How Does Kinetic Energy Affect Force in a 1D Atomic System?

[MaxManus]

Homework Statement

We addrewss a one dimensional system. An atom moves along the x-axis with a kinetic energy K = 0.5*m*v**2. In the range -x0<x<x0 the atom enters the trap, and is affected by a magnetic fiels. The interaction with the magnetic field gives rise to a potential U(x) which we model:

for abs(x)>= x0, U(x) = U0
for abs (x) < x0, U(x) = U0*abs(x)/x0

a) Find the force F(x) on the atom from the magnetic field. Is this force conservative?

Let us also assume that the atom is charged and also subject to a constant electronic force, F0 acting in the positive x-direction

b) If the atom has kinetic energy K = 0 at x = 0, how laarge must F0 be in order for the atom to escape? And if the kinetic energy is K = U0/2 at x = 0, how large must F0 then be in order for the atom to escape.

Homework Equations

The Attempt at a Solution

a)
F = -dU/dx

F = 0 for abs(x) >= x0
F = U0/x0 for -x0<x<0
F = -U0/x0 0for 0<x<x0

The force is conservative for it is only dependent on the position

b) Here I need some help.
Is the idea that the force must give the atom larger total energy than u0?

 

[Redbelly98]

b) Here I need some help.
Is the idea that the force must give the atom larger total energy than u0?

Not sure if that would be the case or not.

The way I think about it is, how is the potential modified due to the presence of the constant electrostatic force?