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682_Dynamics 11ed Manual

682_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics θ = 30 deg c = 0.5 ft Solution: ⎛ b + a ⎞c r=⎜ ⎟ ⎝a⎠ Guesses ω2 = 1 Given Chapter 20 rad s 0 ⎛ ⎞ ⎜ a + b − 2r sin ( θ ) ⎟ rA = ⎜ ⎟ ⎝ 2r cos ( θ ) ⎠ rad α2 = 1 2 ay = 1 s ft 2 ft az = 1 s 2 s Enforce the no-slip constraints 0 ⎛ ⎞ 0⎞ ⎜ ⎟ ⎛⎟ ⎜ ⎜ ω2 cos ( θ ) ⎟ × ⎜ a ⎟ = 0 ⎜ ω + ω sin ( θ ) ⎟ ⎝ 0 ⎠ 2 ⎝z ⎠ 0 0 ⎡⎛ ⎞ ⎛0⎞ ⎛ ⎞⎤ 0 ⎞ ⎛ 0 ⎞ ⎢⎜ ⎟⎜⎟⎜ ⎟⎥ ⎛ ⎟ ⎜ ⎟ ⎜ ⎢⎜ α 2 cos ( θ ) ⎟ + ⎜ 0 ⎟ × ⎜ ω2 cos ( θ ) ⎟⎥ × ⎜ a ⎟ = ⎜ ay ⎟ ⎢⎜ ω' + α sin ( θ ) ⎟ ⎜ ωz ⎟ ⎜ ω + ω sin ( θ ) ⎟⎥ ⎝ 0 ⎠ ⎜ az ⎟ 2 2 ⎝⎠ ⎣⎝ z ⎠ ⎝ ⎠⎝z ⎠⎦ ⎛ ω2 ⎟ ⎜⎞ ⎜ α2 ⎟ ⎜ ⎟ = Find ( ω2 , α 2 , ay , az) ⎜ ay ⎟ ⎜ az ⎟ ⎝⎠ ω2 = −0.8 rad s α 2 = −1 rad 2 s Define terms 0 ⎛ ⎞ ⎜ ⎟ ω = ⎜ ω2 cos ( θ ) ⎟ ⎜ ω + ω sin ( θ ) ⎟ 2 ⎝z ⎠ 0 0 ⎛ ⎞ ⎛0⎞ ⎛ ⎞ ⎜ ⎟⎜⎟⎜ ⎟ α = ⎜ α 2 cos ( θ ) ⎟ + ⎜ 0 ⎟ × ⎜ ω2 cos ( θ ) ⎟ ⎜ ω' + α sin ( θ ) ⎟ ⎜ ωz ⎟ ⎜ ω + ω sin ( θ ) ⎟ 2 2 ⎝z ⎠ ⎝ ⎠⎝z ⎠ Calculate velocity and acceleration. vA = ω × rA ⎛ −1.80 ⎞ ⎜ ⎟ ft vA = 0.00 ⎜ ⎟s ⎝ 0.00 ⎠ aA = α × rA + ω × ( ω × rA) ⎛ −2.25 ⎞ ⎜ ⎟ ft aA = −0.72 ⎜ ⎟2 ⎝ −0.831 ⎠ s 680 ...
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