What Determines the Maximum Kinetic Energy for a Particle in a Bounded Region?

[Nusc]

say I'm givin the potential energy fxn

V(r) = Eo [ (a/r)^3 - (a/r) ]

Eo a constant

After taking the derivatives to find the equilibrium pts and checking for stability we get

r = sqrt(3)*a and this pt is stable

r = -sqrt(3)*a and this pt is unstable

Now let's pose the question

b) What is the max kinetic energy that the particle can have and still remain bounded (ie. remain within a region of finite spatial extent)

Tmax = Vmax - Vmin right?

I am still all little confused about the concept from "stable eq I" Only because that question didn't have 2 equilibrium pts.

 

[Nusc]

I got Tmax = Vmax - Vmin = Eo[ 2/(3sqrt(3)) - ( -2(3sqrt(3)))
Tmax = 4Eo/(3sqrt(3))

Is this correct?