# Find the tension with using forces and torques

• vu10758
In summary: Good night.In summary, the problem involves a traffic light hanging from a structure with a uniform aluminum pole and massless cables. The pole has a mass of 8 kg and is 7.5m long, while the traffic light has a mass of 5kg. Cable 1 is connected 6.31m from the hinge. The goal is to find the tension in both cables and the horizontal and vertical components of the reaction force at the hinge. The solution involves using torque and moments around the hinge, and equating horizontal and vertical forces at the hinge to find the tension in the cables.
vu10758
A traffic light hangs from a structure shown at http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1460004546

The uniform aluminum pole has a mass of 8 kg and is 7.5m long. The traffice light has a mass of 5kg. The cables are massless. Cable 1 is connected 6.31m from the hinge. Find the tension in both cables and hte horizontal and vertical components of the reaction force at the hinge.

I know that for rope two, T-M_2*g = 0

However, I don't know what to do for the pole. It has mg pulling down, but Tension from rope 1 is horizontal. There must be something to balance it but what? Same with rope 1. I can't find something to balance t1 from rope 1.

I know that torque is force times radius. The total torque here is zero since it is not rotating.

T_t1 - T_mg + T_t2 - T_m2*g = 0

However, I am missing relationships between the forces.

vu10758 said:
A traffic light hangs from a structure shown at http://viewmorepics.myspace.com/index.cfm?fuseaction=viewImage&friendID=128765607&imageID=1460004546

The uniform aluminum pole has a mass of 8 kg and is 7.5m long. The traffice light has a mass of 5kg. The cables are massless. Cable 1 is connected 6.31m from the hinge. Find the tension in both cables and hte horizontal and vertical components of the reaction force at the hinge.

I know that for rope two, T-M_2*g = 0

However, I don't know what to do for the pole. It has mg pulling down, but Tension from rope 1 is horizontal. There must be something to balance it but what? Same with rope 1. I can't find something to balance t1 from rope 1.

I know that torque is force times radius. The total torque here is zero since it is not rotating.

T_t1 - T_mg + T_t2 - T_m2*g = 0

However, I am missing relationships between the forces.
Torque is not force times radius, it is force times perpendicular distance from points of rotation.

Take moments around the hinge:
mg*distance+m2g*distance-T2*6.31=0

When I do that I get

8*9.8*6.31 + 5*9.8*7.5* cos(37) = 7.5cos(37) * T2
T2= 88.19

This answer is incorrect. The answer key says that the answers in this problems are 139N, 49N, 139N, 127.4 N for each of the forces. 88.19 is not any of these. What did I do wrong?

vu10758 said:
When I do that I get

8*9.8*6.31 + 5*9.8*7.5* cos(37) = 7.5cos(37) * T2
T2= 88.19

This answer is incorrect. The answer key says that the answers in this problems are 139N, 49N, 139N, 127.4 N for each of the forces. 88.19 is not any of these. What did I do wrong?
your distances are incorrect you need to find the perpendicular distance to the force from the point.

How can the distance to the force mg be 6.31? 6.31 is the perpendicular distance to the force T2

ponjavic said:
your distances are incorrect you need to find the perpendicular distance to the force from the point.

How can the distance to the force mg be 6.31? 6.31 is the perpendicular distance to the force T2

I am not sure if this is right. Mg should be from the center of the pole. So the distance is 7.5/2*cos(37).

If I plug this back in, I would get T2 = 48.38 N. Is this correct?

I know that T2 = m2*g so I should be able to find m2. However, how do I find tension of the first rope since I don't have any other horizontal forces to equate to it?

you know m2 I don't know what you are trying to do.

T2 is the tension of the rope on the left side of the image, the tension in the one on the right is simply mg = 5 * 9.82

Now what you need to do is to equate horisontal and vertical forces for the forces at the hinge.

So for horisontal equilibrium.

Horisontal force at hinge Fh = T2

Vertical equilibrium:

Fv=5*9.82 + 8 * 9.82

I have to go to bed, I might check back tomorrow, good luck!

Okay, thanks very much for your help tonight.

## 1. What is tension in physics?

Tension is a force that is transmitted through a string, rope, cable, or any other type of object that is under tension. It is a pulling force that acts in opposite directions along the length of the object and can cause it to stretch or deform.

## 2. How is tension calculated using forces and torques?

Tension can be calculated by using the principles of Newton's laws of motion and torque. First, identify all the external forces acting on the object and draw a free body diagram. Next, use the equations for torque and equilibrium to find the tension. Tension can also be calculated by measuring the elongation or deformation of the object under tension.

## 3. What factors affect tension?

Tension is affected by the magnitude and direction of the applied forces, the length and thickness of the object under tension, and the material properties of the object. Other factors such as temperature, friction, and elasticity can also influence tension.

## 4. How does tension play a role in everyday life?

Tension is present in many everyday activities such as tying a shoelace, lifting objects with a pulley system, or even playing a musical instrument. It is also used in various engineering applications like bridges, cranes, and suspension systems. Many sports and recreational activities also involve tension, such as rock climbing and bungee jumping.

## 5. What are some real-life examples of tension problems?

Some real-life examples of tension problems include determining the tension in a rope supporting a hanging object, calculating the tension in a cable holding up a bridge, or finding the tension in a string of a guitar. These problems can also involve multiple objects under tension, such as a system of pulleys or a combination of ropes and cables.

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