announcements 4/11/11 prayer wednesday: project show & tell. the lucky winners are: a. a.michael...
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![Page 1: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/1.jpg)
Announcements 4/11/11 Prayer Wednesday: Project Show & Tell. The lucky winners are:
a. Michael Meehan & Nick Prestwich – Doppler effectb. Conrad Rosenbrock & Mike Abrahamson – evaporative coolingc. Matt Pitts, Marcus Holden, Cody Petrie – refraction of lightd. 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
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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: (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: (1)(4) - (2)(5) = -(1)(8) + (2)(1) -6 = -6
0 m/s
?
?
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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???
![Page 4: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/4.jpg)
Relativistic Momentum
“The Truth”:
p mv
before afterThen p p
![Page 5: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/5.jpg)
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)
![Page 6: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/6.jpg)
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
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Momentum vs. Velocity
p mv
p mv
Why do they agree at small velocities?
![Page 8: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/8.jpg)
Reading Quiz
If m is the rest mass of an object, 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
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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
)
v/c
Correct KE
½ mv2
Why can’t anything go faster than c?
![Page 10: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/10.jpg)
A Word About Units
eV MeV MeV/c2
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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
![Page 12: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/12.jpg)
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!
![Page 13: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/13.jpg)
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
![Page 14: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/14.jpg)
Elastic Collision
0.9 c 0.40 c 0.78 c
1 kg 1 kg2 kg 2 kg
0 m/s= 2.2942
![Page 15: 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](https://reader031.vdocuments.site/reader031/viewer/2022032704/56649d615503460f94a43640/html5/thumbnails/15.jpg)
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?