Answer to Question #189486 in Classical Mechanics for Jethro

Question

A rope attached on one end to a vertical wall(forming a 50° angle) helps to support a uniform 800-N beam 7m long the lower end of which is hinged at the same vertical wall (forming a 60° angle) while the other end supports a 1-ton load. Together, the rope, the wall and the beam forms a 50°+60°+70° triangle that points to the right.

Determine tension T in the rope.

Answer 1

$M_1+M_2=M_3,$

$F\frac l2 \cos (90°-60°)+mgl\cos (90°-60°)=Tl\cos(90°-70°),$

$\frac F2\cos 30°+mg\cos 30°=T\cos 20°,$

$T=\frac{\cos30°}{\cos 20°}(\frac F2+mg)=9.4~kN.$