Problem 309 | Equilibrium of Concurrent Force System | Engineering Mechanics Review at MATHalino

Problem 309
A cylinder weighing 400 lb is held against a smooth incline by means of the weightless rod AB in Fig. P-309. Determine the forces P and N exerted on the cylinder by the rod and the incline.

A cylinder supported by a boom and an incline

Solution 309

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$\Sigma F_H = 0$

$P \cos 25^\circ = N \sin 55^\circ$

$P = 0.9038N$

$\Sigma F_V = 0$

$P \sin 25^\circ + N \cos 55^\circ = 400$

$(0.9038N) \sin 25^\circ + N \cos 55^\circ = 400$

$0.9556N = 400$

$N = 418.60 \, \text{ lb}$ answer

$P = 0.9038(418.60)$

$P = 378.34 \, \text{ lb}$ answer

Another Solution (By Rotation of Axes)

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$\Sigma F_x = 0$

$P \cos 30^\circ = 400 \sin 55^\circ$

$P = 378.35 \, \text{ lb}$ (ok!)

$\Sigma F_y = 0$

$N = P \sin 30^\circ + 400 \cos 55^\circ$

$N = 378.35 \sin 30^\circ + 400 \cos 55^\circ$

$N = 418.60 \, \text{ lb}$ (ok!)

Another Solution (By Force Polygon)

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$\dfrac{P}{\sin 55^\circ} = \dfrac{N}{\sin 65^\circ} = \dfrac{400}{\sin 60^\circ}$

$P = 378.35 \, \text{ lb}$ (ok!)

$N = 418.60 \, \text{ lb}$ (ok!)

Problem 309 | Equilibrium of Concurrent Force System

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