Solving Tension in Cables: 20 kg Speaker 2.5 m, 2 Cables 20°

[xgoddess210]

Homework Statement

A 20 kg loudspeaker is suspended 2.5 m below the ceiling by two cables that are each 20 degrees from vertical. What is the tension the cables?

Homework Equations

The Attempt at a Solution

I have no idea on what equation to use, considering we haven't even talked about tension at all in class. These problem seems simple but I don't know how to start it. I don't need the answer, just maybe some information on what I'm supposed to do with the information provided. Thank you in advance!

 

[aeroengineer]

Tension is a force. And these forces in this problem are in equilibrium.

Use vectors and trigonometry.

 

[swuster]

Drawing out the picture, you can see that for the loudspeaker to hang stationary, the downward pull of gravity must be counteracted by an equal upward force, which is the force of tension provided by the two cables. Note also that the two cables have tension in the x and y directions, with total tension given by $$F_T = \sqrt{F_T_x^2 + F_T_y^2}$$.

Because of this, $$2F_T_y = F_g$$, because both cables are exerting an equal upward force on the loudspeaker.

Once you've found the y-component of the tension, you can find the total tension in the cable by analyzing the right triangle made by the cable and its x- and y- components. In this case, $$F_T_y = \frac{F_T}{cos \theta}$$. With your value for the angle, you can now solve for the tension in the cable, which is identical for both cables due to the symmetry of the problem.

 

[xgoddess210]

Thank you! I appreciate your help!