MHB Can You Solve for Tension and Force in Static Equilibrium for a Boom?

[cbarker1]

The uniform boom shown below weighs 668 N, and the object hanging from its right end weighs 386 N. The boom is supported by a light cable and by a hinge at the wall.

Calculate the tension in the cable and the force by the hinge on the boom (both in N). (Enter the magnitudes.)

Tension in the cable Nforce by the hinge N

View attachment 7603

Need help setting up the problem correctly.

 

[tkhunny]

I'm not real clear on your drawing. Is the "boom" the horizontal piece that doesn't seem to attach?

Typically, you use the available angles and some trigonometry to decompose to the vertical and horizontal pieces and use this information to understand the state of equilibrium. Can you find a Stationary Point, around which such a consideration can be based?

 

[skeeter]

Hopefully, the attached diagram is correct ... note the reaction force vector, R , at the hinge is not sketched in since the direction of its y-component is unknown (but it can be determined once the tension, T , is found)

https://www.physicsforums.com/attachments/7614

I would start with rotational equilibrium about the hinge ...

$\displaystyle \sum \tau = 0$

... then continue with the two equations for translational equilibrium

$\displaystyle \sum F_y = 0$

$\displaystyle \sum F_x = 0$oh ... how about responding to your threads once in a while to let us know if you solved the problem (or not).