Mon. Jan. 12 – Physics Lecture #18
Relativity – Relativistic Momentum and Energy
0) Announcements
1) The Trouble with Classical Momentum
2) Updating Momentum and Energy
3) Calculating Energy, Momentum, etc.
4) Light as a massless particle
5) Another Invariant
Warm-Up: Discuss with your neighbors. A particle of mass m moves to the right
with speed 0.6c. It collides with a motionless particle, also of mass m. The
particles stick together. Determine the speed and direction of the combined
particle after the collision.
What physics principle is useful in this situation?
What strategy is useful in this situation?
A particle of mass m moves to the right with speed 0.6c. It collides with a
motionless particle, also of mass m. The particles stick together. Determine the
speed and direction of the combined particle after the collision.
What physics principle is useful in this situation?
What strategy is useful in this situation?
After
Before
m
u1 = 0.6c
m
2m
u2 = 0
u3 = ?
Concept Check:
After
Before
Now, view the same situation
from the from a train moving to
the right at 0.3c.
This means the 2m particle is at
rest in the new (prime) reference
frame, so that u’3 = 0 , and that
the particle which was stationary
in the original (unprimed
reference frame) is moving to
the left so that u’2 = –0.3c.
What is u’1, the speed of the first
particle in a reference frame that
is traveling at 0.3c to the right?
1. 0
4. 0.366c
2. 0.254c
5. 0.6c
3. 0.3c
6. 0.763c
m
u1 = 0.6c
m
2m
u2 = 0
u3 = 0.3c
Before
m
u’1 = ?
After
m
u’2 = 0.3c
2m
u’3 = 0
What about momentum conservation?
Updated definition of momentum for
particle of mass m, velocity u:

p

mu
2
1u / c
2
Energy in
terms of mass and velocity:
E
mc 2
1  u2 /c 2
What is momentum when speed u = 0?
What is momentum when speed is not 0 but small compared to speed of light:
u << c?
Energy in
terms of mass and velocity: E 
mc 2
1  u2 /c 2
Example:
(classical) Kinetic energy of 1 kg book moving at 3 m/s = ?
Energy of 1 kg book moving at 3 m/s = ?
Concept Check:
What is E when u = 0?
1. 0
4. mc2
2. ½ mu2
5. Infinity
3. K + U
6. not enough info
K  E  mc 2

p

mu
1  u2 / c 2
2
E
2
mc 2
1  u2 /c 2
2 2
E  ( pc )  (mc )
K  E  mc 2  E  mc 2  K
2
 c 
u p
E
Units of mass, momentum, and energy
Concept Check:
A particle at rest has an
energy of 3.0 keV. What
is its mass?
1. 3.0 keV/c2
4. 3.3x10-14 keV/c2
2. 1.0x10-8 keV/c2
5. 9.0x108 keV/c2
3. 3.3x10-17 keV/c2
6. 2.7x1017 keV/c2
Concept Check:
The same particle from before (m = 3.0 keV/c2)
now is moving and has momentum 4.0 keV/c.
What is its energy?
Follow ups:
What is its kinetic energy?
What is its speed?
1. 1.0 keV
4. 7.0 keV
2. 3.0 keV
5. 25 keV
3. 5.0 keV
6. 49 keV