1. Aparticle moves along the x-axis while acted on by a singleconservative force

Question

1.      Aparticle moves along the x-axis while acted on by a singleconservative force parallel to the x-axis. The force corresponds tothe potential energy function graphed in the figure below. Theparticle is released from point rest at point A.

a.       What is the direction of theforce on the particle when it is at point A?

b.      At point B?

c.       At what value of x is thekinetic energy of the particle a maximum?

d.      What is the force on the particlewhen it is at point C?

e.       What is the largest value ofx reached by the particle during its motion?

f.       What value or values of xcorresponds to points stable equilibrium?

g.      Of unstable equilibrium?

Explanation / Answer

b) For same reason, force at B is in negative xdirection c) KE is maximum when U is minimum. Looks like this happens atx = 0.75 d) At point C, dU/dx is zero, so the force is zero. e) It looks like the particle never quite makes it to x = 2.5,so the max x is a little less than this. f) stable equlibrium are the lowest local points of U.These are at the bottom of the "dips" where x = 0.75and x = 1.75 g) unstable equilibrium is at point C; the force iszero, but in either direction the particle rolls down thehill.    I hope it helps you

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