A30-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?

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

10.7 N

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