Physics 2D Lecture Slides Lecture : Jan 19th 2005

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Physis D Leture Slides Leture : Jan 19th 005 Vivek Sharma UCSD Physis Definition (without proof) of Relativisti Momentum mu With the new definition relativisti p = = mu momentum is onserved in all 1

1 Physis D Leture Slides Leture : Jan 19th 005 Vivek Sharma UCSD Physis Definition (without proof) of Relativisti Momentum mu With the new definition relativisti p = = mu momentum is onserved in all 1 ( u / ) frames of referenes : Do the exerise New Conepts Rest mass = mass of objet measured In a frame of ref. where objet is at rest = u 1 1 ( u / ) is veloity of the objet NOT of a referene frame 1

Relativisti Fore & Aeleration p= mu 1 (u / ) = mu Relativisti Fore And Aeleration Reason why you ant quite get up to the speed of light no matter how hard you try * dp d ) mu d du d, use F= = + = dt

2 Relativisti Fore & Aeleration p= mu 1 (u / ) = mu Relativisti Fore And Aeleration Reason why you ant quite get up to the speed of light no matter how hard you try * dp d ) mu d du d, use F= = + = dt dt +- 1 # (u / ),. dt dt du m mu #1 #u % du F =$ + & ( )( ) $ 1 # (u / ) (1 # (u / ) )3/ % dt ' ( m # mu + mu % du F =$ 3/ $ (1 # (u / ) ) % dt ' ( m % du : Relativisti Fore F =$ $ (1 # (u / ) )3/ % dt ' ( du Sine Aeleration a =, [rate of hange of veloity] dt 3/ F 1 # (u / ) ( / a= m' Note: As u / 0 1, a 0 0 Its harder to aelerate when you get loser to speed of light Linear Partile Aelerator : 50 GigaVolts Aelating Potential 3/ ee $1 # (u / ) % a= m PEP-II aelerator shemati and tunnel view

3 Relativisti Work Done & Change in Energy x 1, u=0 X, u=u x x dp W = * F. dx = *. dx dt p x1 x1 du m mu dp dt = = 3/ u dt u # 1$ 1$ substitute in W, du u m udt W = dt (hange in var x ) u) * 3/ 0 u # % 1$ & ' ( % & ' (, Relativisti Work Done & Change in Energy X, u=u x 1, u=0 W u mudu m = = m ) 3/ 1/ 0 # u $ # u $ % 1 1 & % & ' ( ' ( = m m Work done is hange in energy (KE in this ase) K = m m or Total Energy E= m = K + m 3

4 K = $ # But Professor Why Can s ANYTHING go faster than light? m 1 u ( ) = 1/ m ( K + m % ' & ( 1 u % $ ' = m 4 K + m % # # & & ( u = 1 ( K m + 1) ) $ * + # (Paraboli in u Vs As u /, Kineti Energy K / 0 ( Need to do infinite amount of work on the partile to rev it up to the speed of light m 1/ 1 u % ' & K m ), Non-relativisti ase: K = 1 mu ( u = K m Relativisti Kineti Energy Vs Veloity 4

5 A Digression: How to Handle Large/Small Numbers Example: onsider very energeti partile with very large Energy E E m + K K = = = 1+ m m m u 1 # Lets Say γ = 3x10 11, Now alulate u from = 1 % $ & ' ( Try this on your el-heapo alulator, you will get u/ =1, u= due to limited preision. In fat u but not exatly, try to get this analytially 1 1 = = 1# (1 # )(1 + ) u Sine = $ 1, 1+ = 1 % 1# 1 # 4 & 1# = = 5' 10, u = & u = Suh partiles are routinely produed in violent osmi ollisions 1/ In Quizzes, you are Expeted to perform Suh simple approximations When Eletron Goes Fast it Gets Fat Total Energy E = m = K + m E = m v As 1, # Apparent Mass approahes # New Conept Rest Mass = partile mass when its at rest 5

6 Relativisti Kineti Energy & Newtonian Physis Relativisti KE K = m m # Remember Binomial Theorem $ & n nx n(n-1) ' & for x << 1; (1+x) = (1+ + x +smaller terms) ' ) 1 * # $ 1 u 1 u % When u < <, & smaller terms ' ( + + ) * 1 u 1 so K ( m [1 + ] m = mu (lassial form reovered) Total Energy of a Partile E = m = KE + m For a partile at rest, u = 0 Total Energy E= m E=m Sunshine Won t Be Forever Q: Solar Energy reahes earth at rate of 1.4kW per square meter of surfae perpendiular to the diretion of the sun. by how muh does the mass of sun derease per seond owing to energy loss? The mean radius of the Earth s orbit is 1.5 x m. r Surfae area of a sphere of radius r is A = 4πr Total Power radiated by Sun = power reeived by a sphere whose radius is equal to earth s orbit radius 6

7 E= m Sunshine Won t Be Forever r Total Power radiated by Sun = power reeived by a sphere with radius equal to earth-sun orbit radius( r in figure) Earth P P sun inident Plost = A = A A r W sun 6 P = 4.0# 10 W lost Earth inident 3 11 earth sun 4 earth sun = (1.4# 10 / m )(4 )(1.5# 10 ) 6 So Sun loses E = 4.0# 10 J of rest energy per seond I ts mass dereases by m = If the Sun's Mass =.0 # 10 6 E 4.0# 10 J = = # 8 (3.0# 10 ) kg per se kg So how long with the Sun last? One day the sun will be gone and the solar system will not be a hospitable plae for life E = m E = m 4 Relationship between P and E p = mu p = m u E # p = m 4 # m u = m ( # u ) = m 1# u ( # u ) = m 4 # u ( # u ) = m 4 E = p + (m )...important relation For partiles with zero rest mass like photon (EM waves) E= p or p = E (light has momentum) Relativisti Invariane : E # p = m 4 : In all Ref Frames Rest Mass is a finger print of the partile 7

8 Mass Can Morph into Energy & Vie Vera In Newtonian mehanis: mass and energy separate onepts In relativisti physis : Mass and Energy are the same thing New word/onept : MassEnergy, just like SpaeTime It is the mass-energy that is always onserved in every reation : Before & After a reation has happened Like squeezing a balloon : Squeeze here, it grows elsewhere If you squeeze mass, it beomes (kineti) energy & vie vera CONVERSION FACTOR = C This exhange rate never hanges Mass is Energy, Energy is Mass : Mass-Energy Conservation Examine Kineti energy Before and After Inelasti Collision: Conserved? S K = mu K=0 Before 1 v v V=0 1 After Mass-Energy Conservation: sum of mass-energy of a system of partiles before interation must equal sum of mass-energy after interation E = E before m m m + = M ' M = > m u u u 1% 1% 1% Kineti energy has been transformed into mass inrease after # ( K m $ M = M - m = = # % m ( # u ( # 1% ( & ) Kineti energy is not lost, its transformed into more mass in final state 8

9 Creation and Annihilation of Partiles γ µ - µ + Sequene of events in a matter-antimatter ollision: e + + e # # µ + µ + Relativisti Kinematis of Subatomi Partiles Reonstruting Deay of a π Meson P ν, Ε ν ν π + At rest µ + P µ, Ε µ + + The deay of a stationary $ µ happens quikly, is invisible, has m # 0; µ + leaves a trae in a B field µ + mass=106 MeV/, KE = 4.6 MeV + What was mass of the fleeting? Energy Conservation: E = E µ + E % & m = ( mµ ) + pµ + p Momentum Conservation : p & = p µ % m = ( mµ ) + pµ + pµ 9

Relativisti Kinematis of Subatomi Partiles Energy Conservation: E =

µ mµ + K µ + K µ mµ Pµ, Εµ Put in all the known #s # m = 111MeV +

10 Relativisti Kinematis of Subatomi Partiles Energy Conservation: E = Eµ + E # m = (mµ ) + pµ + p$ Pν, Ε ν Momentum Conservation : pµ = p # m = (mµ ) + pµ + pµ ν also pµ = Eµ % (mµ ) = (K µ + mµ ) % (mµ ) π+ At rest µ+ =K µ + K µ mµ Substituting for pµ # m = mµ 4 + K µ + K µ mµ + K µ + K µ mµ Pµ, Εµ Put in all the known #s # m = 111MeV + 31MeV = 141MeV # m = 141MeV / Deteting Baby Universes : Need a Camera 10

11 Two Faed Partile : Beauty With Strangeness (Bs) Sometimes Matter Sometimes Antimatter My Disovery (1993): Beauty With Strangeness 11

12 Conservation of Mass-Energy: Nulear Fission M M 1 + M M 3 + Nulear Fission M M M M = + + u u u M > M + M + M 1 3 < 1 < 1 < 1 Loss of mass shows up as kineti energy of final state partiles Disintegration energy per fission Q=(M (M 1 +M +M 3 )) =ΔM 36 9 U # Cs+ Rb+3 n ( 1 AMU= kg = MeV) m= u= = kg MeV= energy release/fission =peanuts What makes it explosive is 1 mole of Uranium = 6.03 x 10 3 Nulei Nulear Fission Shemati : Tikling a Nuleus Absorption of Neutron Exited U Osillation Deforms Nuleus Unstable Nuleus 1

13 Sustaining Chain Reation: 1 st three Fissions Average # of Neutrons/Fission =.5 Neutron emitted in fission of one U Needs to be aptured by another To ontrol reation => define fator K Superritial K >> 1 in a Nulear Bomb Critial K = 1 in a Nulear Reator Shemati of a Pressurized-Water Reator Water in ontat with reator ore serves as a moderator and heat transfer Medium. Heat produed in fission drives turbine 13

Lowering Fuel Core in a Nulear Reator First Nulearr reator :Pennsylvania 1957 Pressure Vessel ontains : 14 Tons of Natural Uranium + 165 lb of enrihed Uranium Power plant rated at 90MW, Retired (8)

14 Lowering Fuel Core in a Nulear Reator First Nulearr reator :Pennsylvania 1957 Pressure Vessel ontains : 14 Tons of Natural Uranium lb of enrihed Uranium Power plant rated at 90MW, Retired (8) Pressure vessel paked with Conrete now sits in Nulear Waste Faility in Hanford, Washington Nulear Fusion : What Powers the Sun Opposite of Fission Mass of a Nuleus < mass of its omponent protons+neutrons Nulei are stable, bound by an attrative Strong Fore Think of Nulei as moleules and proton/neutron as atoms making it Binding Energy: Work/Energy required to pull a bound system (M) apart leaving its omponents (m) free of the attrative fore and at rest: H + M +BE H n = m i=1 i = He MeV = Deuterium Deuterium = Helium + Released Energy Think of energy released in Fusion as Dissoiation energy of Chemistry 6 38 Sun's Power Output = 4 10 Watts # 10 Fusion/Seond 14

15 Nulear Fusion: Wishing For The Star Fusion is eminently desirable beause More Energy/Nuleon (3.5 MeV in fusion Vs 1 MeV in fission) H + 3 H 4 He + n MeV Relatively abundant fuel supply, No danger like nulear reator going superritial Unfortunately tehnology not ommerially available What s inside nulei => protons and Neutrons Need Large KE to overome Coulomb repulsion between nulei About 1 MeV needed to bring nulei lose enough together for Strong Nulear Attration fusion Need to heat partile to high temp suh that thermal energy E= kt 10keV tunneling thru oulomb barrier Implies heating to T 10 8 K ( like in stars) Confine Plasma (± ions) long enough for fusion» In stars, enormous gravitational field onfines plasma Inertial Fusion Reator : Shemati Pellet of frozen-solid Deuterium & tritium bombarded from all sides with intense pulsed laser beam with energy 10 6 Joules lasting 10-8 S Momentum imparted by laser beam ompresses pellet by 1/10000 of normal density and heats it to temp T 10 8 K for S Burst of fusion energy transported away by liquid Li 15

World s Most Powerful Laser : NOVA @ LLNL Size of football field, 3

0 x 1014 watts (100 terawatts) 10 laser beams onverge onto H pellet (0.

Releasing 1013 neutrons ITER: The Next Big Step in Nulear Fusion Visit

16 World s Most Powerful Laser : LLNL Size of football field, 3 stories tall Generates 1.0 x 1014 watts (100 terawatts) 10 laser beams onverge onto H pellet (0.5mm diam) Fusion reation is visible as a starlight lasting S Releasing 1013 neutrons ITER: The Next Big Step in Nulear Fusion Visit for Details of this mega Siene & Engineering Projet This may be future of heap, lean Nulear Energy for Earthlings 16

Physics 2D Lecture Slides Lecture 7: Jan 14th 2004

Physics 2D Lecture Slides Lecture 7: Jan 14th 2004 Quiz is This Friday Quiz will over Setions.-.6 (inlusive) Remaining material will be arried over to Quiz Bring Blue Book, hek alulator battery Write all answers in indelible ink else no grade! Write answers