697_Dynamics 11ed Manual

697_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 Given ⎛ vA ⎟ ⎛ ωx ⎞ ⎛ a ⎞ ⎛ 0 ⎟ ⎜⎞⎜ ⎟⎜⎟⎜⎞ ⎜ 0 ⎟ + ⎜ ωy ⎟ × ⎜ b ⎟ = ⎜ vB ⎟ ⎜ 0 ⎟ ⎜ ω ⎟ ⎝ −c ⎠ ⎜ 0 ⎟ ⎝ ⎠ ⎝ z⎠ ⎝⎠ ⎛ ωx ⎞ ⎛ a ⎞ ⎜ ⎟⎜ ⎟ ⎜ ωy ⎟ ⎜ b ⎟ = 0 ⎜ ω ⎟ ⎝ −c ⎠ ⎝ z⎠ ⎛ αx ⎞⎛ a ⎞ ⎜ ⎟⎜ ⎟ ⎜ αy ⎟⎜ b ⎟ = 0 ⎜ α ⎟ ⎝ −c ⎠ ⎝ z⎠ ⎤ ⎛ −aA ⎞ ⎛ α x ⎞ ⎛ a ⎞ ⎛ ωx ⎞ ⎡⎛ ωx ⎞ ⎛ a ⎞⎥ ⎛ 0 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ 0 ⎟ + ⎜ α y ⎟ × ⎜ b ⎟ + ⎜ ωy ⎟ × ⎢⎜ ωy ⎟ × ⎜ b ⎟⎥ = ⎜ aB ⎟ ⎜ 0 ⎟ ⎜ α ⎟ ⎝ −c ⎠ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎝ −c ⎠⎥ ⎜ 0 ⎟ ⎝ ⎠ ⎝ z⎠ ⎝ z ⎠ ⎣⎝ z ⎠ ⎦⎝⎠ ⎛ ωx ⎞ ⎜⎟ ⎜ ωy ⎟ ⎜ω ⎟ ⎜ z⎟ ⎜ αx ⎟ ⎜ ⎟ = Find ( ωx , ωy , ωz , α x , α y , α z , vB , aB) ⎜ αy ⎟ ⎜α ⎟ ⎜ z⎟ ⎜ vB ⎟ ⎜⎟ ⎝ aB ⎠ ⎛ ωx ⎞ ⎛ 1.33 ⎞ ⎜⎟⎜ ⎟ rad ⎜ ωy ⎟ = ⎜ 2.67 ⎟ ⎜ ω ⎟ ⎝ 3.33 ⎠ s ⎝ z⎠ ⎛ α x ⎞ ⎛ −21.11 ⎞ ⎜⎟⎜ ⎟ rad ⎜ α y ⎟ = ⎜ −2.22 ⎟ 2 ⎜ α ⎟ ⎝ −12.78 ⎠ s ⎝ z⎠ Problem 20-29 Rod AB is attached to collars at its ends by using ball-and-socket joints. If collar A moves along the fixed rod with speed vA, determine the angular velocity of the rod and the velocity of collar B at the instant shown. Assume that the rod’s angular velocity is directed perpendicular to the axis of the rod. Given: vA = 8 a = 8 ft ft s c = 6 ft d = 8 ft 695 vB = 3.00 m s aB = −47.5 m 2 s ...
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