Question

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

Answer 1

Question #81311, 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.

$$\sum M = 0$$ $$- 1 0 \frac {1 2}{2} g + T \sin 3 0 (1 0) = 0$$

The tension in the cable:

$$T = 1 2 g = 1 1 8 N.$$ $$\sum F _ {x} = 0 \rightarrow R _ {x} = T \cos 6 0$$ $$R _ {x} = 1 1 8 \cos 6 0 = 5 8. 8 6 N.$$ $$\sum F _ {y} = 0 \rightarrow R _ {y} + T \sin 3 0 = m g$$ $$R _ {y} = 1 2 (9. 8) - 1 1 8 \sin 3 0 = 5 8. 8 6 N$$

The force exerted by the hinge:

$$R = \sqrt {5 8 . 8 6 ^ {2} + 5 8 . 8 6 ^ {2}} = 8 3 N.$$

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