709_Dynamics 11ed Manual

709_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 rad s ω1 = 8 ω'1 = 12 rad 2 s θ = 30 deg a=2 ft 2 s b = 0.8 ft Solution: ⎞ ⎛ 0 ⎞ ⎛0⎟ ⎛ 0 ⎞ ⎜ cos ( θ ) ⎟ + ⎜ 0 × ⎜ b cos ( θ ) ⎟ vC = v ⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ −sin ( θ ) ⎠ ⎜ ω1 ⎟ ⎝ −b sin ( θ ) ⎠ ⎝⎠ ⎞ ⎞ ⎤ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ 0 ⎟ ⎡⎛ 0 ⎟ ⎛ 0 ⎞⎥ ⎜ cos ( θ ) ⎟ + ⎜ 0 ⎟ × ⎜ b cos ( θ ) ⎟ + ⎜ 0 × ⎢⎜ 0 × ⎜ b cos ( θ ) ⎟ ... aC = a ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ ω'1 ⎟ ⎝ −b sin ( θ ) ⎠ ⎜ ω1 ⎟ ⎢⎜ ω1 ⎟ ⎝ −b sin ( θ ) ⎠⎥ ⎝ −sin ( θ ) ⎠ ⎝ ⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ ⎞ ⎛0⎟ ⎛ 0 ⎞ ⎜ ⎜ ⎟ + 2⎜ 0 ⎟ × v cos ( θ ) ⎜ ⎟ ⎜ ω1 ⎟ ⎝ −v sin ( θ ) ⎠ ⎝⎠ ⎛ −5.54 ⎞ ⎜ ⎟ ft vC = 5.20 ⎜ ⎟s ⎝ −3.00 ⎠ ⎛ −91.45 ⎞ ⎜ ⎟ ft aC = −42.61 ⎜ ⎟2 ⎝ −1.00 ⎠ s Problem 20-41 At the instant shown, the arm OA of the conveyor belt is rotating about the z axis with a constant angular velocity ω1, while at the same instant the arm is rotating upward at a constant rate ω2. If the conveyor is running at a constant rate r' = v, determine the velocity and acceleration of the package P at the instant shown. Neglect the size of the package. Given: ω1 = 6 rad s v=5 ft s 707 ...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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