# Potential energy Function

1. Oct 11, 2008

### veronicak5678

1. The problem statement, all variables and given/known data

A potential energy function is given by U (x) = a/x^2 + bx.
a- Find where the force described is 0, in terms of ab and b.
b- Suppose a = 10.0 J/m^2 and b = 2.00 J/m. if an object has a total energy of 20.0 J, for what values of x would it be limited?

2. Relevant equations

3. The attempt at a solution

I don't understand this. Should I just take the derivative and set it to 0? Then, for part b, set the entire function equal to 20?

2. Oct 11, 2008

### Redbelly98

Staff Emeritus
(a) Yes.

(b) You're close, and would likely receive most of the available credit by doing that.
It says total energy is 20 J, whereas the U(x) expression is for potential energy. They are not the same thing, so setting them equal is not quite right.

3. Oct 13, 2008

### veronicak5678

Thanks for your help, but I ams till having trouble. For part a, I came up with
x = - ( 2a/b) ^ (1/3).

I think that is right, but I have been working on part b for almost half an hour, and I cannot solve it. I have 10mx^2 - x^3 -mx^2K = 0 where K is the unkown kinetic energy. I don't know how to solve this, or if it is only so difficult because I made a mistake somewhere.

4. Oct 13, 2008

### Philosophaie

This may help for part a:

dU=-f*ds=0

For part b You have the right idea:

U(x)=Umax and solve for x.

5. Oct 14, 2008

### veronicak5678

I'm sorry, I don't understand... my answer for part a is wrong? I thought I should just take the derivative, set it to 0, and solve for x. And for part b, how do I solve it? Do I need to use the quadratic equation or something? I feel like I did it all wrong.

6. Oct 14, 2008

### Philosophaie

-2*x^3-20*x^2+10=0
x^3+10*x^2-5=0
solve for x
hint divide by (x-1)

Last edited: Oct 14, 2008