EXERCISE 4.6 Suppose the traffic light is hung so that the tensions T_(1) and T_(2) are both equal to 80.0N. Find the new angles they make with respect to the x-axis.(By symmetry, these angles will be the same.) ANSWER Bothangles are 38.7^circ .

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EXERCISE 4.6 Suppose the traffic light is hung so that the tensions T_(1) and T_(2) are both equal to 80.0N. Find the new angles they make with respect to the x-axis.(By symmetry, these angles will be the same.) ANSWER Bothangles are 38.7^circ .

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Answer 1

Both angles are 38.7 degrees.

Answer 2

This problem is about vector decomposition. The traffic light creates two tensions, T1 and T2, which are equal in this case. Each tension can be decomposed into two components: one along the x-axis and the other along the y-axis. The x-components of T1 and T2 balance each other out, so the system is in equilibrium in the x-direction. The y-components, however, do not balance each other out, which means there is a net force in the y-direction. This net force causes the system to rotate counterclockwise. The angle that the resultant tension makes with the x-axis can be found using trigonometric principles. Since the tensions are equal, the angles they make with the x-axis are also equal. This is due to the symmetry of the problem. The angle can be found using the formula tan(theta) = Fy/Fx, where Fy is the net force in the y-direction and Fx is the force in the x-direction. In this case, Fy = 0 (since the system is in equilibrium in the x-direction) and Fx = 80N (the tension in the ropes). Therefore, tan(theta) = 0/80 = 0, which means theta = 38.7 degrees.

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EXERCISE 4.6 Suppose the traffic light is hung so that the tensions T_(1) and T_(2) are both equal to 80.0N. Find the new angles they make with respect to the x-axis.(By symmetry, these angles will be the same.) ANSWER Bothangles are 38.7^circ .

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