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. A) 4.0 m, 5.0 m B) 1.0 m C) 2.0 m, 3.0 m D) 3.0 m, 5.0 m

Question

Quizplus · Accepted Answer

To find the location(s) where the force on the mass is zero, we need to find the position(s) where the derivative of the potential energy function is zero:

F(x) = -dU(x)/dx

F(x) = (-4/3)x^2 + (15/2)x - 36

Setting F(x) = 0, we get:

(-4/3)x^2 + (15/2)x - 36 = 0

Solving for x, we get:

x = 2.0 m and x = 3.0 m

Therefore, the correct choice is C, 2.0 m and 3.0 m.

The Potential Energy for a Certain Mass Moving in One