112_Dynamics 11ed Manual

112_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 12 0 = r' sin ( θ ) + rθ' cos ( θ ) −v = r' cos ( θ ) − rθ' sin ( θ ) ⎛r⎞ ⎜ r' ⎟ = Find ( r , r' , θ' ) ⎜⎟ ⎝ θ' ⎠ r = 115.47 ft r' = −40 ft θ' = 0.6 s rad s Problem 12-155 For a short distance the train travels along a track having the shape of a spiral, r = a/θ. If it maintains a constant speed v, determine the radial and transverse components of its velocity when θ = θ1. a = 1000 m Given: m θ1 = 9 s π 4 rad θ = θ1 Solution: r= v = 20 a r' = θ −a θ vθ θ' = 2 ⎛ a2 a2 ⎟ 2 ⎞ v = r' + r θ' = ⎜ + θ' ⎜ θ4 θ2 ⎟ ⎝ ⎠ 2 θ' 2 r= a 1+θ 2 2 a vr = −2.802 vθ = 19.803 θ 2 θ' m vθ = rθ' −a r' = θ vr = r' 2 2 m s s *Problem 12-156 For a short distance the train travels along a track having the shape of a spiral, r = a / θ. If the angular rate θ' is constant, determine the radial and transverse components of its velocity and acceleration when θ = θ1. Given: a = 1000 m Solution: θ' = 0.2 rad θ = θ1 r= a θ r' = −a θ 2 θ' r'' = s 2a 2 θ' θ 3 110 θ1 = 9 π 4 ...
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