-Relating Conservative Force and Potential Energy -Energy diagrams and Equilibrium AP Physics C Mrs. Coyle

A Force is “Conservative” if: “ the work this force does on an object that moves between two points depends only on the position of these two points and not on the path.” “the work this force does on an object that moves through a round trip is zero.” Example: gravity, force of a spring.

Consider a ball thrown up and the system is the ball and the earth. The work done by the force of gravity W g =-ΔU

For a particle moving along the x-axis (one dimensional motion)while a conservative force, in the same axis, within the system acts on it: ΔU is the change in potential energy of the system

Solving for F x :

Example: Find the gravitational force for a particle a distance x above the earth’s surface. Start with U= mgx Find F

Example: Find the spring force for a particle attached to a spring: Start with U= ½ kx 2 Find F(x):

Types of Positions of Equilibrium Stable Equilibrium: movement away from this (x=0) position results in a restoring force. Unstable Equilibrium: movement away from this position results in a force directed away from x=0 Neutral equilibrium: movement away from x=0 does not result in either restoring nor disruptive forces.

Energy Diagrams, U(x) vs x

-Energy Diagrams -U(x) is minimum at x=0 (stable equilibrium) x max and –x max : turning points

Unstable equilibrium U(x) is max

Neutral Equilibrium U(x) is constant

Example 1 (#40) A single conservative force acting on a particle varies as F=(-Ax+Bx 2 )i N, where A and B are constants and x is in meters. a) Calculate the potential energy function taking U=0 at x=0 b) Find the change in potential energy and change in kinetic energy as the particle moves from x=2.00m to x=3.00m

Example 2 (#42) A potential energy function for a two dimensional force is U=3x 3 y - 7x Find the force that acts at the point (x, y) Hint find F(x) and F(y).