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23 August, 20:09

A 30-kg chandelier hangs from a ceiling on a vertical 4.4-m-long wire. what horizontal force would be necessary to displace its position 0.16 m to one side?

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  1. 23 August, 20:37
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    Refer to the diagram shown below.

    m = 30 kg, the mass of the chandelier

    W = mg = (30 kg) * (9.8 m/s²) = 294 N, the weight of the chandelier

    Let T = tension in the wire.

    Let F = the horizontal force required to displace the chandelier by 0.16 m.

    The angle that the wire makes with the vertical is given by

    sin (θ) = 0.16/4.4 = 0.0364

    θ = sin⁻¹ 0.0364 = 2.084°

    For equilibrium,

    T cos (θ) = W

    0.9993T = 294

    T = 294.195 N

    Also,

    F = Tsin (θ) = 294.195*0.0364 = 10.709 N

    Answer: 10.7 N
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