announcements 12/3/12
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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?
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