712_Dynamics 11ed Manual

712_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 20 ⎛ 0 ⎞ ⎛ b ⎞ ⎛ 0 ⎟ ⎡⎛ 0 ⎟ ⎛ b ⎞⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎞ ⎢⎜ ⎞ ⎜ ⎟⎥ aP = ⎜ 0 ⎟ × c + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × c ⎥ ... ⎜⎟ ⎜⎟ ⎜ ω'1 ⎟ ⎝ 0 ⎠ ⎜ ω1 ⎟ ⎢⎜ ω1 ⎟ ⎝ 0 ⎠⎥ ⎝⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ ω'2 ⎞ ⎛ ⎛ ω2 ⎞ ⎡⎛ ω2 ⎞ 0 0 ⎞⎤ ⎜ ⎟ ⎛ ⎞ ⎜ ⎟ ⎢⎜ ⎟ ⎛ ⎟⎥ ⎜ −r ⎟ + 0 × 0 × ⎜ −r + ⎜ ω1ω2 ⎟ × ⎜ ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ ω' ⎟ ⎝ 0 ⎠ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎝ 0 ⎠⎥ ⎝ 1 ⎠ ⎣⎝ 1 ⎠ ⎦ ⎝ 1⎠ ⎛ −41.00 ⎞ ⎜ ⎟ ft aP = −17.50 ⎜ ⎟2 ⎝ −0.50 ⎠ s *Problem 20-44 At a given instant, the crane is moving along the track with a velocity vCD and acceleration aCD. Simultaneously, it has the angular motions shown. If the trolley T is moving outwards along the boom AB with a relative speed vr and relative acceleration ar, determine the velocity and acceleration of the trolley. Given: ω1 = 0.5 ω2 = 0.4 vCD = 8 vr = 3 rad s ω'1 = 0.8 rad s ω'2 = 0.6 m s aCD = 9 m s rad 2 s rad 2 s m 2 s ar = 5 m 2 l =3m s Solution: ⎞ ⎛ −vCD ⎟ ⎜ vA = ⎜ 0 ⎟ ⎜0⎟ ⎝ ⎠ ⎛0⎞ ⎜⎟ r= l ⎜⎟ ⎝0⎠ ⎞ ⎛ −aCD ⎟ ⎜ aA = ⎜ 0 ⎟ ⎜0⎟ ⎝ ⎠ vrel ⎛0⎞ ⎜⎟ = ⎜ vr ⎟ ⎜0⎟ ⎝⎠ ⎛ ω2 ⎞ ⎜⎟ ω=⎜0⎟ ⎜ω ⎟ ⎝ 1⎠ arel 710 ⎛0⎞ ⎜⎟ = ⎜ ar ⎟ ⎜0⎟ ⎝⎠ ⎛ ω'2 ⎞ ⎜ ⎟ α = ⎜ ω1 ω2 ⎟ ⎜ ω' ⎟ ⎝ 1⎠ ...
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