The potential energy for a certain mass moving in one dimension is given by .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

The potential energy for a certain mass moving in one dimension is given by  .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

Quizplus · Accepted Answer

The force on the particle is given by the negative gradient of the potential energy function. That is, F(x) = -dU(x)/dx. 
Taking the derivative of the given potential energy function, we get:
U'(x) = 2(2x-7)(x-4)(x-5)

For the force to be zero, we need to find the value(s) of x where U'(x) = 0.
Setting U'(x) = 0, we get:
2(2x-7)(x-4)(x-5) = 0

This equation has roots at x = 2, x = 3, x = 4, and x = 5. 
Therefore, the location(s) where the force on the mass is zero is/are: 2.0 m, 3.0 m, 4.0 m, 5.0 m.

Out of the given answer choices, the best choice is C, which includes the correct locations.

The Potential Energy for a Certain Mass Moving in One