Question #151602

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.



1
Expert's answer
2020-12-17T09:14:34-0500

WB=300 N, WM=600 N, L=5 m, L1=1.5 m.W_B=300~N, ~W_M=600~N,~L=5~m,~L_1=1.5~m.

By the torque:

τR+τB+τM+τT=0,\tau_R+\tau_B+\tau_M+\tau_T=0,

0WBL2WML1+TLsin53°=0,0-W_B\frac L2-W_M L_1+TLsin53°=0,

T=413 N.T=413~N.


RxTcos53°=0,R_x-Tcos53°=0,

Rx=249 N.R_x=249~N.


RyWBWM+Tsin53°=0,R_y-W_B-W_M+Tsin53°=0,

Ry=570 N.R_y=570~N.


R=Rx2+Ry2=622 N.R=\sqrt{R_x^2+R_y^2}=622~N.


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Comments

Boris Iradukunda
19.12.20, 20:45

Thx for the answer. It was helpful

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