chapter 16 Special Relativity - Length, Energy, and Momentum

LENGTH CONTRACTION SIM WITH YOUR PICTURE


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REVIEW FROM CHAPTER 15


From last chapter


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Introduction - Key Concepts


The following are the key concepts that you will learn in this chapter.

 

UNIVERSAL SPEED LIMIT
  • The speed of light (c=3.0x108m/s )is the universal speed limit for all things. Objects with mass cannot be accelerated to the speed of light.

LENGTH CONTRACTION

click here to view diagram of pole in barn paradox solution

  • 1. All motion causes length contraction based on this equation

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.

  • Some numbers to remember:

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, c2. That energy is defined by the equation

rest energy=rest mass x speed of light2

E=mc2

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 1026 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

  • Einsteinís 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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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 on-line 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 Online-Einstein Revealed-Relativity (Lightman Essay)
nova spacetime AVI
nova-approaching the so.l.

 

Check out this page with some excellent sims

http://kspark.kaist.ac.kr/Twin%20Paradox/The%20Pole-Barn%20Paradox.files/Space-time%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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16.1 LENGTH CONTRACTION


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

Bunches more sims for special relativity...


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16.2 MOMENTUM AND INERTIA IN RELATIVITY


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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16.3 EQUIVALENCE OF MASS AND ENERGY


E = mc2

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 = mc2 for particle physics? Find out by reading these lecture notes from Michael Fowler's Modern Physics.


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16.4 KINETIC ENERGY IN RELATIVITY


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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16.5 THE CORRESPONDENCE PRINCIPLE


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

 

More sites to visit...

 
The Physics Classroom
The Physics Classroom
Multimedia Physics Studios
Physics 173 Internet Problems
Chem-Phys Internet Problems
The Quiz Room

The Laboratory
Shockwave Physics Studios
  contraction

 

The Review Session
Miscellaneous Help

 

SPACETIME

Concept of Space and Time in Special relativity

TIME DILATION

Relativistic Time Dilation
The Twin Paradox

LENGTH CONTRACTION

AVI (5.8MB)
C-ship The Lorentz Contraction
 
Mathematical structures and spaces - maths online Gallery
The Mighty Rod Bender
Tompkins Applet
USE CALTECH-Space-Time Physics Ph 1bc

 


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