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(s) where the force is equal to zero, we need to find the derivative of the potential energy function with respect to x, set it equal to zero, and solve for x. So, U(x) = (3.00 N/m)x - (1.00 N/m³)x³ F(x) = -dU/dx = 3.00 N/m - (2.00 N/m³)x³ Setting F(x) = 0, we get: 3.00 N/m - (2.00 N/m³)x³ = 0 x = 1.50 m So, the force is zero at x = 1.00 m and x = -1.00 m. Therefore, the best choice is C.

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