# Static equilibrium of a bar attached to a hinge

• ac7597
In summary, the conversation discusses the calculation of tension in a system consisting of a rod, a hinge, and a wire. The angle between the wire and the horizontal is determined to be 33.7 degrees and the tension in the wire is calculated to be 538.7N. The conversation also addresses the precision of finding the angle and the impact of the wire's radius on the maximum tension it can withstand.
ac7597
Homework Statement
A bar of width w = 3 m and mass m = 8 kg is attached to a wall by a hinge at P. A steel wire of radius r = 0.51464 mm runs from the end of the bar to the wall, attaching to the wall a distance H = 2 m above the point P.

Fred hangs from the middle of the bar, raising money for a worthy charity. The longer he hangs, the more money will be donated. His mass is M = 53 kg.

Make a table showing the forces acting on the bar in the X-direction and in the Y-direction, and the torques acting on the bar as well.
Use your table to determine the tension T in the wire.

Fred grows hungry. His frat brothers bring him pizza and feed it to him so that he can continue to hang from the bar. Assume that the steel wire is made from type G41400 steel, drawn at 1000 F. How much pizza can he eat before the wire will break?
Relevant Equations
 item Fx Fy torque(z) rod 0 -mg -mg* (3/2) Fred 0 -Mg (-Mg) * (3/2) hinge -hx hy 0 wire F* cos(theta) F* sin(theta) 3*F* sin(theta) total 0 0 0

theta= tan^(-1) (2/3) = 33.7 degree
3*F* sin(theta) = (8*9.8)* (3/2) + (53*9.8) * (3/2)
F= 538.7N
tension is 538.7N

#### Attachments

• Screen Shot 2019-11-11 at 8.26.03 PM.png
4.4 KB · Views: 212
Looks good.
ac7597 said:
theta= tan^(-1) (2/3) = 33.7 degree
It is generally unhelpful to find the angle explicitly. You can find the desired trig function from the geometry. In the present case you would have found the sine to be √(4/13). This approach usually results in greater precision.

I was unsure about the answer because the radius of the wire was given as 0.51464 mm. Does this change the tension?

ac7597 said:
I was unsure about the answer because the radius of the wire was given as 0.51464 mm. Does this change the tension?
It does not change the tension required for stasis. But together with the other information about the wire it determines the maximum tension the wire can withstand.

## 1. What is static equilibrium?

Static equilibrium refers to the state of an object or system when all of its forces are balanced and there is no net acceleration.

## 2. How is static equilibrium achieved in a bar attached to a hinge?

In a bar attached to a hinge, static equilibrium is achieved when the forces acting on the bar are balanced and the bar is not moving or rotating. This means that the sum of all the forces acting on the bar must be equal to zero and the sum of all the torques (rotational forces) acting on the bar must also be equal to zero.

## 3. What is the role of the hinge in maintaining static equilibrium?

The hinge acts as a pivot point for the bar, allowing it to rotate freely. It also ensures that the forces acting on the bar are transmitted through the hinge and do not cause it to move or become unbalanced.

## 4. How does the length of the bar affect static equilibrium?

The length of the bar can affect the location of the forces and torques acting on it, which in turn can affect the state of static equilibrium. A longer bar may require more force to maintain equilibrium compared to a shorter bar, as the forces acting on it will have a greater lever arm.

## 5. What happens if the forces or torques acting on the bar are not balanced?

If the forces or torques acting on the bar are not balanced, the bar will not be in a state of static equilibrium and will either move or rotate. This can result in the bar becoming unattached from the hinge or causing the hinge to break if the forces are too great.

Replies
6
Views
2K
Replies
41
Views
1K
Replies
9
Views
1K
Replies
1
Views
1K
Replies
5
Views
1K
Replies
5
Views
4K
Replies
3
Views
12K
Replies
13
Views
2K
Replies
18
Views
3K
Replies
9
Views
3K