Question

ements Constants ents SOLUTION We will look at an example where several forces are acting on an object, but in this case the forces are not all along the same axis. As shown in (Figure 1), a car engine with weight to hangs from a chain that is linked at point to two other chains, one fastened to the ceiling and the other to the wall. Find the tension in each of the three chains, assuming that is given and the wolghts of the chains themselves are negligible ons Figure < 1 of 3 SET UP (Figure 2) is our free body diagram for the engine. Without further ceremony, we can conclude that to (Because we ignore the weights of the chains, the tension is the same throughout the length of each chain.) The horizontal and slanted chains do not exert forces on the engine itself because they are not attached to it, but they do exert forces on the ring point O), where the three chains join. So let's consider the ning as a particle in equilibrium; the weight of the ring itself is negligible. In our free body diagram for the ring (Figure 3), we have three forces T1, T), and T), their directions are specified by the vectors in the diagram. We add any coordinate system and resolve the force with magnitude Tinto its x and y components. Note that the downward force with magnitude of the chain acting on the ring and the upward force with magnitude 7 of the chain acting on the engine are not an action-reaction pair. SOLVE We now apply the equilibrium conditions for the ring, writing separate equations for the and y components. (Note that and y components are never added together in a single equation) We find that ΣF, = 0, Tj cos 60° +(-T) = 0 ΣF, = 0, Ty sin 60° +(-)=0 Because Tw, we can rewrite the second equation as 0 T aces T = 1.155 to ations

Answer 1

46го, 1 cosus°+(-T2 ) =o Та - TimJ4+ (- Т? кого Tz Sin 450+ (-Т) 20 T, г 17Sm45 3 = 5, but The w = 3 100 Та 31x10 paly B is T, — Ta - 31 Хіод 2 palt A 2 past ci T37 а т = 44x10°