Question

The beam is uniform and weighs 60N. if 200N, find the tension in the tie rope x and y components of the force that the hinge exerts on the wall.

Answer 1

see arranged figure,

we have to find torque about the hinged point,

torque due to weight of beam + torque due to weight of object + torque due to tension = 0

or, $-60\times\frac{L}{2}cos30^{\circ}-200\times Lcos30^{\circ}+T\times(0.8Lcos60^{\circ})=0$

or, -60 × 0.5L × √3/2 - 200 × L × √3/2 + T × 0.8 × L × 1/2 = 0

or, -15√3L - 100√3L + 0.4TL = 0

or, 0.4T = 115√3 = 200

or, T = 500N

now, $\displaystyle\Sigma{F_x}$ = -T + H = 0 [ see figure ]

H = 500N

and $\displaystyle\Sigma{F_y}$

= -60 - 200 + V = 0

V = 260N

hence, horizontal component of force is 500N and vertically component is 260N