Question

A 22.6 kg floodlight in a park is supported at the end of a horizontal beam of negligible mass that is hinged to a pole, as shown in the figure below.


A cable at an angle of alpha = 29.0° with the beam helps to support the light. Find the tension in the cable.

Tries 0/10

Find the horizontal force exerted on the beam by the pole.

Tries 0/10

Find the vertical force exerted on the beam by the pole.

Answer 1

a)

Balance Torques

$T=0$

(Tsin29)d-(mg)d=0

So tension in the cable

T=mg/sin29 =22.6*9.8/sin29

T=456.84 N

b)

horizontal Force exerted on the beam by the pole

F_h-TCos30=0

F_h=456.84*Cos29 =399.56 N

c)

Vertical Force exerted on the beam by the pole

F_v+Tsin29-mg=0

F_v=mg-Tsin29 =22.6*9.8-456.84sin29

F_v=0 N

29 Fh Fv