Announcements 12/3/12 Prayer Wednesday: Project Show & Tell

a. Cade & Seth – musical cadencesb. Tess & Brigham - pvc instrumentc. Tyler - sonoluminescenced. Ryan Peterson - particle collision simulatore. 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 andErnest

From warmup

Extra time on?

Other comments?

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, or else

mass not conserved)

From warmup

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

a. There is no maximum momentum!

Momentum vs. Velocity

p mv

p mv

Why do they agree at small velocities?

From warmup

I often call "E=mc2" the most misquoted equation in history. Why might that be?

a. Because E does *not* equal mc^2. E = *gamma* times mc^2. See Eqn 39.26 (8th edition). The quantity mc^2 is only the rest energy.

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

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. 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

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. 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?