Force and potential energy: 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?

Question

Quizplus · Accepted Answer

To find where the force is equal to zero, we need to find the derivative of the potential energy and set it equal to zero. Taking the derivative of U(x) with respect to x gives us F(x) = dU/dx = 3.00 N/m - (1.00 N/m³)2x³. Setting this equal to zero and solving for x, we get: 3.00 N/m - (1.00 N/m³)2x³ = 0 2x³ = 3.00 N/m x = 1.50 m or -1.50 m Therefore, the force is equal to zero at x = 1.00 m and x = -1.00 m. Since the question asks for the position or positions (plural), the answer is C.

Force and Potential Energy: a Potential Energy Function Is Given