•Hour Exam 2: Wednesday, Oct. 27 •In-class (1300 Sterling...
Transcript of •Hour Exam 2: Wednesday, Oct. 27 •In-class (1300 Sterling...
Mon. Oct 25 Phy107 HE 2 review
• Hour Exam 2: Wednesday, Oct. 27• In-class (1300 Sterling Hall)• Twenty multiple-choice questions• Will cover: 8.1-8.6 (Light and E&M)
9.1-9.5 (E&M waves and color)10, 11 (Relativity)
• You should bring– Your student ID– 1 page notes, written double sided– Calculator– Pencil for marking answer sheet
Mon. Oct 25 Phy107 HE 2 review
Today
• Quickly finish material in Chapter 11.
• Review for Hour Exam 2.
Mon. Oct 25 Phy107 HE 2 review
From Last Time…• General relativity motivated by Equivalence Principle
– No experiment can distinguish between force of gravityand an accelerated reference frame.
• General relativity does not consider gravity to be aforce between massive objects– Mass tells space-time how to curve– Curvature of space-time dictates how objects move.– Objects move along straight line in space-time– Motion independent of mass of object (even light bends)
• Leads to effects such as– Gravitational lensing– Black holes
Mon. Oct 25 Phy107 HE 2 review
Black holes
• Light falls in a gravitational field. A sufficientlystrong field should bind light into orbits.
• When escape velocity equals the speed of light,nothing can emerge.
• Inside the Schwarzschild radius light itselfcannot escape.
• An object condensed within it’s Schwarzschildradius is called a black hole.
Mon. Oct 25 Phy107 HE 2 review
How do black holes form?
• Matter in the earth is held apart by electricforces.
• In the Sun, matter is held up by pressureassociated with high temperature by nuclearfusion reactions.
• At higher density when fusion burns out, gravitycan squeeze electrons into protons forming aneutron star.
• At even higher densities, a black hole forms
Mon. Oct 25 Phy107 HE 2 review
Black hole formation
• At sufficient density, no knownforce prevents the completecollapse of matter to a point-a black hole.
• Matter falling into black holesprovides the only explanationfor energetic objects seenthroughout the universe.http://antwrp.gsfc.nasa.gov/apod/ap
010921.html
Black hole roaming theMilky Way.
Mon. Oct 25 Phy107 HE 2 review
Seeing Holes
• Light cannot escape from a blackhole, so can’t see black hole itself,but can see matter falling into ahole.
• Gravitational forces stretch andrip matter: heats up.
• Very hot objects emit in X-rays(interior of Sun)
• Cygnus X-1.
http://www.owlnet.rice.edu/~spac250/steve/ident.html
Mon. Oct 25 Phy107 HE 2 review
Exam Review: Topics by chapter
• Chap 8: Waves, interference, & electromagnetism
• Chap 9: EM radiation, light, color
• Chap 10: Special Relativity time & space
• Chap 11: Special Rel. energy, & General Relativity
Mon. Oct 25 Phy107 HE 2 review
Chapter 8: Wave properties• Amplitude is the maximum displacement of
string above the equilibrium position
• Wavelength, λ, is the distance between twosuccessive points that behave identically
• Period: time required to complete one cycle
• Frequency = 1/Period = rate at which cyclesare completed
• Velocity = Wavelength/Period,v = λ / T, or v = λf
Mon. Oct 25 Phy107 HE 2 review
Different wave motion• Longitudinal wave
– Vibrations are in the direction of motion
• Transverse wave– Vibrations are perpendicular to the direction of
motion.
Mon. Oct 25 Phy107 HE 2 review
Superposition & interference• Superposition of waves• Interference of waves on a string• Interference of sound waves
– Constructive interference– Destructive interference
• Superposition of waves with differentfrequencies– Beat frequencies
• Doppler effect– Change in apparent frequency due to motion
of source or observer
Mon. Oct 25 Phy107 HE 2 review
Interference of sound waves
• Interference arises when waves change their‘phase relationship’.
• Can vary phase relationship of two waves bychanging physical location of speaker.
Constructive Destructive
‘in-phase’ ‘1/2 λ phase diff’
Mon. Oct 25 Phy107 HE 2 review
Superposition & Interference• Consider two harmonic waves A and B meeting at x = 0.
– Same amplitudes, but ω2 = 1.15 x ω1.• The displacement versus time for each is shown below:
A(ω1t)
C(t) = A(t) + B(t) CONSTRUCTIVEINTERFERENCE
DESTRUCTIVEINTERFERENCE
B(ω2t)
Mon. Oct 25 Phy107 HE 2 review
Doppler Effect, Source inMotion
• As the source movestoward the observer (A),the wavelength appearsshorter and the frequencyincreases
• As the source moves awayfrom the observer (B),the wavelength appearslonger and the frequencyappears to be lower
Mon. Oct 25 Phy107 HE 2 review
Chap. 8: Electromagnetism• Coulomb force between charged particles
– Same form as gravitational force• Electric field lines: path followed by charged particle• Electric current: flow of charged particles• Electrostatic potential:
– Measured in volts.– Analogous to gravitational potential.
• Magnetic field:– arises from electric currents (moving charges)– also results in force on an electric current
• Faraday effect:– changing magnetic field induces electric current– Magnetic field from induced currents opposes change in
applied field
Mon. Oct 25 Phy107 HE 2 review
Coulomb’s Law
• Electrostatic force: FE = k Q1 Q2 /r2
k = 9x109 Nm2/C2
– Force between charges q1 and q2separated by a distance r.
– Direction: Like charges repel unlike attract
Similar to gravitational force: FG=GM1M2/ r2
G=6.7x10-11 Nm2/kg2
Mon. Oct 25 Phy107 HE 2 review
Electric Potential• Units Joules/Coulomb≡Volts– Batteries– Power outlets– EKG
• Potential differences• Field lines point down hill• Charge will move
along field lines just asmass falls in gravitationalfield.
Mon. Oct 25 Phy107 HE 2 review
Source of magnetic field?
• Current in wire produces magnetic field.• That magnetic field aligns compass needle
Current
Magneticfield
Mon. Oct 25 Phy107 HE 2 review
Induction (Faraday)
• Changing magnetic fields produce electric fields
• Here the induced current produces a magneticfield, which repels the bar magnet or the ring
Mon. Oct 25 Phy107 HE 2 review
Chapter 9: Electromagnetic waves• EM radiation is a transverse wave
– Amplitudes are perpendicular to propagation dir.– Contains both electric field and magnetic field
• EM radiation propagates at c, speed of light• EM radiation generated by accelerating charges• Visible light is a narrow band of entire EM
spectrum.• Radio waves are EM radiation. Can be generated
by spark jumping a gap.
Mon. Oct 25 Phy107 HE 2 review
General props of EM waves
xz
y
•A Transverse wave.
•Electric and magnetic fields are perpendicular topropagation direction
•Can travel in empty space
f = v/λv = c = 3 x 108 m/s (186,000 miles/second!)
Mon. Oct 25 Phy107 HE 2 review
Chapter 9: Visible light & color• Range of visible light from 400 nm to 700 nm
• Eye interprets different wavelengths as different colorsbut has only three ‘sensors’, cones S, M, L with overlappingsensitivities.
• Lets colors be described as combination of three ‘primaries’
• This makes a ‘color space’, colors can be described as amountof primaries needed.
• Most methods of generating colors have a ‘gamut’, a limitedrange of possible colors that in general to not contain purespectral colors.
Mon. Oct 25 Phy107 HE 2 review
• Visible light is onlya narrow range ofthe entire EMspectrum.
Mon. Oct 25 Phy107 HE 2 review
Eye spectral sensitivity• Eye’s sensitivity to EM
radiation is through threecones sensitive todifferent spectral ranges.
• Overlapping ranges meansthat different lightsources can be seen as thesame color
• Three cones suggests wecan synthesize colors fromthree primary sources.
Mon. Oct 25 Phy107 HE 2 review
Chapter 10: Basic relativity• Galilean Relativity
– Laws of mechanics identical in all inertial ref. frames
• Einstein’s Relativity– All laws of physics identical in inertial ref. frames– Speed of light=c in all inertial ref. Frames
(e.g. independent of velocity of observer, velocity ofsource emitting light)
• One consequence– Events simultaneous in one frame will not be
simultaneous in another.
Mon. Oct 25 Phy107 HE 2 review
Space & time relativistic effects•Events observed to be simultaneous in one
frame may not be simultaneous in another.
•Measured interval between events different fordifferent observers.
— Time dilation. Proper time is that measured inframe where events occur at same spatial location
— All other measured times are longer by factor γ
•Measured distance between events different fordifferent observers.
— Length contraction. Proper length is that measuredin frame where events are simultaneous.
— All other lengths are shorter by factor γ
Mon. Oct 25 Phy107 HE 2 review
Time dilationI am on jet traveling at 500 mph and throw a ball
up and catch it in my hand.You are on the ground and watch me.How do the time intervals compare for you and I?
A. tjet=tEarth
B. tjet>tEarth
C. tjet<tEarth
Proper time is measured in the jet frame(events occur at same spatial location).
Times measured in other frames are longer(time dilation).
Mon. Oct 25 Phy107 HE 2 review
Space-time diagrams• World line : path of particle through space-time.
• World line is made up of sequence of events, plotted aspoints in space-time.
• Different inertial reference frames represented as ‘tilted’coordinate axes on space-time diagram.
• Event has different coordinates (space & time) measuredon these coordinate axes.
• But the combination x2-c2t2 is ‘universal’ in that it ismeasured to be the same for all observers.
Mon. Oct 25 Phy107 HE 2 review
Space-time diagrams
x
ct
x1
ct1
General world linex
ct
World line low ofvelocity object
World line of highervelocity object
World lineof light
Const. vel world line
Mon. Oct 25 Phy107 HE 2 review
Relativistic Momentum
• Momentum can be increased arbitrarily,but velocity never exceeds c
• We still use
so for constant force we still havemomentum = Force x time,but the velocity never exceeds c
• Momentum has been redefined.
€
prelativistic = γmv =mv
1− (v /c)2
0
0.2
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0 1 2 3 4 5
SPEE
D / S
PEED
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RELATIVISTIC MOMENTUM€
vc
=p / pop / po( )2
+1, po = moc
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change in momentumchange in time
= Force
Newton’smomentum
Relativisticmomentum
Relativistic momentum fordifferent speeds.
Mon. Oct 25 Phy107 HE 2 review
Relativistic mass
• Could say that particlebecomes extremelymassive as speedincreases ( m=γmo )
• But could also say thatrelativistic momentumhas new form ( p= γmov )
0
1
2
3
4
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0 0.2 0.4 0.6 0.8 1RELA
TIVI
STIC
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T M
ASS
SPEED / SPEED OF LIGHT
Mon. Oct 25 Phy107 HE 2 review
Mass-energy equivalence
• This results in Einstein’s famous relation
• This says that the total energy of a particle is related to its mass.
• Even when the particle is not moving it has energy.
• We could also say that mass is another form of energy
– Just as the text talks of chemical energy, gravitationalenergy, etc, we can talk of mass energy.
€
E = γmoc2, or E = mc 2
Mon. Oct 25 Phy107 HE 2 review
General Relativity and Gravity• General relativity motivated by Equivalence Principle
– No experiment can distinguish between force of gravityand an accelerated reference frame.
• General relativity does not consider gravity to be aforce between massive objects– Mass tells space-time how to curve– Curvature of space-time dictates how objects move.– Objects move along straight line in space-time– Motion independent of mass of object (even light bends)
• Leads to effects such as– Gravitational lensing– Black holes