700_Dynamics 11ed Manual

700_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics ⎛ ωx ⎞ ⎛ −0.440 ⎞ ⎜⎟⎜ ⎟ rad ⎜ ωy ⎟ = ⎜ 0.293 ⎟ ⎜ ω ⎟ ⎝ −0.238 ⎠ s ⎝ z⎠ Chapter 20 ⎛ α x ⎞ ⎛ 0.413 ⎞ ⎜⎟⎜ ⎟ rad ⎜ α y ⎟ = ⎜ 0.622 ⎟ 2 ⎜ α ⎟ ⎝ −0.000 ⎠ s ⎝ z⎠ ⎛ −2.824 ⎞ ⎜ ⎟ ft vBv = 3.765 ⎜ ⎟s ⎝0⎠ Problem 20-31 Consider again Example 20.5. The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have the angular motions shown. Also, a collar C has velocity vC and acceleration aC along the rod. Determine the velocity and acceleration of the collar at this instant. Solve such that the x, y, z axes move with curvilinear translation, Ω = 0, in which case the collar appears to have both an angular velocity Ωxyz = ω1 + ω2 and radial motion. Given: ω1 = 4 rad s vCB = 3 m s ω2 = 5 rad s aCB = 2 m ω'1 = 1.5 2 s rad 2 a = 0.5 m s ω'2 = −6 rad 2 b = 0.2 m s Solution: ⎛ ω1 ⎟ ⎛ 0 ⎞ ⎜ ⎞⎜⎟ vB = ⎜ 0 ⎟ × 0 ⎜⎟ ⎜ 0 ⎟ ⎝ −a ⎠ ⎝⎠ ⎛0⎞ ⎜ ⎟m vB = 2 ⎜⎟s ⎝0⎠ ⎛ ω'1 ⎞ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎡⎛ ω1 ⎟ ⎛ 0 ⎞⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎞ ⎢⎜ ⎞ ⎜ ⎟⎥ aB = ⎜ 0 ⎟ × 0 + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × 0 ⎥ ⎜⎟ ⎜⎟ ⎜ 0 ⎟ ⎝ −a ⎠ ⎜ 0 ⎟ ⎢⎜ 0 ⎟ ⎝ −a ⎠⎥ ⎝⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ ⎞ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎛ 0 ⎞ ⎜ ⎟⎜ ⎜⎟ vC = vB + ⎜ vCB ⎟ + ⎜ 0 ⎟ × b ⎜⎟ ⎜ 0 ⎟ ⎜ω ⎟ ⎝0⎠ ⎝ ⎠ ⎝ 2⎠ ⎛ −1.00 ⎞ ⎜ ⎟m vC = 5.00 ⎜ ⎟s ⎝ 0.80 ⎠ 698 ⎛0⎞ ⎜ ⎟m aB = 0.75 ⎜ ⎟2 ⎝ 8 ⎠s ...
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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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