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Lesson 4: Length Contraction

Lesson 1: Relativity - What is it?

  1. Fermilab's Time Dilation Challenge.
  2. The Basics of Relativity (6 seconds)
  3. The Relativity Game - Challenge what you know!

Note: For Fermilab's Time Dilation Challenge and The Relativity Game, you need Shockwave. You may painlessly Download Shockwave here if you do not have it.

Lesson 2: Time Dilation

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the basketball analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 3: Length Contraction

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the pole and the barn analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Lesson 4: Relativistic Mass

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the space pool analogy.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

Give me the Alpha Centuri Example?

Let's consider a space ship traveling from here to the nearest star (besides our Sun), Alpha Centuri.

Alpha Centuri's distance is approximately 4 light years away according to us, observers that are stationary with respect the the earth and Alpha Centuri. For this example, the points of reference for the time measurements are in the earth's frame of reference. Thus, the earth will have observers in the reference frame referred to as the mover for the mover.

Consider a space ship traveling at 50% c. We would see a person on this ship travel the distance in 8 years (let me see how to get this), since their ship travels half as fast as light, which makes the trip in 4 years.

This would be different for the space ship, because the space ship would measure a different time predicted by the time dilation equation.

Question:

Would this time measured for the mover by the mover be more than, less than or the same as the time measured for the mover by the stationary frame?

Question:

The earth measured the trip to take about 8 years. How long would this trip take according to the space ship?

(Click on the answer you believe to be correct below)

  1. 8.00 years
  2. 6.93 years
  3. 5.66 years
  4. 9.24 years

Question:

  1. According to the space ship, how far, in light years is it to Alpha Centuri?

    (Click on the answer you believe to be correct below)

  2. 4.00 years
  3. 4.62 years
  4. 2.83 years
  5. 3.46 years

Question:

The space ship is the stationary frame with the length measurement because the reference points are at rest within the earth's frame. Using only the length contraction formula, how much distance would the space ship measure for the 4 light year trip? Show me the Length Contraction equation again.

(Click on the answer you believe to be correct below)

  1. 4.00 light years
  2. 4.62 light years
  3. 2.83 light years
  4. 3.46 light years

In fact the time would be about 6.9 years. So according to the mover, the distance traveled was only 3.46 light years (I want to see that calculation), not 4 light years as was registered by the stationary frame. Therefore, space has been contracted for the mover.

In general, distance is calculated by knowing time and velocity.

d = vt

Here we will refer to the distance measured for the mover by the stationary frame as length, lo.

Also remember to set of a table of contents for this site.

What is L, Lo, v, and c?

 

Lesson 3: Length Contraction

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the Alpha Centuri example.
  4. So what? There's an equation. How do I use the equation in the game?
  5. Practice Problems.
  6. Examples to aid your practice.

     

     

 


© Brian Wegley, 1998
Comments and suggestions can be sent by e-mail to
Brian Wegley of Glenbrook South High School..
This page last updated on 7/23/98.