Question

A 400.0-N sign hangs from the end of a uniform strut. The strut is 4.0 m long and

weighs 600.0 N. The strut is supported by a hinge at the wall and by a cable whose

other end is tied to the wall at a point 3.0 m above the left end of the strut. Find the

tension in the supporting cable and the force of the hinge on the strut.

Answer 1

The tension in the supporting cable

$\sum\tau_B=0\to600×2+400 ×4-4T ×(3/5)=0\to T=1167\ (N)$

The force of the hinge on the strut.

$F_h=T ×(4/5)=1167 ×(4/5)=933\ (N)$

$\sum\tau_A =0\to600 ×2-F_v ×4=0\to F_v=300\ (N)$

$F=\sqrt{933^+300^2}=980\ (N)$