chapter 16 Special Relativity 
Length, Energy, and Momentum
LENGTH CONTRACTION SIM WITH
YOUR PICTURE
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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REVIEW FROM CHAPTER 15
From last
chapter
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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The following are
the key concepts that you will learn in this chapter.
UNIVERSAL SPEED LIMIT
LENGTH CONTRACTION
click here to view diagram of pole in barn paradox
solution
The magnitude of the
contraction is not significant until the amount of motion is
relativistic

All
motion is relative, if you are stationary viewing something
moving relative to you, it looks shorter.

If
you are moving relative to something
stationary, it looks shorter.

It does not matter
which object is moving, or if both are moving.

When observing
something that is moving relative to you, it will look shorter.
You will also look shorter to it!

One reason that
objects with mass cannot reach c or greater is because their
length would reduce to 0 at c.

When moving at any
constant speed, relativistic or not, nothing that is moving in the
same reference frame with you would look different.

Objects that are
not moving relative to you appear normal whether they are moving relative to
something else or not.
s.o.l. =
c = 3.0 x ^{106 }meters/second
Length at
.87c => .5 x Length at rest
Length at
.995c => .1 x Length at rest 
MASS & ENERGY
KEY CONCEPTS
6. Objects with mass
have an energy of being or energy of rest that is a
function of their mass multiplied by a very, very, very large number,
c^{2}. That energy is defined by the equation
rest energy=rest mass x speed
of light^{2} 
E=mc^{2} 
7. Small objects or small quantities
of matter contain enormous amounts of energy.
type & amount 
E0 
units 
electron 
0.511 
MeV 
proton 
938.3 
MeV 
neutron 
939.6 
MeV 
mass unit 
931.5 
MeV 
1 gram of anything 
5.61 x 10^{26} 
MeV 
RELATIVISTIC
MOMENTUM & KINETIC ENERGY
relativistic
momentum


At high Speeds momentum is greater than mv
relativistic
kinetic
energy


CORRESPONDENCE
PRINCIPLE
KEY CONCEPTS

If a new theory is valid, it
must account for the verified results of the old theory in the region where
both theories apply. This requirement of logic is known as the
correspondence principle

Einstein’s equations are valid
for all speeds.

At slow speeds the v2/c2 factor
rapidly approaches 0 and the equations simplify to the form familiar from
Newtonian Mechanics.
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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OTHER RESOURCES
The rest of this page provides you
with a wide variety of ways to explore these concepts.
The other resoiures include sites
with detailed theoretical explanations, movies & animations, interactive
simulations (virtual labs), history, live online tutoring sites, complete
online courses from some of the best universities in the world, and real world
applications. At the bottom of this page and on the
LINKS page there are hundreds of links to related sites. Try them out. IF
there are any you find particularly useful, share them on the appropriate
newsgroup forum.
newsgroup

You will learn much more quickly
and understand much easier if you use a variety of presentations of the same
concepts rather than focusing on one source or presentation mode. Try out
the simulations and calculators. Can you use them to answer your homework
and other questions?

View the animations and movies.
Do they help you understand, remember, or visualize the ideas?

Communicate with the online
forums, it is reassuring to find that you are not the only person in the
world that is struggling with a concept.

Use the web as a resource. Don't
get stuck in a rut!
START
WITH THESE SITES...

nova gravity and acceleration in sr

NOVA OnlineEinstein RevealedRelativity (Lightman Essay)

nova spacetime AVI

novaapproaching the so.l.
Check out this page with some excellent sims
http://kspark.kaist.ac.kr/Twin%20Paradox/The%20PoleBarn%20Paradox.files/Spacetime%20Diagrams.htm
!!!!!Interactive Physics Simulations by A. John Mallinckrodt
Portions of the following are from
CpSurf
Hewitt's Companion Web Page for this chapter
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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Length Contraction
Check out these four animations from the
Physics
Multimedia Studios showing spaceships moving past Earth at various speeds.
Notice how the length of the spaceship relative to the observer changes as the
ship's speed approaches the speed of light.
Relativity Movie
This Quicktime movie (4.1 MB) from the UCLA Large Plasma Device Lab shows
the view of a city as seen by an observer passing over at near the speed of
light
Bunches more sims for special relativity...
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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Conserving Momentum: The Relativistic Mass Increase

As an object approaches the
speed of light, its mass increases without limit! What does this mean
for the conservation of momentum? Find out by reading these lecture
notes from
Galileo and Einstein, a course taught by Michael Fowler of the
University of Virginia.
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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E = mc^{2}

Hear Albert Einstein declare
the equivalence of matter and energy! This historical soundbite is
provided by the American Institute of
Physics
Mass and
Energy

Read about Einstein's Box, an
amusing thought experiment on the equivalence of mass and energy. This
lecture is part of the
Modern
Physics course taught by Michael Fowler at the University of
Virginia.
Transforming Energy into Mass: Particle Creation

What are the consequences of
E = mc^{2} for particle physics? Find out by reading these
lecture notes from Michael Fowler's
Modern
Physics.
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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Relativistic Dynamics
 Part of Michael Fowler's
Modern
Physics lecture notes, this page provides an excellent overview of
relativistic dynamics, including a derivation of relativistic kinetic
energy.
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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Introducing the Light Cone
 If a new theory is valid, it must account for the verified results
of the old theory in the region where both theories apply. This
requirement of logic is known as the correspondence principle.
How
does the theory of special relativity account for classical mechanics?
Find out by reading this lesson from Rob Salgado's online relativity
tutorial
The Light Cone.  Look at this
page!
more related links
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LENGTH
CONTRACTION
MOMENTUM AND INERTIA
EQUIVALENCE OF MASS AND ENERGY
KINETIC ENERGY
CORRESPONDENCE PRINCIPLE
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