1. Announcements 12/6/10 Prayer Tomorrow: last day for exam 3 (late fee after 5 pm). Wednesday: Project Show & Tell. In the end, we had 14 groups volunteer (19 students). The lucky winners are: a. a.Robert McClellan – particle vs. wave character of light b. b.Diana Winn – pedestrian traffic on campus as wave functions c. c.Kaleb Markert – homemade reflecting and refracting telescopes d. d.Brian Jackson & Nick Ortega – 3D standing sound waves You will present in that order; a 10 minute cut-off for each group. Final exam: Thurs Dec 16, 7-10 am. Here in this room. Final exam review? FoxTrot, by Bill Amend

2. 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 ? ?

3. 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) -0.27 = -.41 Х 0 m/s ? ? Is momentum conserved???

4. Relativistic Momentum “The Truth”:

5. 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 kg 2 kg1 kg 2 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) -0.095 = -0.095 0 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) 

6. 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

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

8. 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

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

10. A Word About Units eV MeV MeV/c 2

11. 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

12. 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 0.000001 grams b. b.around 0.01 grams c. c.around 1 gram d. d.around 1 kg e. e.around 100 kg Nuclear power is not alone in converting mass to energy, ALL power sources do this!

13. Elastic Collision 0.9 c 0.40 c 0.78 c 1 kg 2 kg 0 m/s  = 2.2942 How did I find out the two speeds after the collision? Conservation of momentum: Conservation of energy:

14. 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?