Question

A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support, as in Figure 5.10a. The upper cables make angles of 37.0° and 53.0° with the horizontal. These upper cables are not as strong as the vertical cable, and will break if the tension in them exceeds 100 N. Will the traffic light remain hanging in this situation, or will one of the cables break

Answer 1

Forces according to Newton's second law along x-axis (which looks to the right):

$$-T_1\text{ cos}37^\circ+T_2\text{ cos}53^\circ=0,$$

Along y-axis:

$$T_1\text{ sin}37^\circ+T_2\text{ sin}53^\circ-mg=0.$$

Solve for tension in cable 1 and cable 2:

$$T_2=97.4\text{ N},\\ \space\\ T_1=73.4\text{ N}.$$