Question

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end
and supported by a cable which makes an angle of 30º with the rod at its other end.
Calculate the tension in the cable and the force exerted by the hinge.

Answer 1

Question #72843, Physics / Mechanics | Relativity

A horizontal rod with a mass of $10\mathrm{kg}$ and length $12\mathrm{m}$ is hinged to a wall at one end and supported by a cable, which makes an angle of $30{}^{\circ}$ with the rod at its other end. Calculate the tension in the cable and the force exerted by the hinge.

Solution

The net moment around the hinge is zero.

$$\begin{array}{l} \sum M = 0; \\ - 1 0 \times \frac {1 2}{2} \times g + T \sin 3 0 {}^ {\circ} \times 1 0 = 0; \\ T = \frac {6 0 g}{1 0 \times \sin 3 0 {}^ {\circ}} = 1 2 g = 1 1 7. 7 2 \mathrm {N} \\ \sum F _ {x} = 0; \\ R _ {x} = T \cos 6 0 {}^ {\circ}; \\ R _ {x} = 1 1 7. 7 2 \times \cos 6 0 {}^ {\circ} = 5 8. 8 6 \mathrm {N} \\ \sum F _ {y} = 0; \\ R _ {y} + T \sin 3 0 {}^ {\circ} = m g; \\ R _ {y} = m g - T \sin 3 0 {}^ {\circ}; \\ R _ {y} = 1 2 \times 9. 8 1 - 1 1 7. 7 2 \times \sin 3 0 {}^ {\circ} = 5 8. 8 6 \mathrm {N} \\ R = \sqrt {R _ {x} ^ {2} + R _ {y} ^ {2}} = \sqrt {2 \times 5 8 . 8 6 ^ {2}} = 8 3. 2 4 \mathrm {N} \\ \end{array}$$

Answer: tension 117.72 N, the force exerted by the hinge 83.24 N.

Answer provided by https://www.AssignmentExpert.com