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Lesson 4: Relativistic Mass

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! Show me the Proton 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 Proton Analyogy?

The Length Contraction and Time Dilation Tie:

In the earth's frame of reference, the proton travels 256,000,000 m in 1.0 second.

In the proton's frame, we need to determine the time the earth's 1.0 second would take. Understanding that the time of 1.0 second is in the earth's frame, to = 1.0 second. To find the time in the proton's moving frame, we need to determine t.

In the proton's frame, it would see the earth rush by at 0.85 c for 1.9 seconds. Therefore, it would see the distance traveled as:

d = (0.85c)(1.9 s)

d = 484,000,000 meters.

The proton believes the traveled was 484,000,000 meters while the earth beleves the distance traveled was 256,000,000 meters.

Question:

Considering that the earth measures the proton to travel past it at 85% c, how far does the earth measure the proton's 484,000,000 meters to be?
See this calculated.

Bringing It Together:

Using time dilation and relativistic mass, the proton travels 256,000,000 meters in 1.0 second which is less than the 270,000,000 meters we predicted. Since it covers less distance, we observe that it has resisted acceleration (inertia) more than we expected. This is to say that the proton gains mass as it gains speed!

This is a common observation of those who make a living accelerating objects to relativistic speeds. As they attempt to accelerate a proton traveling at 99.96% c, they are not supprised to find it resisting acceleration as much as a 35 combined protons would as its mass has grown to 5.9 x 10-26 kg.

This increase in inertia can be derived mathematically to be:

What is m, mo, v, and c?

Lesson 4: Relativistic Mass

  1. The equation.
  2. Where does that come from?
  3. I still don't get it! Give me the Proton 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.

 


© 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.