Concept #1: Relationship Between Force and Potential Energy (In 1-Dimension)

Concept #2: Partial Derivatives

Concept #3: General Relationship Between Force and Potential Energy

A potential energy function is given by
U = Ax3 + Bx2 - Cx + D
Find the stable equilibrium position for A = 3.45 J/m 3, B = 1.05 J/m 2, C = 1.7 J/m, and D = 4.2 J.

The following graph represents a hypothetical potential energy curve for a particle of mass m.If the particle is released from rest at position r 0, its speed ||→v|| at position 2r0 is most nearly

The plot shown represents the potential energy of a particle that can only move along the x-axis, as a function of the coordinate x. Which of the following statements is correct:[a] In B and D the force is zero;[b] The force in B is positive;[c] A and C are stable equilibrium positions;[d] The force in D is positive;[e] A and C are unstable equilibrium positions.

The potential energy between two neutral atoms is called the Lennard-Jones potential, and is given by the equation
U(x) = A/r12 - B/r6
where A and B are positive constants.
a) What is the force due to this potential energy?
b) For what range of r is the force attractive, and for what range of r is the force repulsive? Note that if the force is positive, it is repulsive, and if the force is negative, it is attractive.