Suspended steel beam

tigerseye

I'm having problems with what equation to use for this question:
A 1000 kg steel beam is supported by two ropes. Each rope has a maximum sustained tension of 6000N. Does either rope break?

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Galileo

Draw a free body diagram.
The two tensions are directed along the ropes.
The sum of the tensions is directed upwards and has magnitude F=mg (m=mass of the beam).

xepma

Well, the weight causes a force of roughly 10*1000 = 10000 [N] on both ropes combined. But because of different angles, the forces caused by the ropes will not be the same. Let F₁ be the force of the left rope (20 degree angle), and F₂ the other force.

You know that the forces will have to keep the weight up, so the vertical components together must add up to 10000 [N] :

F₁ sin[20] + F₂ sin[30] = 10000

Now the horizontal components will be directed in opposite direction, and will, because of that, have to be of equal size. So:

F₁ cos[20] - F₂ cos[30] = 0

You can solve F₁ and F₂ from these equations, and check if any of the ropes will break.