A particle moves along the x axis under the influence of a stationary object.The net force on the particle, which is conservative, is given by F = (8N/m³)x³.If the potential energy is taken to be zero for x = 0 then the potential energy is given by: A)(2 J/m⁴)x⁴ B)(-2 J/m⁴)x⁴ C)(24 J/m²)x² D)(-24 J/m²)x² E)5 J - (2 J/m⁴)x⁴

Question

Quizplus · Accepted Answer

The potential energy (U) associated with a conservative force is given by U = -∫F dx. Given F = (8N/m)x, integrating with respect to x gives U = -(8/2)x^2 = -4x^2. The correct unit for potential energy is Joules (J), so the answer is (-2 J/m^2)x^2, which corresponds to choice B.

A Particle Moves Along the X Axis Under the Influence