Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 10.4, Problem 35P
Determine, g, which locates the centroidal axis z’ for the cross sectional area of the T-beam, and then find the moment of inertia about the z’ axis.
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A thin uniform rod of mass m and length 2r rests in a smooth hemispherical bowl of radius r. A
moment M
=
mgr
horizontal plane.
is applied to the rod. Assume that the bowl is fixed and its rim is in the
HINT: It will help you to find the length l of that portion of the rod that remains outside the
bowl.
M
2r
Ꮎ
a) How many degrees of freedom does this system have?
b) Write an equation for the virtual work in terms of the angle 0 and the motion of the
center of mass (TF)
c) Derive an equation for the variation in the position of the center of mass (i.e., Sŕƒ)
a. HINT: Use the center of the bowl as the coordinate system origin for the problem.
d) In the case of no applied moment (i.e., M = 0), derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation
e) In the case of an applied moment (i.e., M:
=
mgr
4
-) derive an equation that can be used to
solve for the equilibrium angle of the rod. DO NOT solve the equation.
f) Can the angle 0 and…
Solve this problem and show all of the work
Solve this problem and show all of the work
Chapter 10 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
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