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23 February, 23:59

The motor, M, pulls on the cable with a force F = (10t2 + 300) N, where t is in seconds. If the 100 kg crate is originally at rest at t = 0, determine its speed when t = 4 s. Neglect the mass of the cable and pulleys and there is no friction between the box and walls. Hint: First find the time needed to begin lifting the crate.

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  1. 24 February, 02:02
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    14.13 m/s

    Explanation:

    Parameters given:

    Mass, m = 100 kg

    F = 10t² + 300

    We know that force is given as:

    F = m * a

    => ma = 10t² + 300

    Where a = acceleration

    Given that mass, m = 100:

    => a = (10/100) t² + (300/100)

    a = 0.1t² + 3

    To find the velocity, we integrate acceleration, a:

    a = dv/dt = 0.1t² + 3

    v = (0.1/3) t³ + 3t

    When t = 4 secs:

    v = (0.1 * 4³) / 3 + (3 * 4)

    v = 2.13 + 12

    v = 14.13 m/s
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