202_Dynamics 11ed Manual

202_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Given Chapter 13 θ ⌠1 ⌠v ⎮ v dv = ⎮ g cos ( θ ) L dθ ⌡ ⌡0 0 v = Find ( v) v = 5.268 m s ⎛ v2 ⎞ ⎟ ⎝L⎠ TD = M g sin ( θ 1 ) + M⎜ TD = 104.1 N Problem 13-74 A ball having a mass M and negligible size moves within a smooth vertical circular slot. If it is released from rest at θ1, determine the force of the slot on the ball when the ball arrives at points A and B . Given: M = 2 kg θ = 90 deg θ 1 = 10 deg r = 0.8 m g = 9.81 m 2 s Solution: M g sin ( θ ) = M at At A at = g sin ( θ ) θ A = 90 deg ⎞ ⎛ ⌠θ A ⎜ ⎮ sin ( θ ) r dθ⎟ vA = 2g ⎜ ⌡θ ⎟ ⎝1 ⎠ ⎛ vA2 ⎞ ⎟ NA − M g cos ( θ A) = −M⎜ ⎝r⎠ ⎛ vA2 ⎞ ⎟ ⎝r⎠ NA = M g cos ( θ A) − M⎜ At B vB = NA = −38.6 N θ B = 180 deg − θ 1 ⎞ ⎛ ⌠θ B ⎜ ⎮ sin ( θ ) r dθ⎟ 2g ⎜ ⌡θ ⎟ ⎝1 ⎠ NB − M g cos ( θ B) ⎛ vB2 ⎞ ⎟ = −M⎜ ⎝r⎠ ⎛ vB2 ⎞ ⎟ NB = M g cos ( θ B) − M⎜ ⎝r⎠ NB = −96.6 N 200 ...
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