chapter 16 Special Relativity - Length, Energy, and Momentum

LENGTH CONTRACTION SIM WITH YOUR PICTURE

REVIEW FROM CHAPTER 15

From last chapter

• Time Dilation

• Visualizing Proper Time in Special Relativity [with LightClocks

• Twin Paradox java applet

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:

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

7. Small objects or small quantities of matter contain enormous amounts of energy.

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.

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.

• Relativity Physlets from Davidson College

  • Illustration 1: Synchronizing Clocks.

  • Illustration 2: Viewing Synchronizing Clocks.

  • Illustration 3: Simultaneity.

  • Illustration 4: Light Clocks, Time Dilation, and Length Contraction.

  • Illustration 5: Understanding Spacetime Diagrams.

  • Exploration 1: Pole and barn "paradox."

  • Exploration 2: The twin "paradox."

  • Exploration 3: More on the twin "paradox."

  • Exploration 4: Matching Spacetime Trajectories.

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

16.1 LENGTH CONTRACTION

Length Contraction

• contraction

AVI (5.8MB)

C-ship The Lorentz Contraction

Concept of Space and Time in Special relativity

Mathematical structures and spaces - maths online Gallery

nova gravity and acceleration in sr

NOVA Online-Einstein Revealed-Relativity (Lightman Essay)

nova spacetime AVI

nova-approaching the so.l.

The Mighty Rod Bender

Tompkins Applet

USE CALTECH-Space-Time Physics Ph 1bc

The garage and the broomstick

Green Light - Red Light

Virtual Trips to Black Holes and Neutron Stars Page

16.2 MOMENTUM AND INERTIA IN RELATIVITY

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.

16.3 EQUIVALENCE OF MASS AND ENERGY

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.

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!

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more related links

• Elementary Space-time Diagrams
• The Bug-Rivet Paradox · · · Wrong paradox. Infinite deceleration of the rivet head is not in the realm of SR!
• The Rising Window
• The Mighty Rod Grabber
• A light-speed Submarine, to float or to sink?

top   LENGTH CONTRACTION    MOMENTUM AND INERTIA    EQUIVALENCE OF MASS AND ENERGY    KINETIC ENERGY   CORRESPONDENCE PRINCIPLE  bottom

Copyright © 2005 -  S. B. EglI