509_Dynamics 11ed Manual

509_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 17 Solution: h ⌠ 2 1⎤ ⎮ ⎡ ⎮ ⎢ 3⎥ ⎞ ⎮ ⎢r ⎛ x ⎟ ⎥ dx M= γπ ⎜ ⎮ ⎣ ⎝ h⎠ ⎦ ⌡ M = 0.412 slug 0 ⌠ ⎮ ⎮ ⎮ Ix = ⎮ ⌡ h 4 1⎤ ⎡ ⎢ 3⎥ 1 ⎞ ⎢r ⎛ x ⎟ ⎥ dx γπ ⎜ 2 ⎣ ⎝ h⎠ ⎦ Ix = 0.589 slug⋅ in 2 0 Ix kx = kx = 1.20 in M *Problem 17-8 Determine the moment of inertia of the ellipsoid with respect to the x axis and express the result in terms of the mass m of the ellipsoid. The material has a constant density ρ. Solution: a ⌠ ⎮ 2⎛ m = ⎮ ρ π b ⎜1 − ⎜ ⎮ ⎝ ⌡− a ρ= 2⎞ ⎟ dx = 4 a ρ π b2 2⎟ 3 a⎠ x 3m 4aπ b 2 a ⌠ 3m ⎮ 1 ⎡ 2⎛ ⎮ Ix = π ⎢b ⎜ 1 − 2⎮ 2⎢⎜ 4aπ b ⎣⎝ ⌡− a 2 ⎞⎤ 2 ⎟⎥ dx 2 ⎟⎥ a ⎠⎦ x Ix = 2 2 mb 5 Problem 17-9 Determine the moment of inertia of the homogeneous pyramid of mass m with respect to the z axis.The density of the material is ρ. Suggestion : Use a rectangular plate element having a volume of dV = (2x)(2y) dz. 507 ...
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