233_Physics ProblemsTechnical Physics

233_Physics ProblemsTechnical Physics - Chapter 8 P8.46(a...

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Chapter 8 235 P8.46 (a) There is an equilibrium point wherever the graph of potential energy is horizontal: At r = 1 5 . mm and 3.2 mm, the equilibrium is stable. At r = 2 3 . mm, the equilibrium is unstable. A particle moving out toward r → ∞ approaches neutral equilibrium. (b) The system energy E cannot be less than –5.6 J. The particle is bound if < 5 6 1 . J J E . (c) If the system energy is –3 J, its potential energy must be less than or equal to –3 J. Thus, the particle’s position is limited to 0 6 3 6 . . mm mm r . (d) K U E + = . Thus, K E U max min . . . = = − − − = 3 0 5 6 2 6 J J J a f . (e) Kinetic energy is a maximum when the potential energy is a minimum, at r = 1 5 . mm . (f) + = 3 1 J J W . Hence, the binding energy is W = 4 J . P8.47 (a) When the mass moves distance x , the length of each spring changes from L to x L 2 2 + , so each exerts force k x L L 2 2 + F H I K towards its fixed end. The
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