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Lesson 3: 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?

Accelerate a proton from 50% c to 60% c - something's missing: (I know, acceleration doesn't belong with special relativity, but it makes for a good analogy)

At rest, the proton's mass is roughly 1.67 x 10-27 kg. As it travels by us at 50% c, lets say we give it an electrical push of 5.01 x 10-14 Newtons for 1 x 10-6 seconds. Considering Newton's 2nd Law and its rest mass, we would expect the proton to accelerate the proton to 60% c (show me why).

If we can predict its speed, we can predict that in the 1.0 second after the push the proton should cover about 180,000,000 meters (show me why).

However, what we observe is different. We observe the proton accelerate to about 59% c.

From 80% c to 90% c - something's missing:

This whole difference becomes more dramatic if we consider trying to accelerate the proton from 0.8 c to 0.9 c.

Again we give the proton we expect to have a mass o roughly 1.67 x 10-27 kg an electrical push of 5.01 x 10-14 Newtons for 1 x 10-6 seconds. Considering Newton's 2nd Law , we would expect the proton to accelerate the proton to 90% c (show me why).

After the Push:

Let's consider the relativistic mass equation:

What is m, mo, v, and c?

Although we expect the proton to accelerate to 90% c, we observe it to accelerate as though its mass is 3. 2 x 10-27 kg.

Question:

Given the relativistic mass of the proton in the earth's frame of reference, m (mass for the mover by the stationary frame) is 3.2 x 10-27 kg and the rest mass mo , is 1.67 x 10-27 kg, what is the speed with which the proton is traveling?
 

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

  1. 0.48 c
  2. 1.90 c
  3. 0.85 c
  4. 0.73 c

Now we have the speed of the proton after it accelerates and it is less than we expect.

We can explore how this affects our measurement of length.

 

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.