508_Dynamics 11ed Manual

508_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 17 Solution: h ⌠ ⎛ x r2 ⎞ ⎮ ⎟ dx M = ⎮ ρ π⎜ ⎝h⎠ ⌡ M = 15.708 kg 0 ⌠ ⎮ Ix = ⎮ ⎮ ⌡ h 2⎞ ⎛ xr 1 ρπ⎜ 2 ⎝h 2 ⎟ dx ⎠ Ix = 0.052 kg⋅ m 2 0 Ix kx = kx = 57.7 mm M Problem 17-6 Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density ρ. Solution: a ⌠ ⎮ 2⎛ m = ⎮ ρ π b ⎜1 − ⎜ ⎮ ⎝ ⌡0 2⎞ ⎟ dx = 2 a ρ π b2 2⎟ 3 a⎠ x ρ= 3m 2aπ b 2 a ⌠ 3m ⎮ 1 ⎡ 2 ⎛ ⎮ Ix = π ⎢b ⎜ 1 − 2⎮ 2 ⎢ ⎜ 2aπ b ⎣⎝ ⌡0 2 ⎞⎤ 2 ⎟⎥ dx 2 ⎟⎥ a ⎠⎦ x Ix = Problem 17-7 Determine the radius of gyration kx of the body. The specific weight of the material is γ. Given: γ = 380 lb ft 3 h = 8 in r = 2 in 506 2 2 mb 5 ...
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