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, t_{o}
= 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,
m_{o},
v,
and c?
Lesson 4: Relativistic
Mass
 The
equation.
 Where
does that come from?
 I still don't get it!
Give
me the Proton analogy.
 So what? There's an
equation. How
do I use the equation in the game?
 Practice
Problems.
 Examples
to aid your practice.
