Question

Shelf in equilibrium
A uniform shelf of weight 20 N and of width 0.6 m is hinged horizontally to a vertical wall and suspended by a cable as shown in the figure. What is the tension in the cable?

Answer 1

Answer on Question #50119 - Physics - Mechanics - Kinematics - Dynamics

Shelf in equilibrium

A uniform shelf of weight $W = 20 \, \text{N}$ and of width $l = 0.6 \, \text{m}$ is hinged horizontally to a vertical wall and suspended by a cable as shown in the figure. What is the tension $T$ in the cable?

Solution:

Since the shelf is in equilibrium, according to the principle of moments we obtain

$$W \cdot \frac {l}{2} = T \sin \theta \cdot l$$

Therefore

$$T = \frac {W}{2 \sin \theta}$$

Answer: $\frac{W}{2\sin\theta}$