Find the tension with using forces and torques

[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.

 

[ponjavic]

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

 

[vu10758]

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?

 

[ponjavic]

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

 

[vu10758]

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?

 

[ponjavic]

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!

 

[vu10758]

Okay, thanks very much for your help tonight.