495_Dynamics 11ed Manual

# 495_Dynamics 11ed Manual - ⎟ ⎟ ⎠ × P CP ⎛ ⎜ ⎜...

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Engineering Mechanics - Dynamics Chapter 16 v rel a rel v C a Ct Find v rel a rel , v C , a Ct , () = v rel v C 1.70 2.40 m s = a rel a Ct 5.09 0.00 m s 2 = v Cv v C sin 2 θ () cos 2 () 0 = a Cv a Ct sin 2 () cos 2 () 0 v C 2 r cos 2 () sin 2 () 0 + = v Cv 2.40 0.00 0.00 m s = a Cv 0.00 14.40 0.00 m s 2 = Problem 16-140 A ride in an amusement park consists of a rotating platform P , having constant angular velocity ω P and four cars, C , mounted on the platform, which have constant angular velocities CP measured relative to the platform. Determine the velocity and acceleration of the passenger at B at the instant shown. Given: P 1.5 rad s = r 0.75 m = CP 2 rad s = R 3m = Solution: v B 0 0 P R 0 0
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Unformatted text preview: ⎟ ⎟ ⎠ × P CP + ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ r ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ × + = v B 0.00 7.13 0.00 ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ m s = v B 7.13 m s = a B P ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ P ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ R ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ × ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ × P CP + ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ P CP + ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ r ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ × ⎡ ⎢ ⎢ ⎣ ⎤ ⎥ ⎥ ⎦ × + = a B 15.94 − 0.00 0.00 ⎛ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎠ m s 2 = a B 15.94 m s 2 = 493...
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