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?

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