r - 1---Select---stableunstableneutral equilibriumnot an equilibrium position r

Question

r - 1---Select---stableunstableneutral equilibriumnot an equilibrium position r = 0 mm 2---Select---stableunstableneutral equilibriumnot an equilibrium position r = 1.5 mm 3---Select---stableunstableneutral equilibriumnot an equilibrium position r = 2.0 mm 4---Select---stableunstableneutral equilibriumnot an equilibrium position r = 2.3 mm 5---Select---stableunstableneutral equilibriumnot an equilibrium position r = 3.2 mm 6---Select---stableunstableneutral equilibriumnot an equilibrium position r = 4.0 mm 7---Select---stableunstableneutral equilibriumnot an equilibrium position r 8---Select---stableunstableneutral equilibriumnot an equilibrium position A particle moves along a line where its potential energy depends onits position r, as graphed in the figure below. In thelimit as r increases without bound, U(r)approaches +1 J. (a) Identify each equilibrium position for thisparticle. Indicate whether each is a point of stable, unstable, orneutral equilibrium. r arrow - infinity 1 r = 0 mm 2 r = 1.5 mm 3 r = 2.0 mm 4 r = 2.3 mm 5 r = 3.2 mm 6 r = 4.0 mm 7 r arrow infinity 8 (b) The particle will be bound if the total energy of the system isin what range? 9 J

Explanation / Answer

Given : a ) There is an equilibrium point whenever the graph of thepotential energy is horizontal , stable equilibrium at r=1.55mm and 3.2mm. unstableequlibrum at r=2.3mm and neutral as r--> b ) The system energy E cannot be less than -5.6J. Theparticl bound if -5.6J<=E<=1J c ) If the system is -3J, its potential enegy must beless than or equal to -3J.    Thus the particles position is limited to0.6mm<=t<=3.6mm I hope it helps you

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