One Dimensional motion of particle in a potential field

[sabanboy]

A classical particle constrained to move in one dimension (x) is in the potential field V(x) = V0(x – a)(x –b)/(x – c)^2, 0 < a < b < c < ∞.
a. Make a sketch of V
b. Discuss the possible motions, forbidden domains, and turning points. Specifically, if the
particle is known to be at x → ∞ with E = 3V0(b – 4a + 3c)/(c – b), at which value of x
does it reflect?

I'm not sure how to approach this problem any tips or advice would be greatly appreciated.

 

[BvU]

Hello Saban, and welcome to PF.
Here's my tip:
Start with a)

 

[sabanboy]

Thanks I have it drawn and reviewed it with my professor who told me the sketch is correct. I'm still not sure as to how to complete part b though.

 

[BvU]

I don't have your sketch, but I can kind of telepatically pick it up
So you see a big peak at x=c. And a minimum between a and b. Right ?

Good that you already did the first discussion in part b) and now want to complete it.

In the completion of part b the particle comes from the right, with a given E.
Is it clear to you that it doesn't have enough energy to get to x < c ?

So what you know about the turning point is that at that point there is no more kinetic energy, just potential energy.
Since the given E(x≈∞) = E_kin(x≈∞) + V(x≈∞) is the same as E at the turning point x, you obtain an equation in x.