A potential energy function is given by U(x)= ( 3.00 N/m)x - ( 1.00 N/m³)x³.At what position or positions is the force equal to zero? A) m and - m B) 0.00 m, m and - m C) 1.00 m and -1.00 m D) 3.00 m and -3.00 m E) The force is not zero at any location.

Question

Quizplus · Accepted Answer

To find the position or positions where the force is equal to zero, we need to find the derivative of the potential energy function with respect to position (x) and set it equal to zero. dU(x)/dx = 3.00 N/m - (1.00 N/m³)x³ Setting dU(x)/dx = 0: 3.00 N/m - (1.00 N/m³)x³ = 0 Solving for x: x = 1.00 m and -1.00 m So the force is equal to zero at these two positions. Option C is the correct answer.

A Potential Energy Function Is Given by U(x)= ( 3