Download Making predictions In the space below, complete the following table

Exploration: Exploring Relativistic Effects
In this lesson you will use the "Particle in a Magnetic Field" applet to investigate
the relativistic behaviour of charged particles moving at high velocity through
magnetic fields.
Prerequisites:

You should be familiar with the equation Fmagnetic  qvB which relates the
magnitude of the magnetic force on a charge 'q' moving with a velocity v at
right angles to a magnetic field of strength B.

You should know how to use the concept of inward force to explain
mv 2
circular motion and be able to use the expression Finward 
(this is also
r
often called the centripetal force).

You should know how to use the hand rules that relate the direction of the
magnetic force to the direction of motion of the charge and direction of the
magnetic field.
Learning Outcomes:
When finished, you should be able to demonstrate that, at high velocity, the
Newtonian expression for momentum is no longer valid.
Making predictions
1. In the space below, complete the following table and sketch a graph that
shows how you would expect the momentum of an electron to change with
velocity. Plot the velocity along the horizontal axis and the expected
momentum along the vertical axis.
Velocity
(km/s)
Momentum
(N-s)
30 000
60 000
90 000
120 000
150 000
180 000
210 000
240 000
270 000
Testing your predictions
To answer the following, open the Particle in a Magentic Field applet.
1. Complete the following table. You may want to do this in EXCEL so that
you can readily plot the data.
Velocity (km/s)
30 000
60 000
90 000
120 000
150 000
180 000
210 000
240 000
270 000
Momentum (N-s)
2. Discuss whether or not your data agrees with the Newtonian expression
for momentum.
Summary
Your data is similar to data discovered
by the German physicist Walter
Kaufmann in a series of experiments
conducted from 1901 to 1906.
Kaufmann concluded that the mass of
the electron increased with increasing
velocity. In 1905, Einstein published
his theory of special relativity in which
he concluded, among other things,
that the Newtonian expression for
momentum was incorrect. Einstein
showed that the correct expression for
momentum is:
mv
p
v2
1 2
c
You may have learned that the speed
of light is the "speed limit" for the
universe. If you study the relativistic
expression for momentum you can
understand why "c" is the speed limit.
Einstein in 1912
The momentum of a particle becomes
infinite as its velocity approaches the speed of light. That, in fact, is what your
data shows!