today – exam#2 reviebogner/isp209s2010/lectures/exam2review.pdf · isp209s10 exam2 review...

ISP209s10 Exam2 Review -1-

Today – Exam#2 Review• 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 byThursday morning.


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.


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 towork.

Work = mgh = 200 x 9.81 x 1 = 1962 JChemical energy=Work/eff=1962J/.1=19620.#Calories = 19620 J/(4184 J/Cal) = 4.69 Cal


Which of the following is correct concerningtemperature?

A. The average kinetic energy of molecules in a gasincreases at the temperature is increased.

B. Thermal motion Is highly organizedC. As a gas is cooled, the molecules more more rapidly.D. Temperature is a measure of the average potential

energy of atoms.E. Temperature is not related to energy.


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)


Energy and Entropy - Pendulum Example

Ener

gy

The thermalenergy (heat)is “lost”

If there is no friction, the pendulum swingsforever, always following the same trajectory.

The figure shows how the energy is split into KineticAnd Potential energy at each point in the trajectory.


Energy and Entropy - Pendulum Example

Ener

gy

The thermalenergy (heat)is “lost”


Coin Toss Example• Suppose we have 10 coins: HHHHHHHHHH

S = k ln(1) = 0

3.181015.254526.6112037.3821047.6325257.3821066.6112075.254583.18109

Entropy (J/K) *10-23Number of waysHeads


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 theother way. In this case very means so improbably that it neverhappens.

• Time has a direction because going back in time would implythe entropy could be decreased. That is very improbable.

• The Universe tends toward increasing entropy.


Clicker Question

What principle of Nature distinguishes between the forward and backward directions of time?

A) Newton’s 3rd law (“law of force pairs”)B) Time dilationC) Entropy always increases (2nd law of Thermodynamics)D) E = mc2

E) 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 forward and backward flow of time.


Clicker question

Which statement applies to the 2nd law of Thermodynamics?

A) The total entropy or microscopic disorganization of allParticipants in a physical process always increases.

B) It is the reason why we never see a broken egg on the floorspontaneously 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.


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 withthe others– It is very weak compared to the others. Why?

• Our current understanding of nature is by Quantumfield theory: EM - quantum electrodynamics,EM+weak - electroweak theory, Strong - quantumchromodynamics).

• Our understanding of force involves the exchange offorce carrying bosons between particles


The particles of nature

T. Kondo

Charge

+2/3

-1/3

anti-particleshave oppositecharge

0

-1


How nature is put together from the pieces…

Atoms AtomicNucleus

A proton (uud)

Made of nuclei andelectrons. Size: 10-9m

Made of neutrons andproton. Size 10-14 m

Made of quarks:Size 10-15 mA neutron hasddu


A summary of the forces of nature

anything withmass

quarks, electrons(leptons) ,neutrinos

anything withcharge

quarks

Acts on

infiniteGraviton(?)

6x10-39Gravity

10-18

Only 0.001width of proton

VectorBosons

W+, W-, Z0

10-6Weak

infinitephoton1/137Electromagnetic

10-15 size of aproton

Gluon, g1Strong

Range (m)CarrierStrengthForce


Our Picture of Force

A charge creates a field…

!4

htE "##

Virtual particles can exist for a shorttime.

Feynman diagram

Picture ofthe field


Coulombs Law• Charge comes in units of 1.6E-19C.

• The force between two charges is:

• Example (inverse square law): 4 times thedistance

2

2

9

2

12

21 1099.8;C

Nmk

r

qkqF !== 1 2

r12

( ) dd Fr

qkq

r

qkq

r

qkqF

16

1

16

1

4

1

42

12

21

2

12

21

22

12

21

4====


The Earth behaves as a large magnet

The Earth is like a large magnet with a southmagnetic pole at the North geographic pole.

NS

NS

T/F• T North pole of a compass points north innorthern hemisphere• F North pole of a compass points south insouthern hemisphere• T North pole of a compass points towardsthe north in the southern hemisphere


Map for the Electric Field

Note: we could make similar maps for all the fields in nature(gravity, weak, EM, strong).


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)


Sample Problem

What is the magnitude of the electricfield at 2.0 m?

( )( ) C

N

m

V

mm

VVE 0.200.20

04

800

x

V- ==

!

!!=

"

"=


Sample Problem

Electric field is the rate of change of potential with position.

HighestMagnitudeOf e-field

Zero e-field

Zero e-field


Simple Problem

F = E q

If a charge of 1.5 C is placed on an electric field of 15.5V/m, what is the magnitude of the force on the charge?

Answer:F = 15.5 N/C x 1.5 C = 23.3 N


Flow of Charge - Current

• Batteries are like pumps that lift charge to ahigher potential. The charge flows down thehill to the other side of the battery.

A batteryis like apump.

Moving Chargedoes work on theway downV


Quantum Mechanics Review• Light can be described as an electromagnetic wave or a little

bundle of energy (a photon). Light has particle and wavecharacter.

• Waves can overlap – this is called interference. Destructive ifthey cancel, Constructive if they reinforce.

• Particles, for example electrons, have wave and particleproperties.

• The thing that is waving in the case of a particle is probability.The square of the height of the wave (wave function) is ameasure of the probability density.

• All objects (atoms, molecules, etc.) exist in defined states ofenergy. The energy is quantized (quantum mechanics)


The Uncertainty PrincipleWhat is the meaning of the Uncertainty Principle?

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.

!4

hpx "##


Antiparticles and Antimatter

• All particles have a corresponding anti-particle with oppositequantum numbers. We write the anti-particle with a bar overthe top, e.g. proton – p anti-proton p

• Antimatter (matter made of anti-particles) is very difficult tomake. It can artificially be produced only at large particleaccelerators (“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


Why is Quantum Theory so strange?

• What you thought were waves can act likeparticles 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 outcomeWe don’t see any of the weirdness in our daily lives. But if youlook at microscopically small phenomena (atoms), it seems to indeed be reality!


Look closer, you see light acts like a particle…

EEM = 0, 1hf, 2hf, 3hf, 4hf, …

h*f = energy of 1 photon

EM fields are made of discretebundles of energy (quanta or photons)

h = 6.625E-34 Js Planck’s Constant

Particle-like:

We cannot predict the individual dots position. Quantum theoryCan only predict the pattern that emerges with a large number of dots(probabilities).


Particles acting like waves

Electrons show an interference pattern in the double slit experiment.

And the interferencePatterns show a Discrete “lumpiness”If you look closely.

Each “lump” is anElectron hitting the Screen.

As with light, it is impossible to predict the positionOf each individual dot. Nature is intrinsically random!We can only predict “probabilities”, which is to say the overall pattern that emerges with a large # of dots.

“electron gun”


… and a watched electron doesn’t show interferenceIf you try to find outWhich slit each electronGoes thru, the wave featuresGo away

An electron Detector

Many more weird examples…

Observation can alter the outcome in QM


Quantum Nonlocality

1

2

1

2

After interaction the wave functions areentangled.

If we measure 1 and 2 at the same time thedifference in position forms an interferencepattern.

If we measure 2 before 1, the measurementof 2 defines where 1 must hit. Thisinformation travels faster than the speed oflight.This has been confirmed experimentally.

Interaction


What is “waving” for matter waves?

• Probability – all particles described by a “wavefunction” ψ. The square of ψ gives the probabilitydensity of finding a particle per unit volume.

• The ψ extends over all space, which gives weirdconsequences.

= prob. of finding particle in a small volume V centered at the point r.


Neutrinos

• Neutrinos are subatomic particles that do not havecharge. They only interact via the weak force.

• These are very unusual particles and we still don’tknow much about their properties. They have amass, but it is so small we have not been able tomeasure it.

• They account for about 2% of the universe butinteract weakly. One light-year of lead would haveonly a 50% chance of stopping one.


Equations – sort of

Rules for Feynman Diagrams:

1). The number of leptons and baryons must be conserved.

2). Charge must be conserved.

Not allowed


Some examples

Is the following allowed?Production of a quarkand anti-quark by acollision of an electronand an anti-electron. 010neutrino

01-1electron

1/302/3Downquard

1/30-1/3Up quarkBaryonLeptonChargeName

quark + anti-quark

electron +anti-electron

AfterBefore


Some examples

010neutrino01-1electron

1/302/3Downquark

1/30-1/3Upquark

BaryonLeptonChargeName

1/3 + (-1/3)-1 + 1

0 + 01 + -11/3 + (-1/3)0 + 0

Quark + antiquark

Electron +anti-electron

AfterBefore

allowed

BaryonLeptonCharge


Is this possible?

Yes, it is two quarks interacting via the electromagnetic force.Up quarks have electric charge of +2/3.


Force Carriers

• Stong – Gluons – g• Weak – Intermediate vector bosons – Z,W• Electromagnetic – photon - γ

Two quarksinteracting via thestrong force


Feynman Diagrams and rulesCharge, baryon number, and lepton number are conserved

Consider the decay of a +pion into an antimuon by the Weakforce. Which diagram describes this process?

ud!+

+ - " "

time

correct


Other Examplesud!+

+ - " "

time

Decay ofpion

Charge ofW is notcorrect

Baryon andlepton notconserved

Wrong becauseelectric force doesnot act on neutrinos

Wrong becauseelectric force doesnot act on neutrinos

today – exam#2 reviebogner/isp209s2010/lectures/exam2review.pdf · isp209s10 exam2 review...

Documents