgh = ½I (v/r) ² + ½mv²

    Now, putting the values in the equation, we have

    5 * 9.8 * 0.3 = ½ * 10 * (v/2) ² + ½ * 5 * v²

    14.7 = 1.25 v² + 2.5 v²

    14.7 = 3.75 v²

    v² = 14.7/3.75

    v² = 3.92

    v = √3.92

    v = 1.98 m/s

    Thus, the speed is 1.98 m/s
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