A particle experiences a force given by F(x) = α

Question

A particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.) A) U(x) = -αx + x⁴ B) U(x) = αx - x⁴ C) U(x) = 3βx² D) U(x) = -3βx²

Quizplus · Accepted Answer

The potential energy function U(x) is related to the force function F(x) through the equation: U(x) = -∫F(x) dx Integrating F(x) with respect to x, we get: U(x) = αx - βx^2/2 - ³ Since the zero of potential energy is located at x = 0, we can simplify this to: U(x) = αx - βx^2/2 Comparing this with the given choices, we see that choice A matches the potential energy function we derived, and hence is the correct choice.