Question

A uniform 45 kg beam that is 4.35 m in length sticks out from a vertical wall. A lightweight cable connects the end of the beam to the wall, making an angle of 60.0° between the beam and the cable. A 65 kg worker stands on the beam a distance of 1.75 m from the wall. What is the tension in the cable?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the beam = m₁ = 45 kg

Mass of the worker = m₂ = 65 kg

Angle made by the cable with the beam = = 60^o

Tension in the cable = T

Length of the beam = L = 4.35 m

Weight of the beam = W₁

W₁ = m₁g

W₁ = (45)(9.81)

W₁ = 441.45 N

Weight of the worker = W₂

W₂ = m₂g

W₂ = (65)(9.81)

W₂ = 637.65 N

The beam is connected to the wall at point A and the other end of the beam which is connected to the cable is point D.

The beam is uniform hence the center of gravity of the beam is at the center of the length of the beam.

AC = 2.175 m

The worker stands on the beam at a distance of 1.75 m from the wall.

AB = 1.75 m

The moment about point A for the beam is zero as the beam is in equilibrium,

0 = W₂(AB) + W₁(AC) - TSin(AD)

0 = (637.65)(1.75) + (441.45)(2.175) - [TSin(60)](4.35)

T = 551.08 N

Tension in the cable = 551.08 N