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

VTshruti VTshruti · Answer 2 · 2022-07-02T16:10:11+02:00

The horizontal force would be necessary to displace its position 0.16 m to one side will be 10.7 N.

What is horizontal force?

Horizontal force is defined as a force applied in a direction parallel to the horizon. A force exerted on a body has two components: a horizontal component and a vertical component.

Given that,

m = 30 kg,

W = mg = (30 kg)*(9.8 m/s²)

W = 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

θ = 2.084°

For equilibrium,

T cos(θ) = W

0.9993T = 294

T = 294.195 N

We know that,

F = Tsin(θ)

F = 294.195*0.0364

F = 10.709 N

Thus, The horizontal force would be necessary to displace its position 0.16 m to one side will be 10.7 N.

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