# Force Acting on Hinge: 2744 N Torque on Beam Homework: Find Force on Hinge

• jybe
In summary: Yes, the angle between the wire and the beam changes the torque.The torque from the weight of the beam will be mg*length*cos(theta) But then how do you express the torque on the beam from the wire now?The torque from the weight of the beam will be mg*length*cos(theta)
jybe

## Homework Statement

"A beam of mass M = 280kg and length L = 2.2m is attached to a wall with a hinge (at a 90 degree angle to the wall, sticking out horizontally), and is supported at the other end by a wire making an angle of 30 degrees with the horizontal beam.

What is the force acting on the hinge?"

NOW...this isn't actually what I'm trying to figure out. I'll do the work for the question below, but what I really want to know is how my work would change if the beam was not at a right angle to the wall, but raised up, maybe at an angle of 20 degrees from the horizontal/70 degrees from the wall. Say the wire is now at an angle of 30 degrees from the horizontal but not the beam.

How would I account for the beam's weight in the Fy equation at the start? Would it still be mg?
And in the torque equation, I can't wrap my mind around how it would change, as far as both the wire and beam parts are concerned. If anyone could help me I would really appreciate it

## Homework Equations

Fx = 0
0 = FHx - Tcos(theta) (Hx is the x compenent of the hinge force)

Fy = 0
0 = FHy + Tsin(theta) - mg

Net torque = 0
0 = Tsin(theta)*L - mg*(L/2)

T = (mg / 2*sin(theta))

## The Attempt at a Solution

[/B]
FHx = Tcos(theta)
FHx = (mg/2sin(theta))*cos(theta)
FHx = 2376.4 N

FHy = mg - Tsin(theta)
FHy = mg - (mg/2sin(theta))*sin(theta)
FHy = 1372 N

FH = √(FHx2 + FHy2)
FH = 2744 N

tan(theta) = (1372/2376.4)
theta = 30 degrees from horizontal

jybe said:
how my work would change if the beam was not at a right angle to the wall,
You correctly posted the three statics equations, horizontal balance, vertical balance and torque balance.
Studying the details of those, which terms change if the beam is not horizontal?

haruspex said:
You correctly posted the three statics equations, horizontal balance, vertical balance and torque balance.
Studying the details of those, which terms change if the beam is not horizontal?

I think the FHx changes, and also, I think the torque from the weight of the beam changes, but is it still mg, or is it mg multiplied by an angle? I'm just having a really hard time making sense of what changes and what doesn't.

Anyone?

Sorry for the delay. Sometimes the system doesn't give me an alert when there is a reply.
jybe said:
the torque from the weight of the beam changes,
Yes. How does one determine the torque from a force about a given point?
jybe said:
I think the FHx changes
Its value might change, but not its appearance in the equations.

haruspex said:
Yes. How does one determine the torque from a force about a given point?

The torque from the weight of the beam will be mg*length*cos(theta)

But then how do you express the torque on the beam from the wire now?

jybe said:
The torque from the weight of the beam will be mg*length*cos(theta)
You have two different angles, no? One for the wire and one for the beam.

## 1. What is the definition of torque?

Torque is a measure of the turning or twisting force applied to an object. It is calculated by multiplying the force applied by the distance from the pivot point to the point where the force is applied.

## 2. How is torque related to force acting on a hinge?

The force acting on a hinge creates a torque on the object that the hinge is attached to. This torque is equal to the force applied multiplied by the distance from the hinge to the point where the force is applied.

## 3. What is the formula for calculating torque on a beam?

The formula for calculating torque on a beam is torque = force x distance, where force is the force applied to the beam and distance is the distance from the pivot point to the point where the force is applied.

## 4. How can I find the force on a hinge if I know the torque on a beam?

To find the force on a hinge, you can use the formula force = torque / distance. Simply plug in the known torque and distance values to calculate the force acting on the hinge.

## 5. Why is it important to calculate the force on a hinge?

Calculating the force on a hinge is important in order to ensure that the hinge and the object it is attached to can withstand the force acting on it. It can also help in determining the stability and balance of the object.

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