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20 December, 12:02

How much work is done lifting a 12-m chain that is initially coiled on the ground and has a density 2 kg/m so that its top end is 11 m above the ground? (Assume that acceleration due to gravity is g = 9.8 m/s2.)

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  1. 20 December, 12:29
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    2587.2 J.

    Explanation:

    From potential energy,

    The work done to lift the chain = potential energy of the chain.

    W = mgh ... Equation 1

    Where W = work done to lift the chain, m = mass of the chain, g = acceleration due to gravity of the chain, h = height of the chain.

    But,

    m = m'd ... Equation 2

    Where m' = density of the chain, d = length of the chain.

    Substitute equation 2 into equation 1

    W = m'dgh ... Equation 3

    Given: m' = 2 kg/m, d = 12 m, h = 11 m, g = 9.8 m/s²

    Substitute into equation 3

    W = 2 (12) (11) (9.8)

    W = 2587.2 J.
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