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Today – Exam#2 Review
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•
•
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Exam #2 is Tuesday 3/30
The exam is 40 multiple choice questions.
Bring your calculator
You can use 5 (!) pages (front and back) of notes. I
don’t care if you hand write or type them.
• List of topics to study is up on the web under today’s
reading assignment
• As with exam 1, there will be an exam 2 extra credit
opening in CAPA at 4pm on Tuesday 3/30 due by
Thursday morning.
ISP209s10 Exam2 Review
-1-
Energy, Work, etc.
• Two kinds of energy: Kinetic – energy of motion, Potential
– energy of position
• Energy is measured in Joules, J
• Power = Energy/time . The unit is Watts = J/s
• Energy is always conserved. Energy conservation can be
used to find how high something will go.
• Work = force x distance, converts energy from one form to
another.
ISP209s10 Exam2 Review
-2-
Chemical Energy
• 1 Calorie = 4184 J
• How many Calories are used by a person to
lift 200 kg 1m? Assume people are 10%
efficient in converting chemical energy to
work.
Work = mgh = 200 x 9.81 x 1 = 1962 J
Chemical energy=Work/eff=1962J/.1=19620.
#Calories = 19620 J/(4184 J/Cal) = 4.69 Cal
ISP209s10 Exam2 Review
-3-
Which of the following is correct concerning
temperature?
A.
B.
C.
D.
E.
The average kinetic energy of molecules in a gas
increases at the temperature is increased.
Thermal motion Is highly organized
As a gas is cooled, the molecules more more rapidly.
Temperature is a measure of the average potential
energy of atoms.
Temperature is not related to energy.
ISP209s10 Exam2 Review
-4-
Entropy
• Entropy is a measure of the number of ways a system can be
arranged. S = kBln(# of arrangements)
• S = Heat/T – thermal energy goes toward increasing the entropy
• Second Law of Thermodynamics – The entropy of a closed system
always increases.
• As the pendulum swings useful energy is lost to increasing the
random motion of the air and pivot (heat)
• 2nd law => There is no way to recollect the thermal energy and
make the pendulum swing higher as in the frictionless case.
(slighly less correct definition sometimes used that “entropy is
the measure of microscopic disorder” in a system)
ISP209s10 Exam2 Review
-5-
Energy
Energy and Entropy - Pendulum Example
If there is no friction, the pendulum swings
forever, always following the same trajectory.
The thermal
energy (heat)
is “lost”
The figure shows how the energy is split into Kinetic
ISP209s10
Exam2 point
Review in the trajectory.
And Potential energy
at each
-6-
Energy
Energy and Entropy - Pendulum Example
The thermal
energy (heat)
is “lost”
ISP209s10 Exam2 Review
-7-
Coin Toss Example
• Suppose we have 10 coins: HHHHHHHHHH
S = k ln(1) = 0
Heads
Number of ways
Entropy (J/K) *10-23
9
10
3.18
8
45
5.25
7
120
6.61
6
210
7.38
5
252
7.63
4
210
7.38
3
120
6.61
2
45
5.25
1
ISP209s10 Exam210
Review
3.18
-8-
Why does time always move in one direction?
• The Universe was created with very low entropy. Much too
low for its size. It is like the Universe started with all heads.
• Hence, everything in the Universe moves toward reaching the
correct amount of entropy. It is very improbable to go the
other way. In this case very means so improbably that it never
happens.
• Time has a direction because going back in time would imply
the entropy could be decreased. That is very improbable.
• The Universe tends toward increasing entropy.
ISP209s10 Exam2 Review
-9-
Clicker Question
What principle of Nature distinguishes between the
forward and backward directions of time?
A)
B)
C)
D)
E)
Newton’s 3rd law (“law of force pairs”)
Time dilation
Entropy always increases (2nd law of Thermodynamics)
E = mc2
The concept of the “absolute zero” temperature
Indeed, with the exception of some rare subatomic processes, the
Laws of Physics (aside from the 2nd-law of Thermodynamics)
Don’t distinguish between
and backward flow of time.-10ISP209s10forward
Exam2 Review
Clicker question
Which statement applies to the 2nd law of Thermodynamics?
A) The total entropy or microscopic disorganization of all
Participants in a physical process always increases.
B) It is the reason why we never see a broken egg on the floor
spontaneously reassemble itself on the table from which it fell.
C) Thermal energy flows from higher to lower temperatures
D) You can never convert 100% of thermal energy into work.
E) All of the above.
ISP209s10 Exam2 Review
-11-
Our current understanding of Forces
• There are 4 known forces in nature (Gravity, weak,
EM- electromagnetic , strong)
• Gravity does not fit well in our understanding with
the others
– It is very weak compared to the others. Why?
• Our current understanding of nature is by Quantum
field theory: EM - quantum electrodynamics,
EM+weak - electroweak theory, Strong - quantum
chromodynamics).
• Our understanding of force involves the exchange of
ISP209s10 Exam2 Review
-12force carrying bosons
between particles
The particles of nature
Charge
+2/3
-1/3
0
-1
anti-particles
have opposite
charge
ISP209s10 Exam2 Review
-13-
T. Kondo
How nature is put together from the pieces…
Atomic
Nucleus
Atoms
Made of nuclei and
electrons. Size: 10-9m
Made of neutrons and
proton. Size 10-14 m
ISP209s10 Exam2 Review
A proton (uud)
Made of quarks:
Size 10-15 m
A neutron has
ddu
-14-
A summary of the forces of nature
Force
Strong
Electromagnetic
Weak
Gravity
Strength
Carrier
Acts on
1
Gluon, g
quarks
1/137
photon
anything with
charge
10-6
6x10-39
Range (m)
10-15 size of a
proton
infinite
Vector
quarks, electrons 10-18
Bosons
(leptons) ,
Only 0.001
+,
0
W W,Z
neutrinos
width of proton
Graviton
(?)
ISP209s10 Exam2 Review
anything with
mass
infinite
-15-
Our Picture of Force
A charge creates a field…
Feynman diagram
Picture of
the field
h
#E#t "
4!
Virtual particles can exist for a short
time.
ISP209s10 Exam2 Review
-16-
Coulombs Law
• Charge comes in units of 1.6E-19C.
• The force between two charges is:
2
kq1q2
Nm
F = 2 ; k = 8.99 ! 109 2
r12
C
1
2
r12
• Example (inverse square law): 4 times the
distance
kq1q2
1 kq1q2 1 kq1q2 1
F4 d =
= 2 2 =
= Fd
2
2
(4r12 ) 4 r12 16 r12 16
ISP209s10 Exam2 Review
-17-
The Earth behaves as a large magnet
The Earth is like a large magnet with a south
magnetic pole at the North geographic pole.
N
S
T/F
N • T North pole of a compass points north in
S northern hemisphere
• F North pole of a compass points south in
southern hemisphere
• T North pole of a compass points towards
the north in the southern hemisphere
ISP209s10 Exam2 Review
-18-
Map for the Electric Field
Note: we could make similar maps for all the fields in nature
(gravity, weak, EM, strong).
ISP209s10 Exam2 Review
-19-
The relation between electric and magnetic fields
• Charge creates an electric field (and potential, V)
• Moving charge creates a magnetic field
• The photon is responsible for transmitting both the
electric and the magnetic forces
• Maxwell’s equations describe the following;
–
–
–
–
–
Charge makes electric fields
Changing magnetic field makes electric fields
Changing electric fields make magnetic fields
Magnets always come with a north and a south pole
EM waves travel at the speed of light (in a vacuum)
ISP209s10 Exam2 Review
-20-
Sample Problem
What is the magnitude of the electric
field at 2.0 m?
E =-
(0V ! 80V ) = 20.0 V = 20.0 N
"V
=!
(4m ! 0m )
"x
m
C
ISP209s10 Exam2 Review
-21-
Sample Problem
Zero e-field
Zero e-field
Exam2 Review
Electric field is the rateISP209s10
of change
of potential with position.
Highest
Magnitude
Of e-field
-22-
Simple Problem
F=Eq
If a charge of 1.5 C is placed on an electric field of 15.5
V/m, what is the magnitude of the force on the charge?
Answer:
F = 15.5 N/C x 1.5 C = 23.3 N
ISP209s10 Exam2 Review
-23-
Flow of Charge - Current
• Batteries are like pumps that lift charge to a
higher potential. The charge flows down the
hill to the other side of the battery.
A battery
is like a
pump.
Moving Charge
does work on the
way down
V
ISP209s10 Exam2 Review
-24-
Quantum Mechanics Review
• Light can be described as an electromagnetic wave or a little
bundle of energy (a photon). Light has particle and wave
character.
• Waves can overlap – this is called interference. Destructive if
they cancel, Constructive if they reinforce.
• Particles, for example electrons, have wave and particle
properties.
• The thing that is waving in the case of a particle is probability.
The square of the height of the wave (wave function) is a
measure of the probability density.
• All objects (atoms, molecules, etc.) exist in defined states of
energy. The energy is quantized (quantum mechanics)
ISP209s10 Exam2 Review
-25-
The Uncertainty Principle
What is the meaning of the Uncertainty Principle?
h
#x#p "
4!
A. The entropy of a closed system always increases.
B. It is not possible to know the exact position
and momentum of a particle at the same time.
C. It is not possible to ever know the exact position
of a particle.
D. Small objects have a wave function.
E. Energy is conserved in a closed system.
ISP209s10 Exam2 Review
-26-
Antiparticles and Antimatter
• All particles have a corresponding anti-particle with opposite
quantum numbers. We write the anti-particle with a bar over
the top, e.g. proton – p anti-proton p
• Antimatter (matter made of anti-particles) is very difficult to
make. It can artificially be produced only at large particle
accelerators (“atom smashers”).
• Matter and anti-matter are created naturally in pairs
• So far the total amount of antimatter ever produced by
humankind is a few grams.
• Matter and anti-matter annihilate each other when they meet
and ALL the mass is converted to energy
ISP209s10 Exam2 Review
-27-
Why is Quantum Theory so strange?
• What you thought were waves can act like
particles and visa-versa (“wave-particle duality”)
• Quantum uncertainty (Heisenberg)
• Nature is intrinsically random
• Quantum non-locality
• Nature is “digital” and “discrete”
• The very act of observing/measuring can change
the outcome
We don’t see any of the weirdness in our daily lives. But if you
look at microscopically small phenomena (atoms), it seems to
indeed be reality!
ISP209s10 Exam2 Review
-28-
Look closer, you see light acts like a particle…
EM fields are made of discrete
bundles of energy (quanta or photons)
EEM = 0, 1hf, 2hf, 3hf, 4hf, …
h*f = energy of 1 photon
Particle-like:
h = 6.625E-34 Js
Planck’s
Constant
We cannot predict the individual dots position. Quantum theory
Can only predict the pattern that emerges with a large number of dots
ISP209s10 Exam2 Review
-29(probabilities).
Particles acting like waves
Electrons show an interference pattern in the double slit experiment.
And the interference
Patterns show a
Discrete “lumpiness”
If you look closely.
“electron gun”
As with light, it is impossible to predict the position
Of each individual dot. Nature is intrinsically random!
We can only predict “probabilities”, which is to say the
ISP209s10
Exam2#Review
overall pattern that emerges with
a large
of dots.
Each “lump” is an
Electron hitting the
Screen.
-30-
Observation can alter the outcome in QM
… and a watched electron doesn’t show interference
If you try to find out
Which slit each electron
Goes thru, the wave features
Go away
An electron
Detector
Many more weird examples…
ISP209s10 Exam2 Review
-31-
Quantum Nonlocality
After interaction the wave functions are
entangled.
2
2
If we measure 1 and 2 at the same time the
difference in position forms an interference
pattern.
Interaction
1
1
If we measure 2 before 1, the measurement
of 2 defines where 1 must hit. This
information travels faster than the speed of
light.
This has been confirmed experimentally.
ISP209s10 Exam2 Review
-32-
What is “waving” for matter waves?
• Probability – all particles described by a “wave
function” ψ. The square of ψ gives the probability
density of finding a particle per unit volume.
• The ψ extends over all space, which gives weird
consequences.
= prob. of finding particle in a small
volume V centered at the point r.
ISP209s10 Exam2 Review
-33-
Neutrinos
• Neutrinos are subatomic particles that do not have
charge. They only interact via the weak force.
• These are very unusual particles and we still don’t
know much about their properties. They have a
mass, but it is so small we have not been able to
measure it.
• They account for about 2% of the universe but
interact weakly. One light-year of lead would have
only a 50% chance of stopping one.
ISP209s10 Exam2 Review
-34-
Equations – sort of
Rules for Feynman Diagrams:
1). The number of leptons and baryons must be conserved.
Not allowed
2). Charge must be conserved.
ISP209s10 Exam2 Review
-35-
Some examples
Is the following allowed?
Production of a quark
and anti-quark by a
collision of an electron
and an anti-electron.
Before
After
electron +
anti-electron
quark + antiquark
Name
Lepton
Baryon
Up quark -1/3
0
1/3
Down
quard
2/3
0
1/3
electron
-1
1
0
neutrino
0
1
0
ISP209s10 Exam2 Review
Charge
-36-
Some examples
Baryon
Lepton
Charge
Before
After
Name
Charge
Lepton
Baryon
Electron +
anti-electron
Quark + anti
quark
Up
quark
-1/3
0
1/3
1/3 + (-1/3)
Down
quark
2/3
0
1/3
0+0
1 + -1
0+0
electron
-1
1
0
-1 + 1
1/3 + (-1/3)
neutrino
0
1
0
allowed
ISP209s10 Exam2 Review
-37-
Is this possible?
Yes, it is two quarks interacting via the electromagnetic force.
Up quarks have electric charge of +2/3.
ISP209s10 Exam2 Review
-38-
Force Carriers
• Stong – Gluons – g
• Weak – Intermediate vector bosons – Z,W
• Electromagnetic – photon - γ
Two quarks
interacting via the
strong force
ISP209s10 Exam2 Review
-39-
Feynman Diagrams and rules
Charge, baryon number, and lepton number are conserved
Consider the decay of a +pion into an antimuon by the Weak
force. Which diagram describes this process?
!+
ud
-
"
"
time
+
ISP209s10 Exam2 Review
correct
-40-
Other Examples
!+
Wrong because
electric force does
not act on neutrinos
ud
-
"
"
time
+
Decay of
pion
Baryon and
lepton not
conserved
Charge of
W is not Wrong because
correct
electric force does
not act on neutrinos
ISP209s10 Exam2 Review
-41-