The potential energy of an object as a function of position is U(x)= x³ - 12x + 8,where U is measured in joules and x is measured in meters.Where is the object be located if it is in an unstable equilibrium?

Question

Quizplus · Accepted Answer

An unstable equilibrium occurs when a small displacement from an equilibrium position leads to an increase in potential energy. This can happen when the second derivative of the potential energy function is positive. In this case, the second derivative is U''(x) = 2³ + 24, which is positive when x is negative. Therefore, the object is located at x = -2.0 m.

The Potential Energy of an Object as a Function of Position