# Static Equilibrium and a beam

• benny1993
In summary, the conversation is about solving a problem involving ft, lb, and N. The person is having trouble getting the correct answer and is seeking help. They realize they made a mistake by writing the answer in N instead of lbs. They also discuss the direction of F(p), with one person assuming it to be horizontal while the other argues that the assumption is unfounded. The conversation then shifts to finding the correct answer and simplifying the moment balance equation. Finally, there is a discussion about the 75 lb tension in the cable and the magnitude of the force at the hinge.

#### benny1993

I have been trying to work on this problem, but I keep getting the answer wrong. I would appreciate if someone could help me understand what I did wrong.

Below is my answer and solution:

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How can you work with ft and lb and come up with a force in N ?

What is the direction of Fp ? You seem to think it's horizontal. Why ?

It's actually in lbs. I don't know why I wrote 45.2N. The answer is supposed to be in lbs.
And about the direction of F(p), I assumed it would be horizontal since the beam is in static equilibrium while remaining horizontally.

Why not just write the moment balance simply as $$(120)(6)=T_y(12)$$

Chestermiller said:
Why not just write the moment balance simply as $$(120)(6)=T_y(12)$$
Wouldn't the answer still be the same?

benny1993 said:
I assumed it would be horizontal since the beam is in static equilibrium
Assumption is unfounded.

BvU said:
Assumption is unfounded.
Then what would be the correct answer?

benny1993 said:
Wouldn't the answer still be the same?
Yes, but wouldn’t be simpler? This would also allow you to immediately determine the vertical reaction force component at the pin.

But you have the 75 lb right there in your calculations.

The question is what is the magnitude of the force, not what is the horizontal component of the force.

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jack action said:
But you have the 75 lb right there in your calculations.

The question is what is the magnitude of the force, not what is the horizontal component of the force.
Not exactly. The 75lb found in post #1 is for the tension in the cable. However, there is a neat way of seeing that the reaction at the hinge must have the same magnitude.
benny1993 said:
And about the direction of F(p), I assumed it would be horizontal
Easily falsified. Consider moments about the tip of the beam.

Chestermiller

## 1. What is static equilibrium?

Static equilibrium refers to the state of an object where it is at rest and there is no net force or torque acting on it. This means that the object is not moving and all the forces and torques are balanced.

## 2. How does a beam achieve static equilibrium?

A beam achieves static equilibrium when the sum of all the forces acting on it is equal to zero and the sum of all the torques acting on it is also equal to zero. This means that the beam is not moving and is in a state of balance.

## 3. What is the difference between static equilibrium and dynamic equilibrium?

Static equilibrium refers to a state of balance where an object is at rest and not moving. Dynamic equilibrium, on the other hand, refers to a state of balance where an object is moving at a constant velocity.

## 4. How do you calculate the forces and torques on a beam in static equilibrium?

In order to calculate the forces and torques on a beam in static equilibrium, you need to use the principles of Newton's laws of motion and the concept of torque. You can set up equations to balance the forces and torques on the beam and solve for the unknown variables.

## 5. What factors can affect static equilibrium in a beam?

Some factors that can affect static equilibrium in a beam include the distribution of weight or load on the beam, the length and material of the beam, and the support structures that the beam is attached to. Any changes in these factors can alter the forces and torques acting on the beam and affect its state of equilibrium.