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3 October, 07:56

A 5kg bucket of water is raised from a well with a rope. If the upward acceleration of the bucket is 3m/s/s, find the force exerted on the bucket by the rope.

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  1. 3 October, 11:17
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    Apply Newton's second law to the bucket's vertical motion:

    F = ma

    F = net force, m = mass of the bucket, a = acceleration of the bucket

    Let us choose upward force to be positive and downward force to be negative. The net force F is the difference of the tension in the rope lifting the bucket and the weight of the bucket, i. e.:

    F = T - W

    F = net force, T = tension, W = weight

    The weight of the bucket is given by:

    W = mg

    W = weight, m = mass, g = gravitational acceleration

    Make some substitutions:

    F = T - mg

    T - mg = ma

    Isolate T:

    T = ma + mg

    T = m (a+g)

    Given values:

    m = 5kg, a = 3m/s², g = 9.81m/s²

    Plug in and solve for T:

    T = 5 (3+9.81)

    T = 64.05N
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