A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its up

Question

A uniform beam having a mass of 60 kg and a length of 2.8 m is held in place at its lower end by a pin. Its upper end leans against a vertical frictionless wall as shown in the figure. What is the magnitude of the force the pin exerts on the beam?

Answer 1

Take summation of moments about the wall (where the beam touches it).

60*cos 40*9.8*(2.8/2) = Rp(2.8)

where

Rp = reaction of the pin on the beam

Rp = 225.22 Newtons

This pin has two components of its reaction -- a horizontal and a vertical component.

The horizontal reaction = 225.22* sin 40 = 144.77 N

and

the vertical reaction = 225.22 * cos 40 = 172.53 N