766_Dynamics 11ed Manual

766_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 21 0 ⎞ ⎛ Ix' 0 0 ⎞ ⎛ 1 0⎞ 0 0 ⎛1 ⎜ ⎟⎜ ⎜ ⎟ ⎟ IG = 0 cos ( θ ) −sin ( θ ) ⎜ 0 Iy' 0 ⎟ 0 cos ( θ ) sin ( θ ) ⎜ ⎟ ⎜ ⎟ ⎝ 0 sin ( θ ) cos ( θ ) ⎠ ⎜ 0 0 Iz' ⎟ ⎝ 0 −sin ( θ ) cos ( θ ) ⎠ ⎝ ⎠ Guesses Ax = 1 N Az = 1 N Bx = 1 N Bz = 1 N α=1 rad 2 s Given ⎛ Ax ⎞ ⎛ Bx ⎞ ⎛ 0 ⎞ ⎜⎟⎜⎟⎜ ⎟ ⎜ 0 ⎟+⎜ 0 ⎟−⎜ 0 ⎟ =0 ⎜ Az ⎟ ⎜ Bz ⎟ ⎜ mc g ⎟ ⎠ ⎝⎠⎝⎠⎝ ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎛ Bx ⎟ ⎛ 0 ⎞ ⎛ Ax ⎞ ⎛ 0 ⎞ ⎛ 0 ⎞ ⎡ ⎛ 0 ⎞⎤ ⎜ ⎜⎟ ⎜ M ⎟ + ⎜ a ⎟ × 0 + ⎜ −a ⎟ × 0 = I ⎜ α ⎟ + ⎜ −ω ⎟ × ⎢I ⎜ −ω ⎟⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ G⎜ ⎟ ⎜ ⎟ ⎢ G⎜ ⎟⎥ ⎝ 0 ⎠ ⎝ 0 ⎠ ⎜ Bz ⎟ ⎝ 0 ⎠ ⎜ Az ⎟ ⎝ 0 ⎠ ⎝ 0 ⎠ ⎣ ⎝ 0 ⎠⎦ ⎝⎠ ⎝⎠ ⎛ Ax ⎞ ⎜⎟ ⎜ Az ⎟ ⎜ B ⎟ = Find ( A , A , B , B , α ) xzxz ⎜ x⎟ ⎜ Bz ⎟ ⎜⎟ ⎝α⎠ ⎛ Ax ⎞ ⎛ 15.97 ⎞ ⎜ ⎟=⎜ ⎟N ⎝ Bx ⎠ ⎝ −15.97 ⎠ α = −20.65 ⎛ Az ⎞ ⎛ 1.38 ⎞ ⎜ ⎟=⎜ ⎟ kN ⎝ Bz ⎠ ⎝ −1.09 ⎠ rad 2 s Problem 21-57 The uniform hatch door, having mass M and mass center G, is supported in the horizontal plane by bearings at A and B. If a vertical force F is applied to the door as shown, determine the components of reaction at the bearings and the angular acceleration of the door. The bearing at A will resist a component of force in the y direction, whereas the bearing at B will not. For the calculation, assume the door to be a thin plate and neglect the size of each bearing. The door is originally at rest. Given: M = 15 kg c = 100 mm F = 300 N d = 30 mm a = 200 mm e = 30 mm b = 150 mm g = 9.81 m 2 s 764 ...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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