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- Lect19-Phys172s10-(10.8-10.11-Collisions)(2).pdf

Siddharth C.

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Spring 2010PHYS 172: Modern Mechanics Lecture 19 ? Collisions Read 10.9 ? 10.11 EXAM 2 Exam 2 multiple choice paper copies will be discarded tomorrow. Any problem with Exam 2 scores should be addressed by Friday. No complaints will be considered after that date. Scores for 17 lectures are on CHIP. Please check them. No complaints will be considered after Friday. Example: head-on car crash Two identical cars of mass m=1000 kg move toward each other with speeds v1=v2=30 m/s (~65 mph), collide head-on and stick together. CLICKER: What is the speed of the center of mass of the system consisting of these two cars after the collision? A. 30 m/s B. 15 m/s C. 60 m/s D. 0 m/s Example: head-on car crash Two identical cars of mass m=1000 kg move toward each other with speeds v1=v2=30 m/s (~65 mph), collide head-on and stick together. CLICKER: What was the speed of the center of mass of the system consisting of these two cars before the collision? A. 30 m/s B. 15 m/s C. 60 m/s D. 0 m/s Example: head-on car crash Two identical cars of mass m=1000 kg move toward each other with speeds v1=v2=30 m/s (~65 mph), collide head-on and stick together. A. is conserved B. increases C. decreases CLICKER: During the collision, the kinetic energy of the system consisting of these two cars: Example: head-on car crash CLICKER POLL: How much energy is released as heat? ( ) ( )( )221 122 1000 kg 30 m/s 900 kJQ mv= = = mwater= 900 kJ/(4.18 J/g/K a0 100 K) = 2.2 kg (~1/2 gal) Enough to heat up from freezing to boiling: A) 250 gallons of water B) 50 gallons of water C) 10 gallons of water D) 2 gallons of water E) ½ gallon of water Two identical cars of mass m=1000 kg move toward each other with speeds v1=v2=30 m/s (~65 mph), collide head-on and stick together. Solution: Relativistic momentum and energy To get nuclei in physical contact ? need large energies Modern accelerators: v reaches 0.999999 c 1 3 4 3 4 2 1 2 3 4 cos cos 0 sin sin p p p p p E m c E E q f q f = + = - + = + ( ) ( ) ( ) ( ) ( ) ( )2 2 22 2 22 2 2 21 1 2 3 3 4 4p c m c m c p c m c p c m c+ + = + + + Three equations Known: masses, p1 Unknown: p3, p4, q , f Special case: photons (and approximation - neutrino) ( ) ( )22 2E pc mc pc= + = Ep c= Identifying a particle 1 3 4 3 4 2 1 2 3 4 cos cos 0 sin sin p p p p p E m c E E q f q f = + = - + = + There are 8 variables: m1, m2, m3, m4, p1, p3, p4, q , f Can find 3 unknowns Suppose we know everything except m4, p4, f - we can identify this particle! even if we cannot detect it directly The discovery of the neutrino n p e+ -fi +Decay of a neutron: n q f ep pp n e p n e p p p p E E E = + = + ( ) ( ) ( ) ( )2 2222 2 2 0 cos cos 0 sin sin e p e p n e e p p p p p p m c p c m c p c m c q f q f = + = - = + + + These equations failed to describe experiment: added ?antineutrino? + cospn j + sinpn j ( ) ( )22 2 + p c m cn n+ n+ p n j Inelastic collisions and energy levels Excite nucleus 1 3 4 3 4 2 1 3 4 cos cos 0 sin sin p p p p p E Mc E E q f q f = + = - + = + m3 = m m3 = M ( ) ( )22 24 4E p c Mc E= + + D Unknown: p4, f, DE Three equations: can solve and find DE Can study nuclear energy levels! 2 4 /m M E c= + D Change of identity pp p- + - ++ fi + D Accelerator p - H2 gas p - 1950 s: scattering of pions 1 3 4 3 4 2 1 cos cos 0 sin sin p p p p p p E m c E Ep q f q f D = + = - + = + 1,m pp ( ) ( )22 2E pc mc= + 3 equations 3 unknowns: p4, f, mD pm mD > How can the mass of the particle rise?Gain in mass of the particle, or excited state of the system of 3 quarks: 2/ pm m E cD = + D 0p p+ +D fi + 2 0 pE m c= 2 1E m cD= proton D+ Discovering new particles: colliding particles https://project-cernland.web.cern.ch/project-CERNland/ Discovering new particles: LHC Large Hadron Collider 3 0 0 f t 5 miles Discovering new particles Installation of radiation detector module for ALICE (A Large Ion Collider Experiment) Discovering new particles A Compact Muon Solenoid http://www.physics.purdue.edu/~shipsey/research Three of the five barrel yoke rings for the CMS detector at the Large Hadron Collider at CERN. The outer vacuum vessel for the 6m diameter, 13m long 4T superconducting solenoid is inserted into the third ring Discovering new particles Simulation of heavy ion collision http://mediaarchive.cern.ch/MediaArchive/Photo/Public2/photo-bul/bul-pho-2007-073.jpg Discovering new particles Creation of black hole in ATLAS http://cdsweb.cern.ch/record/1073733 Proton-proton collision sergei Microsoft PowerPoint - Lect19-Phys172s10-(10.9-10.11-Collisions).ppt

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