Torque for a hanging sign. Finding Tension

In summary, the sign has a mass of 200 kg, a tension of 835 N, and a distance of 400 cm from the wall.
  • #1
Jbreezy
582
0
1. Homework Statement
Hi I was trying to see if I did this right.

A shop owner wants to hang a sign of mass 200 kg which is supported by which is supported by a uniform 155 N beam. What is the tension in the guy wires and the horizontal and vertical forces that the wall applies to the beam? The length of the beam is 400 cm.
The diagram shows that the angle between the guy wire and the beam is 65 degrees. It also shows that the wall to center of mass for the sign is 350 cm. I hope that gives a good picture.

2. Homework Equations

Mb = mass of beam
r = distance
g = gravity
Ms = mass of sign
t = torque
T = tension

3. The Attempt at a Solution

OK so sum the forces in each direction
Fy = Fu +Tsin(θ) - Mbg - Msg = 0
Fx = Fh - Tcos(θ) = 0
We will return back to the equations after we torque about the beam where it meets the wall.
Ʃt = Tr1 - Mbr2 +Msgr3
r1 = 4tan(65) 4 is in meters it is the length of the beam. Tan(65) is to find the lever arm.
r2 = 2 meters
r3 = 3.5 meters this is from the wall to the signs center of mass. The diagram shows this.
We solve for Tension and get

T = (Mbr2 +Msgr3) / (4tan(65))
T = (155N x 2) + (200kg x 9.8 m/s^2 x 3.5 m) /(4tan(65))
T = 835 N

Then put this back into the summation of forces to get the values for the Fh and Fu
I got .. Fh = 353.2 using Fh = Tcos(65)
And I got Fu = 1357 using Mb + Msg -Tsin(65)

When I plugged my values back into the summation of forces equations with the values I got
.00000071 for summation in the y direction
I got 2.29 E-8 for summation in the y direction.
This is close to 0 but is it OK? Thanks much.
 
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  • #2
Jbreezy said:
We will return back to the equations after we torque about the beam where it meets the wall.
Ʃt = Tr1 - Mbr2 +Msgr3
Don't the two weights have torque in the same direction about that point?
r1 = 4tan(65) 4 is in meters it is the length of the beam. Tan(65) is to find the lever arm.
If you are taking the distance as the length of the beam then you need to take the force component perpendicular to that.
 
  • #3
Thanks
 

Related to Torque for a hanging sign. Finding Tension

1. What is torque and how does it relate to a hanging sign?

Torque is the measure of the force that causes an object to rotate around a fixed axis. In the case of a hanging sign, torque is created by the weight of the sign pulling down on the supporting rope or chain, causing it to rotate.

2. How is torque calculated for a hanging sign?

To calculate torque for a hanging sign, you need to know the weight of the sign and the distance between the attachment point and the center of mass of the sign. The formula for torque is torque = force x distance. In this case, the force is the weight of the sign and the distance is the distance from the attachment point to the center of mass.

3. What is the purpose of finding tension in a hanging sign?

Finding tension in a hanging sign is important because it helps determine the strength and stability of the supporting rope or chain. If the tension is too low, the sign may not hang properly and could fall. If the tension is too high, it could put unnecessary strain on the supporting structure.

4. How is tension calculated for a hanging sign?

To calculate tension for a hanging sign, you need to know the weight of the sign and the angle at which the rope or chain is attached to the supporting structure. The formula for tension is tension = weight / cos(angle). This takes into account the vertical and horizontal components of the force acting on the rope or chain.

5. What factors can affect the tension and torque of a hanging sign?

The weight of the sign, the distance between the attachment point and center of mass, and the angle of the supporting rope or chain are the main factors that can affect the tension and torque of a hanging sign. Other factors may include wind or other external forces acting on the sign, as well as the strength and stability of the supporting structure.

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