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Lecture PowerPoint
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 7
Potential Energy and
Conservation of Energy
Main Points of Chapter 7
• Potential energy
• Conservation of energy
• Energy conservation in more than
one dimension
• Nonconservative forces
7-1 Potential Energy and Conservative
Forces
• For a conservative force, work only
depends on endpoints of motion
• There must be a function of the
endpoints that represents the work
7-1 Potential Energy and Conservative
Forces
• For work done by gravity:
(7-2)
• U0 is an arbitrary constant
• Only differences in potential energy have
physical significance.
7-1 Potential Energy and Conservative
Forces
Using the force rather than the work:
(7-4)
The inverse:
(7-5)
7-1 Potential Energy and Conservative
Forces
Conservation of Energy
Definition of total mechanical energy:
(7-7)
Total mechanical energy is conserved if
only conservative forces are acting.
7-1 Potential Energy and Conservative Forces
Mass on a spring
Spring force:
(7-12)
Potential energy:
(7-13)
7-2 Energy Conservation and Allowed Motion
• Total energy is constant
• As kinetic energy increases, potential
energy decreases, and vice versa
• The maximum potential energy occurs
when the kinetic energy is zero
7-2 Energy Conservation and Allowed Motion
Part of a cycle of a mass on a spring,
showing pure potential energy, a mix,
and pure kinetic energy:
7-2 Energy Conservation and Allowed Motion
Potential energy curves:
Object cannot move farther
than the point where all energy
is potential
7-2 Energy Conservation and Allowed Motion
Equilibrium
• Stable equilibrium: force returns
object to place where F=0
• Unstable equilibrium: force
moves object away from place
where F=0
• Neutral equilibrium: force is zero
over an extended distance
7-2 Energy Conservation and Allowed Motion
Equilibrium
7-3 Motion in Two or Three Dimensions
• Potential surfaces can be visualized as
topographic maps
• Total energy depends on speed and position
in 3-d space:
(7-15)
Potential energy for projectile motion:
• Same as before, as force is only in
y-direction
7-3 Motion in Two or Three Dimensions
Central Forces
General form:
(7-17)
• Force depends only on distance r
from a central point
7-3 Motion in Two or Three Dimensions
Central Forces
Specific example: the gravitational force
Potential energy:
Force:
7-4 Is Energy Conservation a General
Principle?
Yes!
• Need to include all types of energy –
thermal, sound, light, electric, etc
• All fundamental forces are conservative –
conservation of energy always holds
• One of the most fundamental principles of
physics
7-4 Is Energy Conservation a General
Principle?
Energy Conservation and Nonconservative Forces
• Total mechanical energy not conserved when
nonconservative forces present
• Work done by nonconservative forces equals
change in mechanical energy
• Total energy is conserved when all forms are
counted
(7-18)
Summary of Chapter 7
• Potential energy can be defined for
conservative forces
• Total mechanical energy conserved if all
forces conservative
• In repetitive motion, energy changes from
all kinetic to all potential and back
• Stable, unstable, and neutral equilibrium
• Energy conservation – including all forms of
energy – is one of the foundations of physics