Understanding Potential Energy and Stability in Balanse Question

[transgalactic]

the potential energy is given by
U(x)=U0(a/x+x/a -2)

what is the point of balance
which one is stable and which one is not??

i can't imagine this stability thing

and how to solve it??

 

[HallsofIvy]

The force on an object is the negative of the dervative of the potential energy function. A "point of balance" is where that force is 0: in other words where the derivative of the potential energy function is 0.

Sounds a lot like finding "max" and "min" of a function doesn't it? Think of a ball sitting at the top of a hill or the bottom of a hole as opposed to a ball on the side of the hill. A ball at either the top (max) or bottom (min) is in balance while a ball on the side of the hill rolls down hill.

And think about what happens if you give a ball at the bottom or top of a hill a little tap, moving it just a tiny amount. A ball at the top of the hill (maximum potential energy) rolls downward, well away from its original position. While the top of the hill is in balance, an equilibrium, it is not a "stable" equilibrium, it is "unstable". On the other hand, if you move the ball at the bottom of a hole, it rocks a little, then settles right back where it was- that is a "stable" equilibrum.

 

[transgalactic]

so always the maximum point are unstable
and the minimum is stable?