633_Dynamics 11ed Manual

633_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics ⎛ω⎞ ⎜ ⎟ = Find ( ω , vA) ⎝ vA ⎠ Chapter 18 vA = 3.32 ft s ω = 2.21 rad s Problem 18-59 The end A of the garage door AB travels along the horizontal track, and the end of member BC is attached to a spring at C. If the spring is originally unstretched, determine the stiffness k so that when the door falls downward from rest in the position shown, it will have zero angular velocity the moment it closes, i.e., when it and BC become vertical. Neglect the mass of member BC and assume the door is a thin plate having weight W and a width and height of length L. There is a similar connection and spring on the other side of the door. Given: W = 200 lb b = 2 ft L = 12 ft θ = 15 deg a = 1 ft Solution: k=1 Guess lb ft d = 1 ft Given 2 b= 2 ⎛ L ⎞ + d2 − 2d⎛ L ⎞ cos ( θ ) ⎜⎟ ⎜⎟ ⎝2⎠ ⎝2⎠ ⎛ L ⎞ + 2 1 k ⎛ L + b − d⎞ ⎟ ⎜ ⎟ 2 ⎝2 ⎝2⎠ ⎠ 2 0 = −W⎜ ⎛k⎞ ⎜ ⎟ = Find ( k , d) ⎝d⎠ d = 4.535 ft k = 100.0 631 lb ft ...
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