Name: ID Grade:
This is a closed book exam. (You may have, and use, one 3x5-note card with personal notes.) Be careful not to share your answers to this exam with anyone else. (Since the hallmark of science is honesty and integrity, any suspicion of cheating will be dealt with very harshly). Write all of your answers carefully, completely, concisely, and legibly in the spaces provided on these exam sheets (drawing figures may be very helpful!) - anything that can't be easily read and understood by the grader will be marked wrong. There are a total of ten questions in this exam, each worth 10 points.
1. Matching. Choose the item in the column on the right that, on the basis of course readings and class discussions, best associates with the description on the left. (10 points)
a). Measured the velocity of light in a long
1. Newton's first law
b). Superposition of constant horizontal 11 2. Maxwell waves
velocity and constant vertical acceleration.
c). Showed that the speed of light did not depend 3. Simultaneity at distant
upon the speed of the observer. 6 events is not the same
for all observers
d). What happens to the work you do 4. Michael Faraday
when you compress a spring.15
e). What happens when a bullet is fired 5. Hans Christian Oersted
from a gun. 8
f). Kinetic energy of randomly moving 6. Michelson-Morley Experiment.
g). Transversely oscillating electric and 7. Heat energy
magnetic fields. 2
h). A train's length is not the same to 8. Conversion of chemical energy
all observers. 3 to kinetic energy
i). Lines of force contract parallel to
9. Albert A. Michelson
their direction. 4
j). An object dropped from the mast top 10. Longitudinal sound waves
of a steadily moving sailboat lands
at the foot of the mast. 1 11. Parabolic orbit.
12. Nuclear Energy
13. Constructive interference
14. A cannon recoils when it fires a shell
15. Elastic potential energy
2. State whether two observers in relative motion to each other in spaceships
will agree, A or disagree, D, about each of the following quantities: (Just
write "D" or "A" in appropriate blank.) (10 points)
D or A D or A
a) DTheir relative speed f) AThe velocity of light.
b) DThe mass of either ship g) DThe velocity of an object moving inside one of the ships
c) DThe rate at which a clock in the other ship runs h) DThe velocity of sound inside one of the ships
d) DThe length of the other ship i) DThe energy of an object inside one of the ships
e) AThe width of the other ship j) AThe number of windows in each ship
3. A Ford car, of mass 1500kg, is skidding across the icy surface of
a lake with a velocity of 20m/s. It slams into a stationary GM car whose
mass is 2000kg. The two cars lock together and move off as a single unit.
How much momentum has been transferred from the Ford to the GM? Is the
impact elastic or inelastic? Why? (10 points)
Use conservation of momentum: 1500kg*20m/s +2000kg*0m/s = 3500kg*V, where V is the speed of the combined "junk". Solve for V= 8.57m/s. Thus the GM now has momentum of 2000kg*8.57m/s = 17143 kgm/s
which is the amount which has been transfered from the Ford.
The relative velocity of the two cars before them collison was 20m/s and 0m/s afterwards; these are not the same so the collision was inelastic.
4. Copernicus said that the earth could be moving even though we could
not sense the motion. Explain how this would be possible using a Galilean
view of motion but impossible using an Aristotelian view. (10 points)
From a Galilean viewpoint, all objects initially on the earth would have the earth's velocity and continue to hold that velocity after they had left the earth (inertia); thus they would come back to their departure points; you would never notice any change in relative position or speed. An Aristotelian would say that as soon as an object jumped off of the earth, it would come to rest (since rest is the "natural" state of things); thus things would not land in the same spot they left, they would appear to have "fallen off the earth", you would see the difference in relative velocity and position..
5. Describe the similarities and differences between light waves and
sound waves. (10 points)
Light is a transverse electromagnetic wave which can travel through empty space with a speed of 3 x 108 m/s.
Sound is a longitudinal wave which can only propagate through matter, e.g., air, water, steel. In air, its speed is only 340 m/s.
6. In each of the following, describe a real physical situation in which the indicated transformation is taking place. (10 points)
a) Energy of an oscillating electric current converted into electromagnetic
Oscillating electric current in antenna becomes radio (or TV) waves.
Oscillating electric current in microwave oven becomes microwaves.
Oscillating electric current inside atoms molecules becomes light.
b) Chemical energy of food converted into gravitational potential energy.
Eat a hearty breakfast before climbing a mountain.
Eat lunch before throwing a ball up into the air.
Eat dinner before firing an arrow up into the air by stretching and releasing a bow.
Eat a snack before jumping up off a diving board.
c) Chemical energy converted into recoil momentum.
Exploding gunpowder propells a bullet out of a rifle, recoiling the butt into your shoulder.
Burning jet fuel causes very hot gases to rush out of the rear of the jet making the aircraft "recoil" forwards.
d) An object shrinking as its kinetic energy increases.
As an object speeds up its kinetic energy increases. But speeding up means that it is moving fast with respect to you which means that its length parallel to the motion appears shorter to you because of the Lorentz Contraction. Thus as the object's speed with respect to you increases, you perceive an increase of mass and kinetic energy as it shrinks.
e) Binding energy converted into mass deficiency.
When the parts of a system are bound together, they have less total energy than when they are separated and free of each other. Thus a bound system - such as a molecule, atom, nucleus - has an energy deficit compared to its separated constituents. But because of the relation between mass and energy, derived by Einstein, this energy deficiency is also a mass deficiency.
7. In its own rest frame, an object has a mass 4kg, a length of 2.0m, and a lifetime of 2.4s. It is moving, with respect to me, with a velocity v=0.6c, in a direction parallel to its length. Both it and I are in the vacuum of outer space, infinitely far from any other object. Thus its gamma is 1.25
a) What length do I observe it to have?
Using this gamma to get the Lorentz contraction, the length observed by me is 2.0m/1.25 = 1.6m.
b) What lifetime do I observe it to have?
Using this gamma to get the time dilation, I observe a lifetime of 2.4 s* 1.25 = 3 s.
c) What mass do I observe it to have?
Multiplying the rest mass by this gamma , I observe a mass of 4 kg* 1.25 = 5 kg.
d) How much energy do I say the object has?
Total energy is given by the SR formula: E = mc2 = 5kg*(3x108m/s)2 = 45x1016 J
e) How much weight do I say the object has? (10 points)
Since we are infinitely far from any other mass, there is no gravitational force acting, i.e., there is no weight.
8. Consider two massive bodies, near each other in space but isolated
from everything else. Compare and contrast a Newtonian description, a Faraday
type description, and a General Relativity type description, of the gravitational
interaction between the two bodies. (10 points)
According to Newton, the force is the result of an instantaeously acting "action-at-a-distance"; there is nothing connectingthe two objects to mediate or carry the force from one to the other. It is a "0ne-step" process.
According to Faraday, there is a field between the two objects which carries the force from one to the other. One object creates a field in which the other object is immersed; it is the field which then creates the force on the second object. It is thus a "two-step" process. After Maxwell, it was understood that the field was not instantaneous; it took time to propagate from one object to the other; the field carried energy and momentum from one object to the other in order to preserve the conservation laws.
According to Einstein, there was no force between the two objects; each object follows the law of inertia, traveling along a geodesic curve in space=time. But the space-time is curved because of the presence of the bodies so the geodesic is not a straight line; we see the motion as motion in the usual gravitational orbits. Thus this is again a "two-step" process: one body curves the space-time in its vicinity; the second body follows a geodesic in the resultant curved space-time.
9. Explain how the laws of conservation of energy and conservation of
momentum enable you to choose between a "one-step" ("action at a distance")
and a "two-step" ("field") description of the interaction between two separated
objects. (10 points)
According to special relativity,ts may not propagate instantaneously from one place to another. Thus, when considering two interacting bodies, if we change the energy and/or the momentum of one, it should take some time before the expected corresponding changes show up in the other. If you believe in a one step process, in which only the two objects are physically real, energy and/or momentum are not conserved during this time interval; for example, if you have decreased the energy of one, it will be some time before the energy of the other increases accordingly; while waiting, the sytem will have less energy than it should. On the other hand, if you believe in the two-step process, the field is physical, has energy/momentum associated with it, and thus carries energy from one body to the other. Therefore, energy and momentum can be conserved (have constant total values) at each instant along the way.
10. What is "retrograde motion: of the planets? Compare and contrast
how it is explained by Ptolemy and by Kepler. (10 points)
Usually, the planets move across the sky in the same direction as does the sun in its annual motion. But every once in a while, they appear to move backwards: "retrodrade", in the opposite direction. This apparent "disorder" was very troubling and puzzling rly watchers of the sky (as were most people of the times past).
Ptolemy explained this peculiar motion by assuming that the planets traveled in circular orbits ("epicycles") whose centers, in turn, in circles ("cycles") about the sun. [Circles were considered perfect; hence all celestial motions, which were obviously perfect, had to be circular.] Thus, sometimes, the planet in its epicycle would be moving in a direction opposite to the motion of its cycle. We, on earth, see the resultant composite motion as backwards motion = retrograde.
Copernicus put the sun at the center of things rather than the earth, as had Ptolemy. Thus the sun cycled about the earth in circular orbits. He still had to have the planets moving in circular epicycles on the sun's orbit.
Kepler modified Ccpernicus by substituting ellipses for circles -with the sun at one of the two focii of the ellipse. Lo and behold! He no longer needed epicycles to reproduce the observed planetary motions; he could get agreement between his calculations and the observations of Tcho Brache by assuming that all of the planets, includingthe earth, moved in simple elliptical orbits about the sun.
PHY 1040 Fall Semester 2000 Prof. A.M. Saperstein
Final Exam - In class, Tuesday, May 2, 2000
I. This Matching part of the exam is worth 60 points. Be careful in choosing and writing down your answers - there are no partial credits for valiant attempts.
The column on the left (NUMBERS) contains a series of physics observations or experiments; the one on the right (LETTERS) is a list of important physics ideas or theories, which were inferred from these observations and experiments. In the space next to each item in the left (NUMBERS) column place the letter corresponding to the item in the right (LETTERS) column which is mostly closely associated with it. (There may be more than one observation for a given theory.)
i 1) In the absence of air resistance,
all free objects near the earth's surface fall at the same rate.
D 2) A small fraction of the alpha particles fired at a thin gold foil recoil directly backwards.
c or j 3) A heavy object dropped from the top of a mast lands directly at the foot of the mast, on a smoothly moving ship.
c 4) In the absence of friction between plank and ground, the center of mass of a plank with a man walking on it doesn't change even though both plank and man separately move.
b 5) From time to time, planetary motion across the heavens reverses direction (goes "retrograde").
m 6) The ratio of the moon's centripetal acceleration about the earth to the acceleration of a freely falling body at the earth's surface is the square of the ratio of the earth's radius to the earth-moon distance.
d or A 7) The ratio of the work done against friction to the heat generated by the friction is always the same.
c 8) Stepping off of a small boat onto a neighboring pier may land you in the water between boat and pier.
e 9) A comb, rubbed through your hair on a cold dry day, will subsequently pick up small pieces of paper.
E 10) A compass needle next to a loop of wire connected between the two poles of a battery will be deflected when one end of the wire is removed from the battery.
B 11) When light of a "pure color" illuminates two tiny, very close together, slits, more than two images of the slit are seen.
a 12) When a Michelsen - Morley interferometer is rotated through 90_, no change is observed in the interference pattern of the light.
f 13) The force required to give an object a specific acceleration increases as the speed of the object increases.
w 14) The spectra of distant stars is shifted towards the red.
y 15) The relative positions of a group of stars is changed when they are viewed in the vicinity of the sun as compared with their appearance when the sun is in a different part of the sky.
w 16) Careful observation of microwave "static" shows that it is essentially the same in all directions and has the spectral distribution of a 2.8K "blackbody".
k 17) When different compounds can be made from the same chemical ingredients, it is found that the proportions by weight are always simple integer multiples.
g 18) The ratio of charge-to-mass of the particles emitted from the negative electrode in an evacuated gas discharge tube is independent of which gas is left in the tube.
A or k 19) When measuring the pressure of a fixed volume of various gases, as a function of temperature, the extrapolated line crosses the zero pressure axis at the same value of temperature, no matter what gas is used.
k 20) When observed through a microscope, little pollen grains, suspended in water, hop around in a jerky erratic fashion.
x 21) The spectra produced by rarefied incandescent gases are patterns of distinct lines, characteristic of the gas and independent of time.
l 22) Electrons are emitted from a surface only when the light impinging upon the surface exceeds some frequency, characteristic of the surface, no matter how intense the light may be.
s 23) A beam of electrons, incident upon a crystal, leaves the crystal in many different beams.
o 24) A beam of light, incident upon a calcite crystal, becomes two separate beams within the crystal.
p or q 25) Light from a single source, entering two widely separated calcite crystals, shows strongly correlated polarizations in the two crystals.
q 26) Light from a very distant galaxy, seemingly coming from two different parts of the sky because of passage either side of an intermediate-distance galaxy, can be brought together to form an interference pattern.
h or o 27) Light, which is completely blocked by two crossed polarizing filters, will pass through when a third filter is placed at an angle between the first two.
l 28) A very weak intensity light, incident upon a photographic plate, manifests itself as a collection of sharp individual dots.
t 29) White light, passing through a glass prism, is seen as a sequence of many different colors.
r 30) A weak electron beam, incident on a phosphor surface, is seen as a series of point spots of light.
a) The velocity of light is the same for all observers.
b) The planets rotate about the Sun.
c) In the absence of external forces, momentum is conserved.
d) Energy is conserved in an isolated system.
e) Normal matter is made up of two kinds of electricity.
f) The inertial mass of an object increases with its speed.
g) The electron is a universal constituent of matter.
h) A quantum state of one attribute is always a super- position of several states of the conjugate attribute.
i) Einstein's Principle of Equivalence.
j) Newton's First Law-the Law of Inertia.
k) Matter is made up of discrete particles called "molecules".
l) Light is composed of discrete particles called "photons".
m) Newton's Law of Universal Gravitation.
n) Nucleons are made up of quarks.
o) Light acts like a transverse wave which can be polarized.
p) Quantum phenomena are mysteriously non-local.
q) Quantum waves can be coherent over enormous distances.
r) Electrons act like particles.
s) Electrons have wave characteristics.
t) Light can be decomposed into waves of many different frequencies.
u) Nuclei are made up of neutrons and protons.
v) Heat is a form of fluid called "caloric".
w) The universe is expanding from an initial "big bang".
x) Rutherford's Planetary model of the atom is contradicted by Maxwell's laws of Electromagnetism.
y) Light travels along geodesics in a space which is curved by the presence of matter.
z) The Z particle is a form of electromagnetism.
A) Heat is a form of energy.
B) Light has wave characteristics.
D) Most of the mass of the atom is concentrated in a very small central region called the "nucleus".
E) A magnetic field is created by an electric current.
II. There are eight questions in the essay part of the exam, each worth 10 points. Do any four of them. Write all your answers carefully, completely, briefly, and legibly. Anything that cannot be easily read will not be graded. (Total: 40 points)
Useful Numerical Information
C = speed of light = 3 x 10 8 m/s: h = Planck's constant = 4.1 x 10-15
En = Bohr energy levels of hydrogen atom = - (13.6/n2) eV
1. What is the basis for J. J. Thomson's claim that electrons are universal
constituents of atoms? (Describe his and related experiments and the interpretations
which led to his conclusion.)
a) evacuated tube with trace gas of given element
b) high voltage leads to beam from cathode to anode
c) deflection of beam in known electric field shows that beam made up of negative charges
d) balancing deflection of beam by electric field with opposing deflection by known magnetic field leads to determination of value of ration of charge of beam particles to their mass
e) repeat a-d with different gases in tube; always get same numerical value for charge to mass ratio which is thus a universal number for all atoms. So these particles must be in all atoms.
2. A constant force of 50N acts upon an object of mass 5kg, opposed by a frictional force of 10N, over a distance of 100 meters.
a) What is the acceleration of the object?
b) How much work is done by the 50N force?
c) How much of this work goes into increased kinetic energy?
d) What happens to the rest of this work?
a) Net force F = 50N - 10N = 40N;
F=ma so a=F/m= 40N/5kg = 8m/s/s
b)W =Fd = 50N*100m = 5000J
c) Only work due to net force = 40N*100m = 4000J = 80% of total work
d) remaining 20% is lost to heat generated by the friction.
3. a) How does Einsteinian relativity differ from Galilean relativity?
b) The postulate of relativity allows two different observers to disagree about the simultaneity, or relative order, of two separated events but does not allow such disagreement when the two events are at the same place. Why the difference?
a) GR - no universal maximum speed, hence space and time independent of each other
ER - all observers have same max speed, hence space and time can’t be independent of each other and each, separetely must be dependent on observer; hence GR has universal simultaneity whereas ER has observer based simultaneity
b) two events at same time and place can interact with each other producing physical results (e.g., clapping two hands. light signals from these two events start out at same time from same place, hence must reach any observer together (at his time). Physical results - e.g., creation or destruction of something (clap) - must be observed by all if we are to have real physical universe.
4. A clay ball of mass 3kg and velocity 10m/s collides with a stationary mass of 5kg and sticks to it.
a) What was the momentum of the 3kg ball before the collision?
b) What is the velocity of the combined two objects immediately after the collision?
c) How much kinetic energy was lost as a result of the collision?
a) initial momentum = 3kg * 10 m/s = 30 kgm/s
=total momentum = final momentum
b) final momentum = total mass*final velocity = 8kg * v; thus v(final) =30kgm/s / 8kg = 3.75m/s
c) KE(initial) = one-half mass * square of initial velocity = (1/2)*(3kg)*(10m/s)*(10m/s)=150J;
similarly KE(final) = (1/2)*(8kg)*(3.75m/s)*(3.75m/s) = 56.25J;
thus 150J - 56.25J = 93.75J are lost to heat.
5. a) What is meant by "non-locality"?
b) Did it play any role in physics before the advent of quantum physics? (Explain your answers carefully; a simple "yes" or "no" is not acceptable.)
a) A non-local effect is one which propagates at a speed greater than that of light
b) Newton’s Universal Law of Gravitation implied an instantaneous effect of one body on that of others, no matter how far away. Hence this “action at a distance” propagated faster than c, i.e., it was non-local.
6. a) Explain the relation between "quantum tunneling" and Feynman diagrams.
b) What is the difference between the way bosons and the way fermions appear in Feynman diagrams? Explain the difference.
a)Both quantum tunneling and Feynman diagrams allow the propagation of a particle in violation of the conservation of energy - in both, the intermediate state of the system with the propagating particle has more energy than the initial and final states. This is only possible because of the Heisenberg Uncertainty Relation, i.e., the violation (delta E) takes place within the time (delta t) such that (delta E)* (delta t)~h
b) At each vertex of a Feynman diagram, odd or even numbers of bosons can occur whereas only even numbers of fermions canconnect to the vertex. This means that fermions can only be created or destroyed in pairs - particle & antiparticle - whereas single bosons can be created or destroyed.
7. What does Herbert mean by a "rainbow model of reality"? How does it apply to the electron? Is this application changed in any way by the results of Bell's Theorem?
The rainbow doesn’t exist - it isn’t really “there independently of the observer; it isn’t a grabable thing, yet all observers appropriately located will see it, though each differently: it is an observer created reality. Thus in this model, the electron isn’t really “there” though it interacts with the measurement apparatus of each observer, giving different results to different apparatuses. Bell’s results rule out a local rainbow reality buit do allow a non-local raainbow reality: thje observer “creates’ a rainbow non-locallyu, i.e., outside of his own absolute-future-light-cone in space-time.
8. Mu - mesons, whose life time, according to an earth-based observer, is 2 x 109 seconds, are "born" high above the earth's atmosphere and race towards the earth's surface with a speed of 0.8c.
a) How far will they be seen to travel by an earth-based observer during their lifetime? (Ignore all gravitational effects.)
b) If you were to be traveling with these mu-mesons, how far would you see them travel during their lifetime?
c) What lifetime would you say they had?
a) distance = speed *time = 0.8*3*108m/s*2*10-9s = 0.48seconds
b) The moving meson sees the distance of (a) moving with respect to it, thus shrunk by the Lorentz factor, gamma = 1/0.6 =1.67. So it sees a length of 0.48m * 0.6 = 0.288 m
c) Since you have less far to go in a lifetime, at the same relative speed, the lifetime is less by the same gamma factor; so you think you live only 2*10-9s *0.6 = 1.2*10-9s.
HAVE A GOOD SUMMER!