How Do You Calculate the Tension in the Top Rope of a Hanging Stoplight System?

[psycovic23]

http://mimesisprime.rightsidedown.com/homework.jpg

I'm having trouble with this problem...I need to figure out the tension in the top rope (the horizontal one). The diagonal bar is 7.5m long and weighs 8kg, and the thing that's supposed to be a stoplight is 12kg.

So far, I have to figure out the vertical and horizontal components of the hinge (A) and the tension of the rope. I've figured out 2 of the three equations, the ones for forces in the X and in the Y. I can't figure out the torque ones though...Assuming that we choose point A as the pivot point, what's the equation? I know you have a torque coming from the bar, (3.75*8kg*g), a torque from the stoplight (12kg*7.5m*9.8), but I don't what's countering that. The answers are: tension = 2.5 x 10^2, horizontal is 2.5 x 10^2, and vertical is 2.0 x 10^2.

 

[Gokul43201]

Okay, write down the equations you've got so far. One of them should tell you the vertical component of the reaction at the hinge.

As for the torque : what's countering it is the torque from the tension in the rope = T*3.8.

From this, you can find T.

With this value of T and the X-equation, you get the horizontal component.

 

[wais]

It seems like you're on the right track with your approach to this problem. In order to find the tension in the top rope, you will need to use the equations for forces in the X and Y directions and also consider the torque around point A as the pivot point.

To find the torque, you will need to consider the distance between the pivot point and the point where the force is applied. In this case, the force from the bar (3.75*8kg*g) is applied at a distance of 7.5m from the pivot point, while the force from the stoplight (12kg*7.5m*9.8) is applied at a distance of 12m from the pivot point.

In order to find the total torque, you will need to add these two torques together. This total torque will then be equal to the tension in the top rope (since the rope is acting as a force to counter the torques).

Once you have the total torque, you can set it equal to the torque equation (F*d*sin(theta)) and solve for the tension in the top rope.

I hope this helps and good luck with the problem!