Force and potential energy: The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m³)x³- (15 J/m²)x²+ (36 J/m)x - 23 J. Find the location(s) where the force on the mass is zero.

Question

Quizplus · Accepted Answer

The force acting on the mass is given by the negative gradient of the potential energy function, F(x) = -dU(x)/dx. Taking the derivative of U(x), we get:
dU(x)/dx = (6.0 J/m³)x² - (30 J/m²)x + 36 J/m
Setting this equal to zero and solving for x, we get:
(6.0 J/m³)x² - (30 J/m²)x + 36 J/m = 0
Dividing both sides by 6 J/m, we get:
x² - 5x + 6 = 0
Solving for x using the quadratic formula, we get:
x = 2, 3, or 4
Thus, the force on the mass is zero at x = 2 m and x = 3 m, which corresponds to choice C.

Force and Potential Energy: the Potential Energy for a Certain