Question

A shop sign weighing 245 N is supported by a uniform 145 N beam as shown in the figure below. Find the tension in the guy wire. N Find the horizontal and vertical forces exerted by the hinge on the beam.

horizontal________ N

vertical__________ N

Answer 1

A) weight of beam = 145 N acting at l=1.7m/2=0.85 m
weight of sign = 245 N acting at l=1.7m

only the vertical component of force in the wire will be used
because the horizontal component passes through the base

therefore Tvert=Tsin35 acting 1.35 m from the base

so here's the Moment eq

-245x1.7 (down) - 145x0.85 ( down ) + Tsin35 x 1.35 = 0
T=(245x1.7 + 145x0.85)/(1.35xsin35)
=697.055 N (up and to the right )

B) from above the T_vert=Tsin35 = 399.8 N (upwards)
and T_horiz=Tcos35=570.99 N (inward)

Horizontal

horizontal Force + 570.99 N (inward ) = 0

horizontal force = -570.99 N (wall is pushing outward )

Vertical

Sign + beam + T_vert + vert_base_force = 0
-245 (downward ) -145 (downward ) + 399.8 (up) +vert_base_force=0
vert_base_force = 245 +145 - 399.8 = -9.8147 N ( down )