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468_Dynamics 11ed Manual

468_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 16 ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ L cos ( θ ) ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ L cos ( θ ) ⎞⎤ ⎛ aB ⎟ ⎜ ⎟ ⎜⎞ ⎜ 0 ⎟ × ⎜ −L sin ( θ ) ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ −L sin ( θ ) ⎟⎥ = ⎜ 0 ⎟ ⎜ −aA ⎟ + ⎜ ⎟ ⎢ ⎜ ⎟⎥ ⎜ 0 ⎟ ⎜ α ⎟ ⎝ 0 ⎠ ⎜ ω ⎟ ⎣⎜ ω ⎟ ⎝ 0 ⎠⎦ ⎜ 0 ⎟ ⎝⎠ ⎝⎠ ⎝ ⎠⎝⎠ ⎝⎠ ⎛ω⎞ ⎜⎟ ⎜ vB ⎟ = Find ( ω , v , α , a ) B B ⎜α ⎟ ⎜⎟ ⎝ aB ⎠ ω = 1.00 rad vB = 8.66 s α = −0.332 rad 2 ft s aB = −7.88 s ft 2 s *Problem 16-108 The rod of length rAB slides down the inclined plane, such that when it is at B it has the motion shown. Determine the velocity and acceleration of A at this instant. Given: ft rAB = 10 ft vB = 2 rCB = 4 ft θ = 60 deg aB = 1 s ft 2 s Solution: Guesses Given ω=1 rad s α=1 rad 2 vA = 1 s ft s aA = 1 ft 2 φ = 1 deg s rAB sin ( θ − φ ) = rCB sin ( θ ) ⎛ vB ⎞ ⎛ 0 ⎞ ⎛ −rAB cos ( φ ) ⎞ ⎛ vA cos ( θ ) ⎞ ⎜⎟ ⎜ ⎟⎜ ⎟ ⎜ 0 ⎟ + ⎜ 0 ⎟ × ⎜ rAB sin ( φ ) ⎟ = ⎜ −vA sin ( θ ) ⎟ ⎜ 0 ⎟ ⎜ω⎟ ⎜ ⎟⎜ ⎟ ⎝⎠⎝⎠⎝ 0 0 ⎠⎝ ⎠ ⎤ ⎛ aB ⎟ ⎛ 0 ⎞ ⎛ −rAB cos ( φ ) ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ −rAB cos ( φ ) ⎞⎥ ⎛ aA cos ( θ ) ⎞ ⎜⎞ ⎜ ⎟ ⎢ ⎜ ⎟⎜ ⎟ ⎜ 0 ⎟ × ⎜ r sin ( φ ) ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ r sin ( φ ) ⎟⎥ = ⎜ −a sin ( θ ) ⎟ ⎜ 0⎟+ AB AB A ⎜ 0 ⎟ ⎜α ⎟ ⎜ ⎟ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎜ ⎟⎥ ⎜ ⎟ ⎝ ⎠⎝⎠⎝ 0 0 0 ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎝ ⎠⎦ ⎝ ⎠ 466 ...
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