The graph of the potential energy pass through zero origin, cuts across positive x-axis and negative x-axis.
The slope of the graph when the potential energy of a particle constrained in on x-axis is determined as follows;
F = -dU/dx
-dU = Fdx
dU = -Fdx
U = -∫(kx + ax³)dx
U = kx²/2 - ax⁴/4
When, x = 0, U = 0
When U = 0;
[tex]x = \pm \sqrt{\frac{2k}{a} }[/tex]
The graph of the potential energy pass through zero origin, cuts across positive x-axis and negative x-axis.
Complete question is below:
Suppose that the potential energy of a particle constrainedon x-axis and subjected to a force in the same direction, at a fuction of F(x) = -kx + ax³.
Find the functional form of the potential energy.
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