Question

A 23.0 kg beam is attached to a wall with a hinge and its far end is supported by a cable such that the angle between the beam and the cable is 90o. If the beam is inclined at an angle of theta = 25.0o with respect to horizontal, what is the magnitude of the horizontal component of the for ce exerted by the hinge on the beam?

Answer 1

The system is in equilibrium ..

Taking moments about the hinge to find the tension T in the cable ..

Beam length L .. (c of m at the centre point)

T↑ x L = mg↓ x ½L cos25

T = ½mg cos25

Again because the system is in equilibrium, the net horiz force in the system is zero ..

• Th (horiz component of T) acts 'inward' (-ve direction) ..

Th = (-)T sin 25 .. (as T is perp to beam, T is 25º to vertical)

• Fh ('outward' horiz force from the hinge) acts in the +ve direction

For equilibrium .. Fh = Th

Fh = T sin14.1 = ½mg cos25 x sin25

Fh = ½ x 23.0kg x 9.80 x cos25x sin25  
Fh = 43.16N