Announcements 4/11/11 Prayer Wednesday: Project Show & Tell. The lucky winners are: a. a.Michael Meehan & Nick Prestwich – Doppler effect b. b.Conrad Rosenbrock.

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Announcements 4/11/11 Prayer Wednesday: Project Show & Tell. The lucky winners are: a. a.Michael Meehan & Nick Prestwich – Doppler effect b. b.Conrad Rosenbrock & Mike Abrahamson – evaporative cooling c. c.Matt Pitts, Marcus Holden, Cody Petrie – refraction of light d. d.Alan Snow – demos: air & water “whirlpools” You will present in that order; a 10 minute cut-off for each group. Final exam: Sat, Apr 16 – Wed Apr 20, in Testing Center Final exam review – On Thurs or Friday. Vote for times! FoxTrot, by Bill Amend

HW 37-3: Elastic Collision 9 m/s 3 m/s6 m/s v 1,after = ? v 2,after = ? Check: (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: (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 rest mass of an object, 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) v/c 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?