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

Transcription

1 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 on onseutive pages: Don t leave blank pages All nighters don t work for these quizzes Get plenty of Sleep.ome with a fresh mind! Physis D Leture Slides Leture 7: Jan 4th 004 Vivek Sharma UCSD Physis

2 Relativisti Fore & Aeleration p mu = =γ mu ( u/ ) Relativisti Fore And Aeleration dp d mu F = = dt dt ( u/ ) F = 3/ ( ( u/ ) ) Sine Aeleration a = m F ( u/ ) m du : Relativisti Fore dt du a =,[rate of hange of veloity] dt 3/ Reason why you ant quite get up to the speed of light no matter how hard you try! Note: As u/, a 0!!!! Its harder to aelerate when you get loser to speed of light Linear Partile Aelerator : Parallel Plates With Potential Differene - e - F=-eE E d V + Parallel Plates E= V/d F= -ee Charged partile q moves in straight line in a uniform eletri field E with speed u aelarates under f ore F=qE du F u qe u a = = = dt m m larger the potential differene V aross 3/ 3/ plates, larger the fore on partile Under fore, work is done on the partile, it gains Kineti energy New Unit of Energy ev =.6x0-9 Joules MeV =.6x0-3 Joules GeV =.6x0-0 Joules

3 Linear Partile Aelerator : 50 GigaVolts Aelating Potential ee a = ( u/ ) m 3/ PEP-II aelerator shemati and tunnel view Magneti Confinement & Cirular Partile Aelerator Classially v F = m r V B v qvb = m r F B r dp d( γ mu) du F = = = γ m = qub dt dt dt du u = (Centripetal aelaration) dt r u γm = qub γmu = qbr p = qbr r

4 Charged Form of Matter & Anti-Matter in a B Field Antimatter form of eletron = Positron (e + ) Same Mass but opposite Charge Positron urls the other way from eletron in a B Field Aelerating Eletrons Thru RF Cavities

5 A Cirular Aelerator : Using B Field to Confine the eletron and RF avity to power it Cirular Partile Aelerator: CERN, Geneve Aelerated eletron through an effetive voltage of 00 Billion Volts! To be upgraded to 7 trillion Volts by 007 Swiss Border Frenh Border irular trak for aelerating eletron Geneva Airport

6 In Tunnel 50m underground, 7km ring of Magnets Keep eletron in Cirular Orbit Inside A Cirular Partile Aelerator Tunnel : Monorail!

7 Test of Relativisti Momentum In Cirular Aelerator mu p = = γ mu ( u / ) γ mu γ = = qbr qbr mu = p Proof That p mu x, u=0 Relativisti Work Done & Change in Energy X, u=u x x dp W = F. dx =. dx dt p x = = 3/ u dt u W = W 0 3/ u mudu m = = m = 3/ / 0 u u Wo rk K = u x du m mu dp dt du m dt u udt, substitute in W, (hange in var x u) γ m done is hange in Kineti energy K γ m m or m Total En ergy E= γ m = K + m

8 But Professor Why Can s ANYTHING go faster than light? m m K = m / ( K + m ) = / u u u = + 4 m K m K u = ( + ) m As K, u K (Paraboli in u Vs ) m Non-relativisti ase: K = K mu u = m Relativisti Kineti Energy Vs Veloity

9 A Digression: How to Handle Large/Small Numbers Example: onsider very energeti partile with very large Energy E E m + K K γ = = = + m m m u = Lets Say γ = 3x0, Now alulate u from γ Try this on your el-heapo alulator, you will get u/ =, u= due to limited preision. In fat u but not exatly!, try to get this analytially γ = = β ( β)( + β) u Sine β=, + β = γ β 4 β = = 5 0, u = β γ u = !! Suh partiles are routinely produed in violent osmi ollisions / In Quizzes, you are Expeted to perform Suh simple approximations When Eletron Goes Fast it Gets Fat Total Energy E = γ m = K + m E = γ m v As, γ Apparent Mass approahes New Conept Rest Mass = partile mass when its at rest

10 Relativisti Kineti Energy & Newtonian Physis Relativisti KE K = γ m m Remember Binomial Theorem n nx n(n-) for x << ; (+x) = (+ + x +smaller terms)!! u u When u< <, -...smaller terms + + u so K m [ + ] m = mu (lassial form reovered) Total Energy of a Partile E = γ 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.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.5 x 0 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 P P P= A= 4π r A A 6 P= W = (.4 0 W / m )(4 π )(.5 0 ) 3 6 So Sun loses E=4.0 0 J of rest energy per seond 6 E J 9 Its mass dereases by m= = = kg!! 8 If the Sun's Mass =. ( ) kg how long with the Sun last? So

11 E = γ m E = γ m 4 Relationship between P and E p = γ mu p = γ mu 4 E p = γ m γ m u = γ m ( u ) m m = ( ) ( ) 4 4 u = u = m u u E = p + ( m )...important relation For partiles with zero rest mass like photon (EM waves) E E= p or p = (light has momentum!) Relativisti Invariane : E p = m 4 : In all Ref Frames Rest Mass is a "finger print" of the partile Mass Can Morph into Energy & Vie Vera Unlike in Newtonian mehanis 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!