new today – exam#2 review energy, work, etc. · 2010. 3. 25. · isp209s10 exam2 review -1-today...

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. Idon’t care if you hand write or type them.

• List of topics to study is up on the web under today’sreading assignment

• As with exam 1, there will be an exam 2 extra creditopening 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 tolift 200 kg 1m? Assume people are 10%efficient in converting chemical energy towork.

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


Which of the following is correct concerning

temperature?

A. The average kinetic energy of molecules in a gas

increases at the temperature is increased.

B. Thermal motion Is highly organized

C. 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 bearranged. S = kBln(# of arrangements)

• S = Heat/T – thermal energy goes toward increasing the entropy

• Second Law of Thermodynamics – The entropy of a closed systemalways increases.

• As the pendulum swings useful energy is lost to increasing therandom motion of the air and pivot (heat)

• 2nd law => There is no way to recollect the thermal energy andmake 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 -6-

Energy and Entropy - Pendulum Example

Ener

gy

The thermal

energy (heat)

is “lost”

If there is no friction, the pendulum swings

forever, always following the same trajectory.

The figure shows how the energy is split into Kinetic

And Potential energy at each point in the trajectory.


Energy and Entropy - Pendulum Example

Ener

gy

The thermal

energy (heat)

is “lost”


Coin Toss Example

• Suppose we have 10 coins: HHHHHHHHHH

S = k ln(1) = 0

3.18101

5.25452

6.611203

7.382104

7.632525

7.382106

6.611207

5.25458

3.18109

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


Why does time always move in one direction?

• The Universe was created with very low entropy. Much toolow for its size. It is like the Universe started with all heads.

• Hence, everything in the Universe moves toward reaching thecorrect 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 dilation

C) 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 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 -12-

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-particles

have opposite

charge

0

-1


How nature is put together from the pieces…

AtomsAtomic

NucleusA proton (uud)

Made of nuclei and

electrons. Size: 10-9m

Made of neutrons and

proton. Size 10-14 m

Made of quarks:

Size 10-15 m

A neutron has

ddu


A summary of the forces of nature

anything with

mass

quarks, electrons

(leptons) ,

neutrinos

anything with

charge

quarks

Acts on

infiniteGraviton

(?)6x10-39Gravity

10-18

Only 0.001

width of proton

Vector

Bosons

W+, W-, Z0

10-6Weak

infinitephoton1/137Electromagnetic

10-15 size of a

proton

Gluon, g1Strong

Range (m)CarrierStrengthForce


Our Picture of Force

A charge creates a field…

!4

htE "##

Virtual particles can exist for a short

time.

Feynman diagram

Picture of

the field


Coulombs Law

• Charge comes in units of 1.6E-19C.

• The force between two charges is:

• Example (inverse square law): 4 times the

distance

2

2

9

2

12

21 1099.8;C

Nmk

r

qkqF !== 1 2

r12

( ) ddF

r

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 south

magnetic pole at the North geographic pole.

N

S

N

S

T/F

• T North pole of a compass points north in

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


Map for the Electric Field

Note: we could make similar maps for all the fields in nature

(gravity, weak, EM, strong).ISP209s10 Exam2 Review -20-

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 theelectric 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 electric

field 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.

Highest

Magnitude

Of 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 15.5

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


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 downV


Quantum Mechanics Review

• Light can be described as an electromagnetic wave or a littlebundle 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 Principle

What 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 byhumankind is a few grams.

• Matter and anti-matter annihilate each other when they meetand 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 changethe 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!


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 discrete

bundles of energy (quanta or photons)

h = 6.625E-34 Js Planck’s Constant

Particle-like:

We cannot predict the individual dots position. Quantum theory

Can only predict the pattern that emerges with a large number of dots

(probabilities). ISP209s10 Exam2 Review -30-

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.

Each “lump” is an

Electron hitting the

Screen.

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

overall pattern that emerges with a large # of dots.

“electron gun”


… 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…

Observation can alter the outcome in QM


Quantum Nonlocality

1

2

1

2

After interaction the wave functions are

entangled.

If we measure 1 and 2 at the same time the

difference in position forms an interference

pattern.

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.

Interaction


What is “waving” for matter waves?

• Probability – all particles described by a “wave

function” !. The square of ! gives the probability

density of finding a particle per unit volume.

• The ! extends over all space, which gives weird

consequences.

= prob. of finding particle in a small

volume V centered at the point r.


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.


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 quark

and anti-quark by a

collision of an electron

and an anti-electron. 010neutrino01-1electron

1/302/3Down

quard

1/30-1/3Up quark

BaryonLeptonChargeName

quark + anti-

quark

electron +

anti-electron

AfterBefore


Some examples

010neutrino

01-1electron

1/302/3Down

quark

1/30-1/3Up

quark

BaryonLeptonChargeName

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

0 + 01 + -1

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

Quark + anti

quark

Electron +

anti-electron

AfterBefore

allowed

Baryon

Lepton

Charge


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 - "

Two quarks

interacting via the

strong force


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

correct


Other Examples

ud!+

+ - " "

t ime

Decay of

pion

Charge of

W is not

correct

Baryon and

lepton not

conserved

Wrong because

electric force does

not act on neutrinos

Wrong because

electric force does

not act on neutrinos

new today – exam#2 review energy, work, etc. · 2010. 3. 25. · isp209s10 exam2 review -1-today...

Documents