Physics 2D Lecture Slides Oct 13 Vivek Sharma UCSD Physics Quiz - - PowerPoint PPT Presentation

Physics 2D Lecture Slides Oct 13

Vivek Sharma UCSD Physics

Quiz 2 : Wild Wild West got a Bit too wild

x 50m/s ScarFace MadBull

In the old west, a sheriff riding on a train traveling 50m/s sees a shootout between two bandits standing on the earth 50m apart parallel to the

• train. The sheriff’s instruments indicate that in his reference frame

the two men fired simultaneously. (a) Which of the two bandits, the first one the train passes from the left (ScarFace) or the second one (MadBull) sould be arrested for firing the first shot? (b) how much earlier did he fire? (c) who was struck first? Hint: Deduce your answers from the Lorentz transformation rules.

Relativistic Kinetic Energy & Newtonian Physics

2 1 2 2 2 2 2 2 2 2 2 2 2

Relativistic KE = 1 When , 1- 1 ...smaller terms 2 1 so [1 ] (classical form recovered) 1 2 2 u u u c c c u K mc mc mc c mc mu γ

−

− ⎡ ⎤ << ≅ + + ⎢ ⎥ ⎣ ⎦ ≅ + − =

2 2 2

For a particle Total Energy of a Pa at rest, u = 0 Total Energy E= r m ticle c E mc KE mc γ = = + ⇒

Sunshine Won’t Be Forever

Q: Solar Energy reaches earth at rate of 1.4kW per square meter of surface perpendicular to the direction of the sun. by how much does the mass of sun decrease per second owing to energy loss? The mean radius of the Earth’s orbit is 1.5 x 1011m.

• Surface area of a sphere of radius r is A = 4πr2
• Total Power radiated by Sun = power received by a sphere whose radius is equal to earth’s orbit radius

r

2 3 2 11 2 26 26 9 2 8 2 30 2 6

(1.4 10 / )(4 )(1.5 10 ) 4.0 10 So Sun loses E=4.0 10 J of rest energy per secon 4 E 4.0 10 J mass decreases by m= 4.4 10 !! ( d Its If the Sun's Mass = 2. 3 0 10 So .0 10 ) how P P P A r A A k W m P W g kg c π π = = × = = × × = × × = × × × long with the Sun last ?

Relationship between P and E

2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 4 2 2

1 ( ) = ( ) ( ) ........important relation F (

• r

) E m c p c m u c E p c m c m u c m c u c u c c u m c m c c u c E mc p mu E p c m u c m c γ γ γ γ γ γ γ = = ⇒ = ⇒ = ⇒ − = − = − − = − − − + = =

2 2 2 2 4

E E= pc or p = (light has momentu particles with zero rest mass like pho m!) c Relativistic Invariance ton (EM waves) : In all Ref Frames Rest : E p c m c − = Mass is a "finger print" of the particle

Mass Can “Morph” into Energy & Vice Verca

• Unlike in Newtonian mechanics
• In relativistic physics : Mass and Energy are the same

thing

• New word/concept : Mass-Energy , just like spacetime
• It is the mass-energy that is always conserved in every

reaction : Before & After a reaction has happened

• Like squeezing a balloon :

– If you squeeze mass, it becomes (kinetic) energy & vice verca !

• CONVERSION FACTOR = C2
• This exchange rate never changes !

Mass is Energy, Energy is Mass : Mass-Energy Conservation

be 2 f 2

• re

after 2 2 2 2 2 2 2 2 2 2

2 2 1 Kinetic energy has been transformed E E into mass increase 2 2

• 2

1 1 1 mc mc Mc K m u u c c M M m M m m u c c c c u = + = ⇒ − − ∆ = = = = > − −

2 2 2

mc c ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ − ⎜ ⎟ ⎜ ⎟ ⎝ ⎠

Examine Kinetic energy Before and After Inelastic Collision: Conserved? S 1 2 Before v v 2 1 After V=0 K = mu2 K=0 Mass-Energy Conservation: sum of mass-energy of a system of particles before interaction must equal sum of mass-energy after interaction

Kinetic energy is not lost, its transformed into more mass in final state

Creation and Annihilation of Particles

µ+ µ-

+

Sequence of events in a matter-antimatter collision: e e µ µ γ

+ − −

→ + + →

Relativistic Kinematics of Subatomic Particles

Reconstructing Decay of a π Meson π+

ν

µ+

At rest

Pν , Εν

Pµ , Εµ

2

is invisible, has m 0; leaves a trace in a B The decay of a stationary happens quickly, mass=106 MeV/c , field What was mass of the fleeting KE = Energy Conservati 4.6 MeV

• n:

E ? E E

π µ

π µ υ υ π µ µ +

+ + + +

≅ = → +

2 2 2 2 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Momentum Conservation : ( ) ( ) ( ) m ( ) ( ) Substituting for = 2 m 2 2 p p p c E m c K m c m c K c m c K K m c c m c p c p c m c m K m c c p c p c also p c K K

ν π µ µ υ π µ µ µ µ µ ν µ µ µ µ µ µ µ µ µ µ µ π µ µ µ

⇒ = ⇒ = − = + − + = + + = + + + + ⇒ = + +

2 2 2

Put in all the known #s 111 31 141 141 / m M m c MeV MeV Me V V c c e m

π π µ µ

⇒ = = + = ⇒

Detecting Baby Universes : Need a “Camera”

My Discovery (1993): Beauty With Strangeness

Two Faced Particle : Beauty With Strangeness (Bs) Sometimes Matter Sometimes Antimatter

Conservation of Mass-Energy: Nuclear Fission

2 2 2 2 3 1 2 1 2 3 2 2 2 1 2 3 2 2 2

1 1 1 M c M c M c Mc u u u c c M M c M M = + − > + + − + ⇒ −

M

M1 M2

M3

+ +

Nuclear Fission < 1 < 1 < 1

Loss of mass shows up as kinetic energy of final state particles Disintegration energy per fission Q=(M – (M1+M2+M3))c2 =∆Mc2

90 9 236 92 143

• 27

55 1

• 28

2

U 931.49 Me + +3 n ( ) m=0.177537u=2 Cs 1 AMU= 1.6605402 10 energy release/fission =peanuts .9471 10 165.4 MeV= b V R kg kg ∆ × = × = →

What makes it explosive is 1 mole of Uranium = 6.023 x 1023 Nuclei !!

Energy Released by 1 Kg of Fissionable Uranium

2

• 23

24 24 3 3

6.023 10 N = 1000 2.55 10 236 / 1 Mole of Uranium = 236 gm, Avagadro''s # = 6.023 10 Nuclei So in 1 kg nu Note 1 MeV = 4.45 2. clei 1 Nuclear fission = 165.4 MeV 10 165.4 MeV 1 1 55 g g g mole × × × × ∴ = × = × ×

20 6

If the power plant has conversion efficiency = 40% Energy Tr 1 100 lamp ca ansformed = n be lit for 748 85 1 00 yea ! rs kWh kWh W × ⇒

Nuclear Fission Schematic

Absorption of Neutron Excited U Oscillation Deforms Nucleus Unstable Nucleus

Sustaining Chain Reaction: 1st three Fissions

To control reaction => define factor K

Supercritical K >> 1 in a Nuclear Bomb Critical K = 1 in a Nuclear Reactor Average # of Neutrons/Fission = 2.5 Neutron emitted in fission of one U Needs to be captured by another

Schematic of a Pressurized-Water Reactor

Water in contact with reactor core serves as a moderator and heat transfer

• Medium. Heat produced in fission drives turbine

Lowering Fuel Core in a Nuclear Reactor

First Nuke Reactor :Pennsylvania 1957 Pressure Vessel contains : 14 Tons of Natural Uranium + 165 lb of enriched Uranium Power plant rated at 90MW, Retired (82) Pressure vessel packed with Concrete now sits in Nuclear Waste Facility in Hanford, Washington

Nuclear Fusion : What Powers the Sun

Mass of a Nucleus < mass of its component protons+Neutrons Nuclei are stable, bound by an attractive "Strong Force Think of Nucle " i as

Opposite of Fission

Binding Energy: Work/Energy required to pull a bound system (M) apart leaving its components (m) free of molecules and proton/neut the attractive force and ron as atoms at rest: making it

4 2 2 2 1 1 n 2 2 i i=1

He + = H + H Helium Deuterium Deuterium Th Mc ink of ene +BE= m rgy r 23.9 Me elease c n V d i

∑

26 38

Fusion as in Chem Sun's Power Output = 4 10 Watts 10 No wonder S Dissociati un is consi Fusion/Sec dered a God

• n en

in

• n

m ergy any d cultures ! × ⇒

Nuclear Fusion: Wishing For The Star

• Fusion is eminently desirable because

– More Energy/Nucleon

• (3.52 MeV in fusion Vs 1 MeV in fission)
• 2H + 3H 4He + n + 17.6 MeV

– Relatively abundant fuel supply – No danger like nuclear reactor going supercritical

• Unfortunately technology not commercially available

– What’s inside nuclei => protons and Neutrons – Need Large KE to overcome Coulomb repulsion between nuclei

• About 1 MeV needed to bring nuclei close enough together

for Strong Nuclear Attraction fusion

• Need to

– heat particle to high temp such that kT ≈ 10keV tunneling – High density plasma at high temp T ≈ 108 K like in stars – Confine Plasma (± ions) long enough for fusion » In stars, enormous gravitational field confines plasma

Inertial Fusion Reactor : Schematic

Pellet of frozen-solid Deuterium & tritium bombarded from all sides with intense pulsed laser beam with energy ≈106 Joules lasting 10-8 S Momentum imparted by laser beam compresses pellet by 1/10000 of normal density and heats it to temp T ≈ 108 K for 10-10 S Burst of fusion energy transported away by liquid Li

World’s Most Powerful Laser : NOVA @ LLNL

Generates 1.0 x 1014 watts (100 terawatts)

Size of football field, 3 stories tall 10 laser beams converge onto H pellet (0.5mm diam) Fusion reaction is visible as a starlight lasting 10-10 S Releasing 1013 neutrons