-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 Wg =-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:
xf
WC   Fx dx  U
xi
ΔU is the change in potential
energy of the system
Solving for Fx:
dU
Fx  
dx
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 kx2
• 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)
xmax and –xmax :
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+Bx2 )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=3x3y - 7x
• Find the force that acts at the point
(x, y)
• Hint find F(x) and F(y).