Problem 310 - 311 | Equilibrium of Concurrent Force System | Engineering Mechanics Review at MATHalino

Required Force to Hold the Box in a Smooth Plane - Equilibrium of Force System

Problem 310
A 300-lb box is held at rest on a smooth plane by a force P inclined at an angle θ with the plane as shown in Fig. P-310. If θ = 45°, determine the value of P and the normal pressure N exerted by the plane.

Block supported by a force in the incline

Solution 310

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$\Sigma F_x = 0$

$P \cos \theta = W \sin 30^\circ$

$P \cos 45^\circ = 300 \sin 30^\circ$

$P = 212.13 \, \text{ lb}$ answer

$\Sigma F_y = 0$

$N = P \sin \theta + W \cos 30^\circ$

$N = 212.13 \sin 45^\circ + 300 \cos 30^\circ$

$N = 409.81 \, \text{ lb}$ answer

Problem 311
If the value of P in Fig. P-310 is 180 lb, determine the angle θ at which it must be inclined with the smooth plane to hold 300-lb box in equilibrium.

Solution 311

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$\Sigma F_x = 0$

$P \cos \theta = W \sin 30^\circ$

$180 \cos \theta = 300 \sin 30^\circ$

$\cos \theta = \frac{5}{6}$

$\theta = 33.56^\circ$ answer

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