REMARKS It's very easy to make sign errors in this kind of problem. One way to avoid them is to always measure the angle of a vector from the positive x-direction. The trigonometric functions of the angle will then automatically give the correct signs for the components. For example, T, makes an angle of 1800 - 370 = 1430 with respect to the positive x-axis, and its x-component, I, cos 1430, is negative, as it should be. QUESTION Which of these would increase if a second traffic light were attached to the first? Assume the cables do not change their lengths. (Select all that apply.) O the angle of the cable with tension I 1 Oithe tension I 1 the tension I 2 O the angle of the cable with tension I 2 PRACTICE IT Use the worked example above to help you solve this problem. A traffic light weighing 1.18 x 10- N hangs from a vertical cable tied to two other cables that are fastened to a support, as shown in Figure (a). The upper cables make angles of 8, = 36.50 and 82 = 53.50 with the horizontal. Find the tension in each of the three cables. X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N X Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. N EXERCISE HINTS: GETTING STARTED | I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. Suppose the traffic light is hung so that the tensions , and 7, are both equal to 76 N. Find the new angles they make with respect to the x-axis. (By symmetry, these angles will be the same. ) X The correct answer is not zero.GOAL Use the second law in an equilibrium problem requiring two free-body diagrams. PROBLEM A traffic light weighing 1.00 x 102 N hangs from a vertical cable tied to two other cables that are fastened to a support. as in gure {a}. The upper cables make angles of 310 and 53.0\" with the horizontal. Find the tension in each of the three cables. (b) {aj A traffic light suspended by cables. [b] A freebody diagram for the traffic light. [c] A freebody diagram for the knot joining the cables. 6) STRATEGY There are three unknowns, so we need to generate three equations relating them, which can then be solved. lCline equation can be obtained by applying Newton's second law to the traffic light, which has forces in the Jr-direction only. Two more equations can be obtained by applying the second law to the knot joining the cables-one equation from the x-component and one equation from the 3:- component. SOLUTION Find 33 from figure (b)I using the ER 2 D > I - F = 0 condition of equilibrium. 3 Using gure (c), resolve all three Force :c- Component ur-Component tension forces into components and T1 ;7'l cos 310 I1 sin 3?.00 construct a table for convenience. T2 I2 cos 5330 32 sin 53.0.3 T3 0 -1.o0 x 1D2 N f-'ipply the conditions for equilibrium to (1) EFX = -'1"1 cos 310 + T2 cos 53.00 the knot, using the components in the = 0 t bl . . . a e (2) EFF = T1 Sin 37.00 + T2 5m. 53.00 1.oo x 102 N U ' {I There are two equations and two L. _ 3.1 If cos 3?.0 1\" _ 3.1 If 0.?991' _ 1.331