Chapter 12.6, Problem 53PPSE

Solution

To find: To find the weight of the stoplight.

The stoplight weighs 30 units.

Given information:

Given, when an object is not moving, all the forces acting on it must sum to 0. The object is said to be in equilibrium. Two cables of different lengths hold a stoplight over an intersection. The force vectors being applied along the two cables are $〈20,18〉$ and $〈-20,12〉$ The magnitude of each vector is measured in pounds. A third force vector in this situation is the force due to gravity, and its straight downward.

Calculation:

The resultant of the force vectors is given by:

  $\begin{array}{l}F=〈20,18〉+〈-20,12〉\\ F=〈20-20,18+12〉\\ F=〈0,30〉\end{array}$

The resultant of the force vectors is 30 units upwards.

For the object to be in equilibrium, the weight of the object needs to be 30 units downwards.

Hence, the stoplight weighs 30 units.

Conclusion:

The stoplight weighs 30 units.