A particle moves along the x-axis while acted by a conservative force described

Question

A particle moves along the x-axis while acted by a conservative force described by the potential energy function as shown in the figure. What is the direction of the force on the particle at Point A? At Point C? At Point E? At Point G? If the particle is released from rest at point B, describe the motion of the particle. At what point does the particle have the most kinetic energy? What are the positions corresponding to points of stable equilibrium? Of unstable equilibrium? Describe the motion of the particle if it is instead released from rest at Point H?

Explanation / Answer

a) F = - dU / dx

at A,

dU/dx = -ve

so F = +ve x direction

at C

dU/dx = 0

F = 0

at E.

dU/dx = 0

F = 0

at G ,

dU/dx = +ve

F = along -ve x direction

b) at B, particle have more potential energy then C

to particle will try to acquire less potential energy state.

hence particle will try to come to position C.

c) PE + KE = constant ( energy conservation)

for lowest PE position, particle will have maximum KE.

max KE at point C

d) C and f are stable equilibrium.

e)particle will come to F via G.

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