Question

A uniform rod AB is of length l and weight 2W. It can turn freely about a smooth hinge at its upper end A. The rod is held in equilibrium by means of a horizontal force P applied at B, which is at a distance a from the vertical line through A. Find the value of P and show that the reaction at the hinge is W [(4l^2-3a^2)/(l^2-a^2)] ^1/2

Answer 1

Answer on Question #74175-Physics-Mechanics-Relativity

A uniform rod AB is of length I and weight 2W. It can turn freely about a smooth hinge at its upper end A. The rod is held in equilibrium by means of a horizontal force P applied at B, which is at a distance a from the vertical line through A. Find the value of P and show that the reaction at the hinge is W [(4I^2-3a^2)/(I^2-a^2)] ^1/2

Solution

$$P = T \sin \alpha = T \frac {a}{l}$$ $$W = T \cos \alpha = T \frac {\sqrt {1 ^ {2} - a ^ {2}}}{l}$$

Thus,

$$P = W \frac {a}{\sqrt {1 ^ {2} - a ^ {2}}}$$

The reaction at the hinge is

$$T = \frac {W}{\cos \alpha} = W \frac {l}{\sqrt {1 ^ {2} - a ^ {2}}}$$

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