Announcements 12/5/11 Prayer Office hours:

a. Today: Colton regular; Chris regularb. Wed: Colton none; Chris 5-7 pm

Wednesday: Project Show & Tella. Darren & Lisa - constructing a vowel synthesizerb. Linea - creating a virtual "marching band" string quartetc. Joshua M and Ryan - measuring the speed of sound in gasesd. Mike and James - Christmas caroling with PVC pipesYou 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 andErnest

HW 37-3: Elastic Collision

1000 0.59 1200 0.4 2200 0.05c c c

9 m/s

3 m/s 6 m/s

v1,after = ? v2,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 1 kg2 kg 2 kg

1 kg 2 kg 1 kg 2 kg

5 m/s

5 m/s

Check momentum cons: (1)(4) - (2)(5) = -(1)(8) + (2)(1)

-6 = -6

0 m/s

?

?

Elastic Collision

1000 0.59 1200 0.4 2200 0.05c c c

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 1 kg2 kg 2 kg

1 kg 2 kg 1 kg 2 kg

0.5 c

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???

Relativistic Momentum

“The Truth”:

p mv

before afterThen p p

Elastic Collision

1000 0.59 1200 0.4 2200 0.05c c c

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 1 kg2 kg 2 kg

1 kg 2 kg 1 kg 2 kg

0.5 c

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)

Thought Question

What is the maximum momentum that a particle with mass m can have?

a. p = mcb. p = 2 mcc. p = 0.5 mcd. There is no maximum momentume. None of the above

Momentum vs. Velocity

p mv

p mv

Why do they agree at small velocities?

Reading Quiz

If m is the mass of an object (sometimes called “rest mass”), what does mc2 equal?

a. The gravitational energy of an objectb. The kinetic energy of an objectc. The potential energy of an objectd. The rest energy of an objecte. The total energy of an object

Relativistic Energy

Momentum Force (F = dp/dt) Force Work (W = Fdx) Work Energy (Ebef + W = Eaft)

Result:

2( 1)KE mc

2restE mc

2totE mc

0.0 0.2 0.4 0.6 0.8 1.0

2 1016

4 1016

6 1016

8 1016

For mass = 1 kg

KE

(jo

ules

)

Correct KE

½ mv2

Why can’t anything go faster than c?

A Word About Units

eV MeV MeV/c2

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. The mass of an electron plus the mass of a proton

b. Something a little BIGGER than (a)c. Something a little SMALLER than (a)d. Something entirely different from (a)

Ebef + W = Eaft

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. around 0.0001 gramsb. around 0.01 gramsc. around 1 gramd. around 0.1 kge. around 10 kg

Nuclear power is not alone in converting mass to energy, ALL power sources do this!

Elastic Collision

1000 0.59 1200 0.4 2200 0.05c c c

0.9 c 0.40 c 0.78 c

1 kg 1 kg2 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:

before aftermv mv

2 2

before aftermc mc

Elastic Collision

0.9 c 0.40 c 0.78 c

1 kg 1 kg2 kg 2 kg

0 m/s= 2.2942

Relationship between E and p

Classical: KE = ½ mv2 = ? (in terms of p)

Relativistic: E = mc2 = ? (in terms of p) 1 22 2 2 2( )E p c mc

2 2 2 2( ) ( )E pc mc

Proof: 22 2 2 2( ) ( ) ( )mc mv c mc ?

What if m=0?