What Happens to X When Force and Total Energy Are Defined by U(x)?

[veronicak5678]

Homework Statement

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?

Homework Equations

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?

 

[Redbelly98]

(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.

 

[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.

 

[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.

 

[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.

 

[Philosophaie]

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