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Announcements

Announcements. For the lab this week, you will have 2 lab session to complete it. They will be collected after week 1 and redistributed the following week. Pick up HW assignments: Due next Wednesday.

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Announcements

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  1. Announcements • For the lab this week, you will have 2 lab session to complete it.They will be collected after week 1 and redistributed the following week. • Pick up HW assignments: Due next Wednesday. • Read page 7-13 in Schwarz. Do exercises 1-6. In http://particleadventure.org/particleadventure/frameless/startstandard.html read through the Section “Particle Decays and Annihilations” Slides a-h (see slide key on Course Assignments Web page)

  2. Conservation Laws

  3. Conservation Laws Conservation laws in Physics can give explanations as to why some things occurand other do not. Three very important Conservation Laws are: I. Conservation of Energy II. Conservation of Momentum III. Conservation of Charge

  4. Energy Conservation (I) There are many forms of energy.For now, we’ll focus on two types 1. Kinetic Energy (KE) – Energy of motion KE = ½ mv2 if v is much less than c (v << c) 2. Mass Energy m = mass c = speed of light = 3x108 [m/sec] E = mc2 That is, mass is a form of energy, and the “conversion” is to just multiply the mass by a constant number (the speed of light squared)!

  5. D A B vA vB Conservation of Energy (II) Total Energy (initially) = ED = mDc2 Suppose D “decays” into 2 particles A and B, what is the energy of the system afterward? Total Energy (after decay) = EA + EB = (KEA+mAc2) + (KEB+mBc2) Since energy must be conserved in the “decay” process, mDc2 =(KEA+mAc2) + (KEB+mBc2)

  6. ED EA EB Before Decay After Decay Conservation of Energy (III) mDc2 =(KEA+mAc2) + (KEB+mBc2) • Important points here: • This equation DOES NOT say that kinetic energy is conserved • This equation DOES NOT say that mass is conserved • This equation states that the total energy is conserved Total energy before decay = Total energy after decay

  7. KEA = ½ mAvA2 > 0 KEB = ½ mBvB2 > 0 Conservation of Energy (IV) mDc2 =(KEA+mAc2) + (KEB+mBc2) Since mA and mB must be larger than zero, and vA2>0 and vB2>0, the KE can only be positive (KE cannot be negative!) If I subtract off the KE terms from the RHS* of the top equation, Iwill no longer have an equality, but rather an inequality: mDc2 mAc2 + mBc2 and dividing both sides by c2, This is also true if particle D has KE>0 also! mD mA + mB

  8. KEA KEB MBc2 MAc2 MDc2 MBc2 MAc2 MDc2 Conservation of Energy (V) LHS = RHS LHS > RHS

  9. I D A B mB=0.1 kg mA=0.2 kg II D B A mA=0.2 kg mB=0.4 kg III D A B mA=0.49 kg mB=0.0 kg IV D mA=0.1 kg A mB=0.1 kg B Energy Conservation (VI) Consider some particle (call it “D”) at rest which has a mass of 0.5 kg D Which of the following reactions do you think can/cannot occur?

  10. Fig. A t Bam q q t Energy Conservation (VII) A particle (q) and an anti-particle (q) of equal masseach having1 [TeV] of energy collide and produce two other particles t and t (of equal mass) as shown in Fig. A. (1 [TeV] = 1012 [eV])

  11. What is total energy of the t and t (individually)?A) 0 B) 2 [TeV] C) 1 [TeV] D) 0.5 [TeV] • What can be said about the mass energy of the “t” particle ?A) It’s equal to the mass of “q” B) It must be less than 0.5 TeV C) It must be less than 1 [TeV] D) It’s equal but opposite in direction to that of the t particle Energy Conservation (VIII) • What is the total energy in the collision ?A) 0 B) 2 [TeV] C) 1 [TeV] D) 0.5 [TeV]

  12. m1 p1 = m1v1 v1 v2 m2 Note that particles moving in opposite directions have momenta which are opposite sign! p2 = -m2v2 Momentum Conservation (I) Momentum (p) = mass xvelocity = mv p = mv Momentum has a direction, given by the direction of v Momentum Conservation: In any process, the value of the total momentum is conserved.

  13. Consider a head-on collision of two particles m1 m2 v1 v2 Momentum Conservation (II) What is the total momentum before the collision ? A) m1v1+m2v2 B) m1v2-m2v1 C) zero D) (m1+m2)(v1+v2) If m1= m2, what can be said about the total momentum? A) it’s zero B) it’s positive C) it’s negative D) can’t say? If m1= m2 and v1 > v2, what can be said about the total momentum? A) it’s zero B) it’s positive C) it’s negative D) can’t say?

  14. Consider a head-on collision of two particles m1 m2 v1 v2 Momentum Conservation (III) If m1< m2 and v1 > v2, what can be said about the total momentum? A) it’s zero B) it’s positive C) it’s negative D) can’t say? If m1= m2 and v1 = v2 (in magnitude), what can be said about the total momentum? A) it’s zero B) it’s positive C) it’s negative D) can’t say? In this previous case, what can be said about the final velocities of particles 1 and 2 ? A) their zero B) equal and opposite C) both in the same direction D) can’t say?

  15. I D A B vA vB mB mA Momentum Conservation (IV) Consider a particle D at rest which decays into two lighter particles A and B, whose combined mass is less than D. If mA > mB, answer the following questions: • What can be said about the total momentum after the decay? • A) Zero B) Equal and Opposite C) Equal D) Opposite, but not equal • If mA= mB, what can be said about the magnitudes of the velocities of A and B? A) vA>vB B) Equal and Opposite • C) vB>vA D) Same direction but different magnitudes

  16. I D A B vA vB mB mA Momentum Conservation (V) • Which statement is most accurate about the momentum of A ? • A) Zero B) Equal to B C) Equal and opposite to B D) Opposite, but not equal • Can mA+mB exceed mD ? • A) Not enough data B) Yes, if vA and vB are zero C) No D) Yes, if vA and vB are in opposite directions

  17. n neutron  proton + electron + neutrino (n  p + e + n ) When the neutrino is included, in fact momentum is conserved. Momentum Conservation (VI) mP p Consider a neutron, n,which is at rest, and then decays. mp+me < mn n me e • Can this process occur? • No, momentum is not conserved • Yes, since mn is larger than the sum of mP and me • No, energy cannot be conserved • Yes, but only between 8 pm and 4 am The observation that momentum was not conserved in neutron decay lead to theprofound hypothesis of the existence of a particle called the neutrino

  18. mP p n n me e When the neutrino is included, in fact momentum is conserved. Discovery of the Neutrino The observation that momentum conservation appeared to beviolated in neutron decay lead to the profound hypothesis of the existence of a particle called the neutrino neutron  proton + electron + neutrino (n  p + e + n )

  19. Consider the previous example of neutron decay: n  p + e + n Charge 0 +1 -1 0 Charge Conservation The total electric charge of a system does not change. Can these processes occur? p + p  p + n Charge +1 +1 +1 0 NO p + e  n + n Charge +1 -1 0 0 YES n + n  p + p Charge 0 0 +1 +1 NO

  20. Summary of Conservation Laws • Total Energy of an isolated system is conserved • D  A + B cannot occur if mA+mB > mD • Total momentum of an isolated system is conserved - missing momentum in neutron decay signaled the existence of a new undiscovered particle • Total Charge of an isolated system is conserved - the sum of the charges before a process occurs must be the same as after the process We will encounter more conservation laws later which will help explainwhy some processes occur and others do not.

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