1
Phy107 Lecture 19
1
Hour Exam 2
: Wednesday, March 8
• Inclass, covering waves, electromagnetism, and
relativity
• Twenty multiplechoice questions
• Will cover:
March Chap 67,912
Griffith Chap 12,15,16
All lecture material
• You should bring
– 1 page notes, written double sided
– #2 Pencil and a Calculator
– Review Monday March 6
– Review questions online under “Review Quizzes” link
Exam
Phy107 Lecture 19
2
Massenergy equivalence
• This results in Einstein’s famous relation
• This says that the total energy of a particle
is related to its mass.
• Even when the particle is not moving it has
energy.
• We could also say that mass is another form of
energy
– Just as we talk of chemical energy, gravitational
energy, etc, we can talk of
mass energy
E
=
"
m
o
c
2
,
or
E
=
mc
2
Phy107 Lecture 19
3
Example
• In a frame where the particle is at rest,
its total energy is
E
=
m
o
c
2
• Just as we can convert electrical energy to
mechanical energy, it is possible to tap mass
energy
• A 1 kg mass has (1kg)(3x10
8
m/s)
2
=9x10
16
J of
energy
– We could power
30 million 100 W light bulbs for one year!
(~30 million sec in 1 yr)
Phy107 Lecture 19
4
Nuclear Power
• Doesn’t convert whole
protons or neutrons to energy
• Extracts some of the binding
energy of the nucleus
–
90
Rb and
143
Cs + 3n have less
rest mass than
235
U +1n:
E = mc
2
Phy107 Lecture 19
5
Energy and momentum
• Relativistic energy is
• Since
γ
depends on velocity, the energy is measured to be
different by different observers
• Momentum also different for different observers
–
Can think of these as analogous to space and time, which individually
are measured to be different by different observers
• But there is something that is the same for all observers:
• Compare this to our spacetime invariant
E
=
m
o
c
2
E
2
"
c
2
p
2
=
m
o
c
2
( )
2
= Square of rest energy
x
2
"
c
2
t
2
Phy107 Lecture 19
6
A relativistic perspective
• The concepts of space, time, momentum, energy
that were useful to us at low speeds for Newtonian
dynamics are a little confusing near light speed
• Relativity needs new conceptual quantities,
such as spacetime and energymomentum
• Trying to make sense of relativity using space and
time separately leads to effects such as time
dilation and length contraction
• In the mathematical treatment of relativity,
spacetime and energymomentum objects are
always considered together
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
Phy107 Lecture 19
7
General Relativity and Gravity
• Special Relativity deals with
inertial reference frames
,
frames moving with a constant relative velocity.
• It has some rather unusual predictions
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 n/a
 Energy, Mass

Click to edit the document details