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

• MHB
• cbarker1
In summary, a uniform boom weighing 668 N is supported by a light cable and a hinge at the wall. An object weighing 386 N hangs from its right end. To calculate the tension in the cable and the force exerted by the hinge on the boom, one must use rotational and translational equilibrium equations. The reaction force vector at the hinge is not shown since its direction is unknown, but it can be determined once the tension in the cable is found.
cbarker1
Gold Member
MHB
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.

Last edited by a moderator:
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?

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).

## 1. What is static equilibrium for a boom?

Static equilibrium for a boom refers to the state in which all forces acting on the boom are balanced, resulting in no net force or acceleration. This means that the boom is at rest and not moving.

## 2. How do you determine if a boom is in static equilibrium?

To determine if a boom is in static equilibrium, you need to calculate the sum of all the forces acting on the boom. If the sum is equal to zero, then the boom is in static equilibrium. Additionally, the sum of all the torques acting on the boom must also be equal to zero for it to be in static equilibrium.

## 3. What factors affect static equilibrium for a boom?

The factors that affect static equilibrium for a boom include the weight of the boom, the weight of the load being lifted, and the forces applied by any supporting structures or cables. Additionally, the direction and magnitude of these forces can also impact the static equilibrium of the boom.

## 4. How do you maintain static equilibrium for a boom?

To maintain static equilibrium for a boom, the sum of all the forces acting on the boom must be equal to zero. This can be achieved by adjusting the position of the load, the position of the boom, or the forces applied by supporting structures or cables. Additionally, proper maintenance and regular inspections of the boom can help ensure that it remains in static equilibrium.

## 5. What are the consequences of not achieving static equilibrium for a boom?

If a boom is not in static equilibrium, it can lead to an unbalanced load, causing the boom to tip over or collapse. This can result in damage to the boom and surrounding structures, as well as potential injuries or fatalities. It is crucial to always ensure that a boom is in static equilibrium before operating it to avoid any accidents or mishaps.

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