The sign shown in the figure weighs 200 N.The boom is of uniform construction.If the force exerted by the hinge on the boom is 300 N and acts at an angle of 20º above the horizontal,the tension in the tie cable is
A)~205 N
B)~145 N
C)~413 N
D)~625 N
E)None of these is correct.

Question

The sign shown in the figure weighs 200 N.The boom is of uniform construction.If the force exerted by the hinge on the boom is 300 N and acts at an angle of 20º above the horizontal,the tension in the tie cable is 
A)~205 N 
B)~145 N 
C)~413 N 
D)~625 N 
E)None of these is correct.

Quizplus · Accepted Answer

Using the equilibrium equations:

ΣFx = 0 => Tcos(40º) = 300 => T = 385.50 N

ΣFy = 0 => Tsin(40º) - 200 - 300sin(20º) = 0 => Tsin(40º) = 413.00 N

Therefore the tension in the tie cable is approximately 413 N.

The Sign Shown in the Figure Weighs 200 N