Announcements 12/5/11 Prayer Office hours: a. a.Today: Colton regular; Chris regular b. b.Wed: Colton none; Chris 5-7 pm Wednesday: Project Show & Tell a. a.Darren & Lisa - constructing a vowel synthesizer b. b.Linea - creating a virtual "marching band" string quartet c. c.Joshua M and Ryan - measuring the speed of sound in gases d. d.Mike and James - Christmas caroling with PVC pipes You will present in that order; a 10 minute cut-off for each group. Final exam: Mon, Dec 12 – Thurs Dec 15, in Testing Center Final exam review: please vote! Frank and Ernest

HW 37-3: Elastic Collision 9 m/s 3 m/s6 m/s v 1,after = ? v 2,after = ? Check momentum cons: (1)(9) + (2)(0) = -(1)(3) + (2)(6) 9 = 9  4 m/s 8 m/s 1 m/s 1 kg 2 kg 1 kg 2 kg1 kg 2 kg 5 m/s Check momentum cons: (1)(4) - (2)(5) = -(1)(8) + (2)(1) -6 = -6  0 m/s ? ?

Elastic Collision 0.9 c 0.3 c 0.6 c Check: (1)(0.9) + (2)(0) = -(1)(0.3) + (2)(0.6) 0.9 = 0.9  0.73 c 0.70 c 0.14 c 1 kg 2 kg 1 kg 2 kg1 kg 2 kg 0.5 c Check: (1)(0.73) - (2)(0.5) = -(1)(0.70) + (2)(0.14) = -.41 Х 0 m/s ? ? Is momentum conserved???

Relativistic Momentum “The Truth”:

Elastic Collision 0.9 c 0.40 c 0.78 c Check: (2.29)(1)(0.9) + 0 = -(1.09)(1)(0.4) + (1.60)(2)(0.78) 2.06 = 2.06  0.73 c 0.75 c 0.46 c 1 kg 2 kg 1 kg2 kg1 kg2 kg 0.5 c Check: (1.46)(1)(0.73) – (1.15)(2)(0.5) = -(1.51)(1)(0.75) + (1.13)(2)(0.46) = m/s ? ?  = 2.29  = 1.09  = 1.60  = 1.51  = 1.13  = 1.46  = 1.15 Momentum,    mv, is conserved in every reference frame!!! (disclaimer: has to be elastic collision) 

Thought Question What is the maximum momentum that a particle with mass m can have? a. a.p = mc b. b.p = 2 mc c. c.p = 0.5 mc d. d.There is no maximum momentum e. e.None of the above

Momentum vs. Velocity Why do they agree at small velocities? 

Reading Quiz If m is the mass of an object (sometimes called “rest mass”), what does mc 2 equal? a. a.The gravitational energy of an object b. b.The kinetic energy of an object c. c.The potential energy of an object d. d.The rest energy of an object e. e.The total energy of an object

Relativistic Energy Momentum  Force (F = dp/dt) Force  Work (W =  Fdx) Work  Energy (E bef + W = E aft ) Result: For mass = 1 kg KE (joules)  Correct KE ½ mv 2 Why can’t anything go faster than c?

A Word About Units eV MeV MeV/c 2

Thought Question Hydrogen atoms consist of one electron which is bound to a proton by electromagnetic forces. If I very carefully “weigh” a hydrogen atom, what will I get? a. a.The mass of an electron plus the mass of a proton b. b.Something a little BIGGER than (a) c. c.Something a little SMALLER than (a) d. d.Something entirely different from (a) E bef + W = E aft

Thought Question A nuclear power plant generates 10 million Watts of power nonstop for a day. How much less do the fuel rods weigh at the end of the day? a. a.around grams b. b.around 0.01 grams c. c.around 1 gram d. d.around 0.1 kg e. e.around 10 kg Nuclear power is not alone in converting mass to energy, ALL power sources do this!

Elastic Collision 0.9 c 0.40 c 0.78 c 1 kg 2 kg 0 m/s  = How did I find out the two speeds after the collision? Conservation of momentum: Conservation of energy:

Elastic Collision 0.9 c 0.40 c 0.78 c 1 kg 2 kg 0 m/s  =

Relationship between E and p Classical: KE = ½ mv 2 = ? (in terms of p) Relativistic: E =  mc 2 = ? (in terms of p) Proof: ? What if m=0?