Question

On a particle placed at origin, a variable force F = - ax (where a is a positive constant) is applied. If U(0) = 0, the graph between potential energy of particle U(x) and x is best represented by A. B. C. D.

          On a particle placed at origin, a variable force F = - ax (where a is a positive constant) is applied. If U(0) = 0, the graph between potential energy of particle U(x) and x is best represented by
A. 
B. 
C. 
D.
        

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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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On a particle placed at origin, a variable force F = - ax (where a is a positive constant) is applied. If U(0) = 0, the graph between potential energy of particle U(x) and x is best represented by A. B. C. D.
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Transcript

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00:01 We are given the force is equal to minus a x and u at x is equal to 0 is equal to 0 means in the question we are given on a particle placed at origin a variable force this is the force variable force f is equal to minus a x is applied if u 0 is is equal to 0 the graph between potential energy of particle u x and x is best described by so we have to find the graph between potential energy and the x so b no force is negative gradient of potential energy so negative of d u divided by d x where u is potential energy and x and x and x is is displacement f is equal to minus d u divided by d x is equal to minus a x and we are given a is a positive constant so from the other formula equation we get d u is equal to a x t x now integrating both sides we get integration of d u is equal to integration of a x d x which is equal to a integration of x d x so we get u is equal to a x squared by 2 and it's limit lies from 0 to x 0 to x so we get u x is equal to a x squared by 2 because u0 is equal to that is given in the question floating ux along y x and x along x x x we have y is equal to 1x2 a where a is constant the graph will look like a parabola which is passing through the origin and it will be an upward parochial...
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