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. (a) At which labeled points does the force act to the left? To the right? At which labeled points is the force zero? (b) What are the positions corresponding to points of stable equilibrium? Of unstable equilibrium? (c) If the panicle is released from rest at point B. describe the motion of the particle. At what point does the particle have the most kinetic energy? (d) 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

a) F= -dU/dx

so where slope -ve means F = +ve means right point = A,B, F,G

slope +ve , F= -ve menas left points = D,J,K,L

slope = zero means F = zero points = C,E,H

b) equilibrium = point at which F = zero means points C,E,H

Stable = C,H because potential energy has minima

unstable = E because potential energy has maxima

C) by energy conservation

Gain in K.E = loss in P.E

so minimum P.E corresponds to Maximum K.E so point H  

D) point L

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