The potential energy of a particle moving along the x axis is given by U(x)= (8.0 J/m²)x² + (2.0 J/m⁴)x⁴. If the total mechanical energy is 9.0 J, the limits of motion are: A)-0.96 m; +0.96 m B)-2.2 m; +2.2 m C)-1.6 m; +1.6 m D)-0.96 m; +2.2 m E)-0.96 m; +1.6 m

Question

Quizplus · Accepted Answer

The potential energy function U(x) = 8x^2 + 2x^4 represents a symmetric potential well about the x=0 axis. The total mechanical energy is given as 9.0 J. The limits of motion are the points where the total mechanical energy equals the potential energy, i.e., where 9 = 8x^2 + 2x^4. Solving this equation for x gives the symmetric limits of motion, indicating choice A is correct due to the symmetry of the potential energy function about the x=0 axis.

The Potential Energy of a Particle Moving Along the X