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,

Question

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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Thông Đạt 3 years 2021-08-25T03:23:58+00:00 1 Answers 152 views 0

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  1. thienan
    0
    2021-08-25T03:25:04+00:00
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    Answer:

    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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