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

Question

A particle moves along the x-axis while acted on by a conservative force described by the potential energy function shown in the figure below. At which labeled points does the force act to the left? To the right? At which labeled points is the force zero? What are the positions corresponding to points of stable equilibrium? Of unstable equilibrium? 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? Describe the motion of the particle if it is instead released from rest at Point L? At what point does the particle have the most kinetic energy?

Explanation / Answer

F=-dU/dx

where F is force applied

U=potential energy

x=distance

part a:

F is applied to the left where slope is negative and applied to right , slope is positive

when slope is zero, F is zero.

hence at points A, B,F, G force is to the left.

at points D,J,K and L, force is to the right

at points C,E and H force is zero.

part b:

a system is in equilibrium , if slope of U-x curve is zero.

the equilibrium is a stable one, if it is a local minimum

the equilibrium is unstable, if it is a local amximum

hence at points C,E and H the system is in equilibrium

at point E, it is unstable equilibrium

at points C and H, it is stable equilibrium

part c:

if it is released from rest at point B, it will move towards lower potential energy i.e. point C.

at point C it will have most kinetic energy.

part d:

if it is released at point L, it will move towards point H

at point H it will have the most kinetic energy.

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