Question

A uniform horizontal beam 5.00 m long and weighing 3×10^2𝑁 is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53 degrees with the horizontal. If a person weighing 6×10^2𝑁 stands 1.50 m from the wall, find the magnitude of the tension in the cable and the force 𝑅 exerted by the wall on the beam.

Answer 1

$W_B=300~N, ~W_M=600~N,~L=5~m,~L_1=1.5~m.$

By the torque:

$\tau_R+\tau_B+\tau_M+\tau_T=0,$

$0-W_B\frac L2-W_M L_1+TLsin53°=0,$

$T=413~N.$

$R_x-Tcos53°=0,$

$R_x=249~N.$

$R_y-W_B-W_M+Tsin53°=0,$

$R_y=570~N.$

$R=\sqrt{R_x^2+R_y^2}=622~N.$