Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
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Chapter 10.4, Problem 39P
To determine
The moment of inertia of the beam about the
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Problem 2 (40 Points)
A particle of mass m is embedded at a distance a from the center of a massless circular disk of
radius r. The disk rolls without slipping down a plane inclined at an angle a with the horizontal.
A horizontal force of Ễ = −Fxî + Fyĵ resists motion of the disk down the plane by pushing on
the disk at the axle that runs through the center of the disk.
a) Find the kinetic energy T. (10 points)
b) Find the potential energy V. (10 points)
c) Write a position vector to the axle at the center of the wheel in terms of x and y. (10
points)
d) Using virtual work, find the applied force Q₁ that would go in Lagrange's Equations. DO
NOT WRITE OUT OR SOLVE LAGRANGES'S EQUATIONS. (10 points)
x
r
m
e
10
g
F
α
HINTS
1) Consider using the STATIONARY red xy frame a reference frame from which to draw
vectors
2) The red xy system DOES NOT move. It is stationary.
3) Consider that the disk rolls a distance of re down the ramp
Draw a counter balance circuit of a vertical cylinder.
using counter balance valve and external load.
Chapter 10 Solutions
Engineering Mechanics: Statics
Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Determine the moment of inertia of the shaded area...Ch. 10.3 - Prob. 1PCh. 10.3 - Prob. 2PCh. 10.3 - Prob. 3PCh. 10.3 - Prob. 4PCh. 10.3 - Prob. 5PCh. 10.3 - Prob. 6P
Ch. 10.3 - Prob. 7PCh. 10.3 - Prob. 8PCh. 10.3 - Determine the moment of inertia of the area about...Ch. 10.3 - Solve the problem in two ways, using rectangular...Ch. 10.3 - Prob. 11PCh. 10.3 - Prob. 12PCh. 10.3 - Prob. 13PCh. 10.3 - Prob. 14PCh. 10.3 - Prob. 15PCh. 10.3 - Prob. 16PCh. 10.3 - Prob. 17PCh. 10.3 - Prob. 18PCh. 10.3 - Prob. 19PCh. 10.3 - Prob. 20PCh. 10.3 - Prob. 21PCh. 10.3 - Prob. 22PCh. 10.3 - Prob. 23PCh. 10.3 - Prob. 24PCh. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine me moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the composite...Ch. 10.4 - Determine the moment of inertia of the composite...Ch. 10.4 - Prob. 27PCh. 10.4 - Prob. 28PCh. 10.4 - Prob. 29PCh. 10.4 - Prob. 30PCh. 10.4 - Prob. 31PCh. 10.4 - Prob. 32PCh. 10.4 - Prob. 33PCh. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Determine, g, which locates the centroidal axis z...Ch. 10.4 - Prob. 36PCh. 10.4 - Prob. 37PCh. 10.4 - Prob. 38PCh. 10.4 - Prob. 39PCh. 10.4 - Prob. 41PCh. 10.4 - Determine the moment of inertia of the beams...Ch. 10.4 - Prob. 43PCh. 10.4 - Prob. 44PCh. 10.4 - Determine the distance x to the centroid C of the...Ch. 10.4 - Determine the moment of inertia of the area about...Ch. 10.4 - Determine the moment of inertia of the area about...Ch. 10.4 - Prob. 50PCh. 10.4 - Prob. 51PCh. 10.4 - Determine the moment of inertia of the...Ch. 10.4 - Determine the moment of inertia of the...Ch. 10.7 - Determine the product of inertia of the thin strip...Ch. 10.7 - Prob. 55PCh. 10.7 - Determine the product of inertia of the shaded...Ch. 10.7 - Prob. 57PCh. 10.7 - Determine the product of inertia of the shaded...Ch. 10.7 - Prob. 59PCh. 10.7 - Prob. 60PCh. 10.7 - Prob. 62PCh. 10.7 - Determine the product of inertia for the beams...Ch. 10.7 - Prob. 64PCh. 10.7 - Prob. 65PCh. 10.7 - Determine the product of inertia of the cross...Ch. 10.7 - Prob. 67PCh. 10.7 - For the calculation, assume all comers to be...Ch. 10.7 - Prob. 69PCh. 10.7 - Prob. 70PCh. 10.7 - Prob. 71PCh. 10.7 - Prob. 72PCh. 10.7 - Prob. 73PCh. 10.7 - Prob. 74PCh. 10.7 - Prob. 75PCh. 10.7 - Prob. 76PCh. 10.7 - Prob. 77PCh. 10.7 - Prob. 78PCh. 10.7 - Prob. 79PCh. 10.7 - Prob. 80PCh. 10.7 - Prob. 81PCh. 10.7 - Prob. 82PCh. 10.7 - using Mohrs circle.Ch. 10.8 - Determine the moment of inertia of the thin ring...Ch. 10.8 - The material has a constant density .Ch. 10.8 - Prob. 86PCh. 10.8 - Determine the radius of gyration kx of the...Ch. 10.8 - The material has a constant density .Ch. 10.8 - Hint: For integration, use thin plate elements...Ch. 10.8 - Prob. 90PCh. 10.8 - Prob. 91PCh. 10.8 - Determine the moment of inertia Iy. The specific...Ch. 10.8 - Prob. 93PCh. 10.8 - The total mass of the solid is 1500 kg.Ch. 10.8 - Prob. 95PCh. 10.8 - Prob. 96PCh. 10.8 - Determine the location y of the center of mass G...Ch. 10.8 - Prob. 98PCh. 10.8 - 15 lb. and 20 lb, respectively, determine the mass...Ch. 10.8 - The density of the material is 7.85 Mg/m3.Ch. 10.8 - The material has a density of 200kg/m3. Prob....Ch. 10.8 - The pendulum consists of a plate having a weight...Ch. 10.8 - Prob. 103PCh. 10.8 - The material has a density of 200kg/m3.Ch. 10.8 - Prob. 105PCh. 10.8 - Determine its mass moment of inertia about the y...Ch. 10.8 - Prob. 107PCh. 10.8 - Prob. 108PCh. 10.8 - Prob. 109PCh. 10.8 - Determine the moment of inertia for the shaded...Ch. 10.8 - Prob. 111RPCh. 10.8 - Determine the product of inertia of the shaded...Ch. 10.8 - Determine the area moment of inertia of the...Ch. 10.8 - Determine the area moment of inertia of the shaded...Ch. 10.8 - Determine the moment of inertia for the shaded...Ch. 10.8 - Prob. 117RPCh. 10.8 - Prob. 119RP
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