Nobel Prize in Physics 2008 Yoichiro Nambu Makoto Kobayashi Toshihide Maskawa "for the discovery of...
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Transcript of Nobel Prize in Physics 2008 Yoichiro Nambu Makoto Kobayashi Toshihide Maskawa "for the discovery of...
Nobel Prize in Physics 2008
Yoichiro NambuMakoto Kobayashi Toshihide Maskawa
"for the discovery of the mechanism of spontaneous broken symmetry in subatomic physics"
"for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature"
Broken Symmetries
Particles and Forces 2
The origin of mass
Higgs Mechanism: A field fills all of space because of a mechanism called spontaneous symmetry breaking. It ‘sticks’ to particles, making it ‘harder for them to move’. This is what gives quarks and leptons their mass. Spontaneous symmetry breaking
As a consequence, there should also be a spin-0 boson, the Higgs boson.It has not been found yet.
Similar to thecelebrity effect in a crowd.
Credit: CERN
Ph
ysic
s
H
Part
icle
The Standard Model (SM) describes all these particles and 3 of 4 forces. We have confirmed the existence of those in the laboratory experiments.
The Standard Model
+ Higgs bosonHiggs has not yet been discovered
The mass is constrained from LEP and Tevatron data:
114 GeV<MH<154 GeV
Precision Cosmology at the LHC 3
proton
SPUTNIK: spaceflight era begins
October 4, 1957
184-pound basketball-size satellite
Lasted 3 months
R-7 launcher: world’s first intercontinental ballistic missile
Total mass: 367 tonsPayload: about 1 tonThrust: 3.9x106 N
November 3, 1957: Sputnik 2, 1120 pounds
LaikaMay 15, 1958: Sputnik 3, 1.5 tons
January 15, 1958: Explorer 1 launched (US)
April 12, 1961Yuri Gagarin
February 20, 1962John Glenn
Early timeline
April 12, 1961: the first human in space (Yuri Gagarin)
February 20, 1962: the first American on orbit (John Glenn)
1963: the first woman in space (Tereshkova)1965: the first spacewalk (Leonov)
1969: first men on the moon (Collins, Armstrong, Aldrin)
1971: first space station (Salyut)
1981: first space shuttle flight (Columbia)
Robotic missions to all planets
Sergei Korolyov1907-1966
Fathers of space programs
Werner von Braun1912-1977
All forces are
CONSERVATIVE or
NON-CONSERVATIVE
Chapter 8
A force is conservative if:
The work done by the force in going from to is independent of the path the particle follows
The work done by the force when the particle goes from around a closed path, back to , is zero.
or
1r
2r
1r
1r
Non-conservative: doesn’t satisfy the above conditions
Theorem: if a force can be written as the gradient (slope) of some scalar function, that force is conservative.
U(x) is called the potential energy function for the force F
If such a function exists, then the force is conservative
1D case:dx
dUFx
conW does NOT depend on path!
)]()([ 12
2
1
2
1
xUxU
dxdx
dUdxFW
x
x
x
x
xcon
If Fx(x) is known, you can find the potential energy function as
CdxxFxU x )()(
dx
dUFx
Work-energy theorem:
nccontotal WWWKK 21212112
ncWUUKK 211212
ncWUKUK 211122
const,0If 112221 UKUKW nc
Energy conservation law!
Then use
0if, 211122 ncWUKUK
ncWUKUK 211122 or
A strategy: write down the total energy E = K + U at the initial and final positions of a particle;
Examples
Force of gravity
Spring force
y
CmgyyU )(
xx0
Cxxk
xU
2
)()(
20
)( 0xxkFx
mgFy
A block of mass m is attached to a vertical spring, spring constant k.
A
If the spring is compressed an amount A and the block released from rest, how high will it go from its initial position?
A particle is moving in one direction x and its potential energy is given by U(x) = ax2 – bx4 . Determine the force acting on a particle.Find the equilibrium points where a particle can be at rest. Determine whether these points correspond to a stable or unstable equilibrium.
Potential Energy Diagrams
• For Conservative forces can draw energy diagrams
• Equilibrium points– If placed in the
equilibrium point with no velocity, will just stay (no force) 0 dx
dUxF
Fx >0
a) Spring initially compressed (or stretched) by A and released;b) A block is placed at equilibrium and given initial velocity V0
Stable vs. Unstable Equilibrium Points
The force is zero at both maxima and minima but…– If I put a ball with no velocity there would it stay?– What if it had a little bit of velocity?
Block of mass m has a massless spring connected to the bottom. You release it from a given height H and want to know how close the block will get to the floor. The spring has spring constant k and natural length L.
H
y=0
L
z
zyxUF
y
zyxUF
x
zyxUF zyx
),,(;),,(
;),,(
Several dimensions: U(x,y,z)
Compact notation using vector del, or nabla:
kz
jy
ix
UF
,
Another notation:rd
dUF
Partial derivative is taken assuming all other arguments fixed
Geometric meaning of the gradient :UDirection of the steepest ascent;
Magnitude : the slope in that directionU
:UF
Direction of the steepest descent
Magnitude : the slope in that direction F
http://reynolds.asu.edu/topo_gallery/topo_gallery.htm
)]()([ 12 rUrUW con
Ifrd
dUF
)()( 12
)(
)(
2
1
rUrUdUrdrd
dUrdFW
rU
rUL
z
zyxUF
y
zyxUF
x
zyxUF zyx
),,(;),,(
;),,(
or
then
H
Water SlideWho hits the bottom with a faster speed?
Roller CoasterYou are in a roller coaster car of mass M that
starts at the top, height H, with an initial speed V0=0. Assume no friction.
a) What is the speed at the bottom?b) How high will it go again?
c) Would it go as high if there were friction?
H
Roller Coaster with FrictionA roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2).
Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?
A gun shoots a bullet at angle θ with the x axis with a velocity of magnitude Vm. What is magnitude of the velocity when the bullet returns to the ground? How high it will go?
PowerPower is a rate at which a force does work
If work does not depend on time:
t
WP
Otherwise: vFdt
rdF
dt
WP
Even if instantaneous power depends on time, one can talk about the average power
How many joules of energy does 100 watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of energy?
Power could also define the rate at which any form of energy is spent, not only mechanical