Transcript Document

Physics 111: Elementary
Mechanics – Lecture 7
Carsten Denker
NJIT Physics Department
Center for Solar–Terrestrial Research
Introduction
 Potential
Energy and Conservation of
Energy
 Conservative Forces
 Gravitational and Elastic Potential Energy
 Conservation of (Mechanical) Energy
 Potential Energy Curve
 External Forces
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Work and Potential Energy
Potential Energy
U  W
General Form
W   F  x  dx
xf
xi
U    F  x  dx
xf
xi
Gravitational Potential Energy
U  mgy
Elastic Potential Energy
1
U  kx 2
2
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(Non-)Conservative Forces
The system consists of two or more objects.
 A force acts between a particle–like object in the
system and the rest of the system.
 When the system configuration changes, the
force does work W1 on the particle–like object,
transferring energy between the kinetic energy K
of the object and some other form of energy of
the system.
 When the configuration change is reversed, the
force reverses the energy transfer, doing work W2
in the process.
 W1 = –W2  conservative force

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Path Independence of
Conservative Forces


The net work done by a conservative force on a particle
moving around every closed path is zero.
The work done by a conservative force on a particle
moving between two points does not depend on the path
taken by the particle.
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Conservation of Mechanical Energy
Mechanical Energy
Emec  K  U
Conservation of
Mechanical Energy
K2  U 2  K1  U1
In an isolated system where
only conservative forces cause
energy changes, the kinetic
and potential energy can
change, but their sum, the
mechanical energy Emec of the
system, cannot change.
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Potential Energy Curve
1D Motion
F  x  


dU  x 
dx
Turning Points
Equilibrium Points



Neutral
Equilibrium
Unstable
Equilibrium
Stable Equilibrium
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A plot of U(x), the potential energy
function of a system containing a particle
confined to move along the x axis. There is
no friction, so mechanical energy is
conserved.
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Conservation of Energy


The total energy of
a system can
change only by
amounts of energy
that are transferred
to or from the
system.
The total energy E
of an isolated
system cannot
change.
Thermal Energy/Friction
Eth  f k d
W  E  Emec  Eth  Eint
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