Traffic Light Static Tension

Solution

The free-body diagram for the traffic light must show three forces acting on it:

1. Gravitational force $\vec{F}_g$: Acts vertically downward with magnitude $F_g = m \cdot g = 100 \cdot 9.81 = 981\,\mathrm{N}$.

2. Tension $\vec{T}_1$: Acts along the left rope. Since the rope makes an angle $\theta_1 = 39^\circ$ with the horizontal ceiling, the tension vector points upward and to the left at an angle of $180^\circ - 39^\circ = 141^\circ$ from the positive $x$-axis (or equivalently, $39^\circ$ above the negative $x$-axis).

3. Tension $\vec{T}_2$: Acts along the right rope. Since the rope makes an angle $\theta_2 = 41^\circ$ with the horizontal ceiling, the tension vector points upward and to the right at an angle of $41^\circ$ from the positive $x$-axis.

The correct free-body diagram shows:

• $\vec{F}_g$ pointing straight down (at $270^\circ$)
• $\vec{T}_1$ upward and to the left, making $39^\circ$ with the horizontal)
• $\vec{T}_2$ upward and to the right, making $41^\circ$ with the horizontal)