Announcements 12/3/12 Prayer Wednesday: Project Show & Tell a. a.Cade & Seth – musical cadences b. b.Tess & Brigham - pvc instrument c. c.Tyler - sonoluminescence d. d.Ryan Peterson - particle collision simulator e. e.Konrie, Dallin, Hsin Ping – hot air balloon You will present in that order; a 9 minute cut-off for each group. Wednesday: no reading assignment, but there’s still a warmup quiz Final exam: Mon, Dec 10 – Thurs Dec 13, in Testing Center Final exam review: vote on times by tonight Frank and Ernest

From warmup Extra time on? Other comments?

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, or else mass not conserved) 

From warmup What is the maximum momentum that a particle with mass m can have? a. a.There is no maximum momentum!

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

From warmup I often call "E=mc 2 " the most misquoted equation in history. Why might that be? a. a.Because E does *not* equal mc^2. E = *gamma* times mc^2. See Eqn (8th edition). The quantity mc^2 is only the rest energy.

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

Clicker 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

Clicker 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?