Force and potential energy: A particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.)

Question

Quizplus · Accepted Answer

The potential energy is given by the negative of the anti-derivative of the force:

U(x) = - ∫ F(x) dx

= -∫ (α - βxS1U1P13S1S1P0) dx   (Note: S1U1P13S1S1P0 means "to the power of 1/3" in superscript format, which is not supported on this platform)

= -αx + βxS1U1P43S1S1P0 + C

As we need to find the potential energy U(x) with respect to the zero potential at x = 0, we set the constant C to be zero.

Therefore, the potential energy function is:

U(x) = -αx + βxS1U1P43S1S1P0

which is equivalent to choice A.

Force and Potential Energy: a Particle Experiences a Force Given