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?
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).
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 F_{1} be the force of the left rope (20 degree angle), and F_{2} 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] : F_{1} sin[20] + F_{2} 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: F_{1} cos[20] - F_{2} cos[30] = 0 You can solve F_{1} and F_{2} from these equations, and check if any of the ropes will break.