345_Physics ProblemsTechnical Physics

345_Physics ProblemsTechnical Physics - Chapter 11 P11.54...

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Chapter 11 347 P11.54 For the cube to tip over, the center of mass (CM) must rise so that it is over the axis of rotation AB. To do this, the CM must be raised a distance of a 21 ej . ∴− = Mga I 1 2 2 cube ω From conservation of angular momentum, 4 3 8 3 2 1 2 8 3 4 32 1 2 22 2 a mv Ma mv Ma Ma m v Ma Mga v M m ga = F H G I K J = F H G I K J =− A D CM A B C D 4 a /3 FIG. P11.54 P11.55 Angular momentum is conserved during the inelastic collision. Mva I Mva I v a = == 3 8 The condition, that the box falls off the table, is that the center of mass must reach its maximum height as the box rotates, ha max = 2 . Using conservation of energy: 1 2 2 1 2 8 3 3 8 2 16 3 4 3 2 2 2 2 12 IM g aa
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