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

Click here to show or hide the solution

$\Sigma F_x = 0$

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

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

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

Click here to show or hide the solution

$\Sigma F_x = 0$

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

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

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

$\theta = 33.56^\circ$ answer

Tags:

Add new comment
122696 reads

More Reviewers

Algebra	Structural Analysis
Plane Trigonometry	Engineering Mechanics
Spherical Trigonometry	Strength of Materials
Solid Geometry	Derivation of Formulas
Plane Geometry	General Engineering
Analytic Geometry	Reinforced Concrete Design
Integral Calculus	Fluid Mechanics and Hydraulics
Differential Calculus	Surveying and Transportation Engineering
Elementary Differential Equations	Timber Design
Advance Engineering Mathematics	Geotechnical Engineering
Engineering Economy