Final Exam Solutions

Physics 106 - How Things Work - Spring, 2000

Final Examination - Solutions

Given Friday, May 12, 2000, from 9:00 AM to 12:00 Noon

PART I: MULTIPLE CHOICE QUESTIONS

Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with #2 pencil. Part I is worth 67% of the grade on this examination.

Problem 1:

Light travels long distances through the glass core of an optical fiber. The glass in this core is exceptionally clear so that very little light is absorbed during its travel. When a short pulse of white light passes through a very long fiber,

(A) the white light emerges from the fiber with all of its wavelengths together.

(B) it emerges from the fiber as a pulse of infrared light.

(D) red light emerges from the fiber first.

Answer: (D) red light emerges from the fiber first.

Why: Dispersion separates the colors of light as the light passes through the fiber. Violet and blue lights travel slower than red light and so the red portion of the spectrum emerges before the blue and violet portions of the spectrum.

Problem 2:

The plastic covering of a fake leather couch bends and stretches but can’t be pulled apart easily. The plastic resists pulling apart because

(A) its crystals are very small and it can’t undergo slip.

(B) its magnetic poles are aligned and they attract one another.

(D) its temperature drops as you stretch it and it freezes into a stiff material before it separates.

Answer: (C) its long molecules are entangled with one another.

Why: Plastics are made from giant polymer molecules. These molecules are often entangled and their elastic and leathery characteristics are the results of entanglements among those giant molecular chains.

Problem 3:

Lead absorbs X rays because each of its atoms has a large

(A) number of protons to attract X rays.

(B) nucleus with many nucleons in it.

(D) number of neutrons to attract X rays.

Answer: (C) number of electrons.

Why: Atoms absorb X rays most strongly when those X rays can transfer electrons from one orbital or energy level to another. These radiative transitions use the X ray’s energy to change the energy of an electron. In the photoelectric effect, an electron shifts from one bound orbital to an orbital that is actually unbound… a free electron. This sort of radiative transition can occur over a wide range of X ray photon energies, but is strongest when the X ray photon has just enough energy to barely remove an electron. Since a lead atom has so many different electrons, there is usually one that is suitable for absorbing a given X ray photon and producing a low-energy free electron.

Problem 4:

A pair of squirrels is building a nest. One squirrel carries a mouthful of lightweight leaves up one tree, across some branches at the top and back down another tree to where the nest is. A second squirrel caries a mouthful of heavy sticks straight up the tree with the nest. Both squirrels start from the ground and end up at the same nest.

(A) Neither squirrel does work on their building materials; the materials do work on them.

(B) The first squirrel does more work on the leaves than the second squirrel does on the sticks.

(D) The second squirrel does more work on the sticks than the first squirrel does on the leaves.

Answer: (D) The second squirrel does more work on the sticks than the first squirrel does on the leaves.

Why: The complicated path that the first squirrel takes has no effect on the overall work done. In both cases, the squirrels effectively lift their burdens upward the same total distance. Since the second squirrel’s load is heavy, that squirrel does more work (upward force exerted on the burden times distance the burden traveled upward).

Problem 5:

Your neighbor's house loses power during a windstorm. To help out, you run a long extension cord from your house to your neighbor’s house. Your neighbor’s appliances don't run properly when plugged into this cord because too much power is wasted in its thin wires. As current goes from you house to your neighbors, its

(A) current and voltage both gradually decrease along the length of the cord

(B) voltage gradually decreases along the length of the cord.

(D) voltage gradually decreases along the length of the cord and current gradually increases to partly compensate.

Answer: (B) voltage gradually decreases along the length of the cord.

Why: The charges traveling through the cord gradually lose energy, so their voltage gradually decreases during their trip. But the current that enters the cord must all reach the end because charge is conserved and no charge is leaving or entering the cord except at its start and finish.

Problem 6:

As a figure skater leaps into the air with her arms extended, she pushes off of the ice in a twisting motion to start herself spinning. When she is in the air she is initially spinning slowly, but when she pulls her arms in near her body she spins rapidly because her moment of inertia

(A) becomes larger, but her angular momentum stays the same.

(B) becomes smaller and her angular momentum increases.

(D) stays the same, but her angular momentum becomes smaller.

Answer: (C) becomes smaller, but her angular momentum remains the same.

Why: In isolation, the skater experiences zero net torque and cannot exchange angular momentum with anything else. Her angular momentum is therefore constant. But as she pulls her arms in, her moment of inertia (her rotational inertia) decreases. To maintain a constant angular momentum, her angular velocity must increase and so it does.

Problem 7:

Which one of the following items emits radio waves?

(A) A stationary, uniformly charged metal flagpole that is vertical.

(B) A uniformly charged plastic stick that is spinning end-over-end in the air.

(D) A stationary loop of wire that has a steady electric current flowing in it.

Answer: (B) A uniformly charged plastic stick that is spinning end-over-end in the air.

Why: Only accelerating charge can emit electromagnetic waves and only (B) and (D) involve accelerating charge. However, to launch an electromagnetic wave, the accelerating current must also produce a changing magnetic field. In (D), the steady current’s magnetic field is also steady. Therefore, (D) does not radiate any electromagnetic waves.

Problem 8:

You jump off of a diving board into a swimming pool. As you fall toward the water, your velocity

(A) remains constant because your acceleration is zero.

(B) remains constant because your acceleration is constant.

(D) increases because your acceleration increases.

Answer: (C) increases, but your acceleration remains constant.

Why: You become a freely falling object, subject only to the downward force of gravity. You accelerate steadily downward and your velocity increases in the downward direction.

Problem 9:

The amount of information a DVD can hold is limited by physics. Which of the following changes would lead to the biggest increase in a DVD’s capacity?

(A) Spin the disc much faster during reading and writing.

(B) Use a gold reflective layer rather than an aluminum layer.

(D) Make the plastic disc thinner while keeping it equally stiff.

Answer: (C) Shift to a much shorter wavelength laser for reading and writing.

Why: An electromagnetic wave cannot resolve features on a surface when those features are much smaller than the wavelength of the wave. This fundamental problem limits the density at which information can be packed on the recording surface of the DVD. By shifting to a shorter wavelength laser, an optical playback system would be able to read information that had been packed more tightly on the recording surface.

Problem 10:

When a xerographic copier first applies electric charges to the surface of its photoconductor, it does so in the dark. The reason for applying these charges in the dark is that light exposure would

(A) release magnetic poles that would cancel the electric charges.

(B) allow the charges to flow through the photoconductor so that they wouldn’t accumulate on its surface.

(D) expand the coherence of the waves and prevent the charges from forming a real image on the surface.

Answer: (B) allow the charges to flow through the photoconductor so that they wouldn’t accumulate on its surface.

Why: When exposed to light, the photoconductor becomes a conductor and will not allow the accumulation of separated charge.

Problem 11:

A downhill skier goes off a jump and remains in the air for more than a second. While the skier is in the air, what force is pushing the skier forward?

(A) Momentum.

(B) Gravity.

(D) Nothing.

Answer: (D) Nothing.

Why: Inertia alone propels the skier forward, not a force.

Problem 12:

You have a flashlight that requires 4 “D” batteries but you only have 3 of them. You find a piece of metal that has the same shape as a “D” battery, wrap its side with tape so that it won’t cause any short circuits, and load the flashlight. All the connections are made properly and there is no short circuit. You’ve simply formed a circuit with a chain of 3 batteries instead of the chain of 4 that the flashlight was designed for. You turn on the flashlight and

(A) its bulb fails to light at all.

(B) its bulb glows, but rather dimly.

(D) its bulb glows at full brightness, but the batteries run out relatively quickly.

Answer: (B) its bulb glows, but rather dimly.

Why: The voltage rise through your chain of batteries is only 4.5 volts, rather than the normal 6.0 volts. The current entering the lamp has less energy per charge and delivers less power to the lamp. A small current of these reduced energy charges flows as well. Overall, the lamp is underpowered and glows dimly.

Problem 13:

The mercury atoms in a fluorescent lamp emit ultraviolet light. If the lamp used barium atoms instead of mercury atoms, the barium atoms would emit green light. In that case, the lamp wouldn’t be able to produce white light because its phosphors wouldn’t be able to emit

(A) red light.

(B) green light.

(D) yellow light.

Answer: (C) blue light.

Why: When a phosphor absorbs energy from a light photon and then emits a new photon of its own, it can’t emit a photon with more energy than the one it absorbed. Since blue photons have more energy than green photons, a phosphor can “convert” a green photon into a blue photon.

Problem 14:

Car tires can't be melted for recycling because

(A) the polymer molecules in rubber are just too long to reptate (move along their length).

(B) the polymers in tires have been crystallized, which causes them to burn before they melt.

(D) the crosslinked polymers are kept from reptating (moving along their length) as temperature is increased.

Answer: (D) the crosslinked polymers are kept from reptating (moving along their length) as temperature is increased.

Why: A tire is one giant molecule. While natural rubber is thermoplastic, meaning that it contains countless individual molecules, the molecular chains in vulcanized rubber are cross-linked into one giant network. The chains in natural rubber can move about enough to melt, but those in vulcanized rubber can never get apart.

Problem 15:

A wax sphere can act as a converging lens for microwaves and will focus a beam of microwaves to a narrow spot. Evidently, when microwaves enter wax from air, they

(A) speed up.

(B) undergo total internal reflection.

(D) slow down.

Answer: (D) slow down.

Why: The wax sphere is acting as a converging lens and it has convex surfaces. For a convex structure to bend “light” rays together, it must slow the rays down and that is just what the wax in the wax sphere does.

Problem 16:

The sky is blue because the tiny particles in air

(A) scatter long wavelength light more efficiently than short wavelength light.

(B) resonantly absorb red light and then emit lots of it out into space.

(D) scatter short wavelength light more efficiently than long wavelength light.

Answer: (D) scatter short wavelength light more efficiently than long wavelength light.

Why: The particles in air are poor antennas for light, but they handle short wavelength light more effectively than long wavelength light. They therefore redirect more blue and violet light than red light and make the sky appear blue.

Problem 17:

An AM radio station transmits its signal from a tall antenna because

(A) only a tall antenna can produce the large amplitude signals required for amplitude-modulated transmissions.

(B) a tall antenna will transmit the signal farther.

(D) the band of frequencies set aside for AM transmissions have short wavelengths.

Answer: (C) the band of frequencies set aside for AM transmissions have long wavelengths.

Why: By convention, AM radio transmission uses radio waves with wavelengths of roughly 300 meters. An efficient antenna for such waves should be about a quarter of the wavelength long, or roughly 75 meters.

Problem 18:

If you "cook" a CD or compact disc briefly in a microwave oven,

(A) it becomes permanently magnetized.

(B) it vibrates back and forth violently in response to the fluctuating electric field.

(D) it becomes hot enough to soften and sparks leap about its surface.

Answer: (D) it becomes hot enough to soften and sparks leap about its surface.

Why: The thin aluminum layer can’t tolerate the large currents driven through it by the microwave electric fields and it overheats. The CD swells and tears the aluminum layer into sharp fragments, which then produce sparks.

Problem 19:

If you rub a balloon in your hair it will become electrically charged. When you put this charged balloon against an insulating wall it can stick because the wall becomes

(A) charged.

(B) electrically polarized.

(D) magnetically polarized.

Answer: (B) electrically polarized.

Why: The wall never acquires a net charge, but the balloon’s charge makes the wall’s charge rearrange. Opposite charges in the wall migrate toward the balloon while like charges migrate away from the balloon. The wall becomes electrically polarized and attracts the balloon.

Problem 20:

A charged particle moving to the left can be accelerated by

(A) neither an electric field that points up nor a magnetic field that points up.

(B) an electric field that points up, but not a magnetic field that points up.

(D) an electric field that points up or a magnetic field that points up.

Answer: (D) an electric field that points up or a magnetic field that points up.

Why: While stationary charge only experiences electric forces, a moving charge can also experience a force from a magnetic field. After all, a moving charge is itself magnetic.

Problem 21:

Laser light exhibits much stronger interference effects than light from an incandescent lamp because laser light is

(A) much narrow than incandescent light

(B) a single electromagnetic wave while incandescent light is not.

(D) emitted by atoms while incandescent light is not.

Answer: (B) a single electromagnetic wave while incandescent light is not.

Why: The coherent nature of laser light, in which all the photons of light are part of one giant electromagnetic wave, allows all the photons to interfere with one another and produce enormous interference effects.

Problem 22:

You are throwing a ball straight up and then catching it as it returns to your hand. When the ball leaves your hand, its momentum is in the upward direction but when it returns to your hand, its momentum is in the downward direction. During its flight above your hand, what happens to the ball's initial upward momentum?

(A) The upward momentum is converted into kinetic energy.

(B) The upward momentum is transferred to the earth.

(D) The upward momentum is converted into gravitational potential energy.

Answer: (B) The upward momentum is transferred to the earth.

Why: Gravity exerts a steady downward force on the ball, providing an impulse that gradually shifts the ball’s momentum more and more downward. The ball pulls up on the earth and overall, the ball’s upward momentum is transferred to the earth.

Problem 23:

You are showing some friends slides from your latest vacation, using a slide projector. The slide is placed behind a lens and its image is projected onto the wall. More friends show up and you want to make the image larger so that everyone can see. To do this the projector must be

(A) kept in the same position, but its lens must be moved farther from the slide.

(B) kept in the same position, but its lens must be moved closer to the slide.

(D) moved closer to the wall and its lens moved farther from the slide.

Answer: (C) moved farther from the wall and its lens moved closer to the slide.

Why: To form a larger real image, that image must form farther from the lens so you move the projector away from the wall. But now you must change the focus so that the image forms on the wall again. You need to delay the focusing of the light rays and you do this by moving the slide closer to the lens (or lens closer to the slide) so that the rays of light reaching the lens from the slide are more diverging and harder to bring together. They reach a focus farther from the lens on the now distant wall.

Problem 24:

One of the problems with tubes that emit X rays is that their targets can overheat and melt. Carbon has the highest melting temperature of any element, yet it’s not used as a target in X-ray tubes because

(A) its nuclei have too little mass and charge, and its atoms have too few electrons.

(B) it is an insulator and can’t be electrically charged.

(D) it is black and absorbs X rays.

Answer: (A) its nuclei have too little mass and charge, and its atoms have too few electrons.

Why: X rays are formed when electrons accelerate rapidly around heavy atomic nuclei or when complicated atoms undergo radiative transitions from highly excited states to much less excited states. Both of these actions require large, complicated, massive atoms and carbon is not one of these.

Problem 25:

You walk to class at a steady pace along a flat, horizontal path. Your backpack weighs 100 newtons and your trip is 500 meters long. How much work do you do on your backpack?

(A) 0 joules (0 newton-meters).

(B) 1/5 joule (1/5 newton-meters).

(D) 5 joules (5 newton-meters).

Answer: (A) 0 joules (0 newton-meters).

Why: The force you exert on the backpack is exactly upward while the distance that backpack travels is exactly horizontal. Since the force exerted on the backpack is at right angles to the distance traveled by the backpack, zero work is done on it.

Problem 26:

Spring steel is brittle because

(A) it contains a mixture of small iron crystals and small iron carbide crystals.

(B) it contains a mixture of large iron crystals and large iron carbide crystals.

(D) it is held together by very strong ionic bonds.

Answer: (A) it contains a mixture of small iron crystals and small iron carbide crystals.

Why: Spring steel is heat treated so that it can’t undergo slip and won’t change shapes permanently (no plastic deformation). The mechanism for this hardening is the formation of tiny iron carbide crystals scattered through the relatively smaller iron crystals in the metal. These carbide crystals pin the iron crystals in place so that their layers can’t slip across one another to let the metal deform permanently.

Problem 27:

When an electron makes a radiative transition in an atom, it emits

(A) a neutron.

(B) an electromagnetic wave.

(D) a gamma ray.

Answer: (B) an electromagnetic wave.

Why: While certain nuclear processes in atoms can produce the other three types of particles, they involve more energy than the electrons in an atom can summon together. That’s why a radiative transition involving electrons in an atom can only produce an electromagnetic wave (and one with less energy than a gamma ray).

Problem 28:

A makeup mirror is concave—its center is bent away from your face. When you stand close to the mirror, you see an enlarged and upright virtual image of your face located far behind the mirror. However, when you back away far enough, you see an inverted real image of your face hovering between the mirror and you. If you hold a small piece of paper in the place where you see this real image,

(A) a rainbow pattern of light will appear on the paper, but it will contain only those wavelengths of light that are reflected by your face.

(B) the inverted real image of your face will appear as a pattern of light on the paper.

(D) an inverted real image of the mirror will appear on the paper.

Answer: (D) an inverted real image of the mirror will appear on the paper.

Why: Real images are true patterns of light in space. If you put paper in the place where a real image appears, the pattern of light will illuminate the paper and you’ll see the image projected on the paper.

Problem 29:

If you quickly poke at a starch-and-water solution, it feels hard. If you push slowly on the same solution your finger will sink into it and become coated with the sticky starch paste. The starch solution feels hard when you poke at it because

(A) the starch crystals don't have time to slip and rearrange.

(B) the heat from your body does not have time to flow into the starch solution.

(D) the long polymer molecules don't have time to move around your finger.

Answer: (D) the long polymer molecules don't have time to move around your finger.

Why: In solution, the polymer molecules are all tangled together and they need time to separate from one another in order to flow around your finger. If you poke hard, the molecules can’t get untangled and the solution feels rigid.

Problem 30:

It’s important not to overheat good steel tools because that can cause them to lose their hardness. This thermal softening occurs because at high temperatures

(A) steel crystallizes into aluminum.

(B) steel becomes a non-crystalline (or amorphous) metal.

(D) carbon atoms can move and shift within the steel.

Answer: (D) carbon atoms can move and shift within the steel.

Why: Part of the steels hardness comes from the placement and structure of iron carbide crystals within the crystals of iron itself. At high temperatures, the carbon in these iron carbide crystals dissolves in the iron and the iron-carbide-based hardness disappears.

Problem 31:

A skydiver leaps out of an airplane and begins to fall. After a few seconds, she reaches a constant downward speed of about 300 kilometers-per-hour (190 miles-per-hour). The net force she is experiencing at that point is

(A) zero, because the upward drag force exerted on her by the air is equal to her weight.

(B) upward, because she is in free fall and the only force she experiences is an upward centrifugal force.

(D) downward, because the only force acting on her is gravity. She is in free fall.

Answer: (A) zero, because the upward drag force exerted on her by the air is equal to her weight.

Why: She is falling at constant velocity, so you know that the net force on her is zero. Although she still has her full weight, it is being balanced by an upward drag force that is equal in magnitude to her weight.

Problem 32:

You are driving eastward on the highway and the sun is setting behind you. You are following a pickup truck with a large flat rear window. There is a blinding glair from the sun’s reflection off of the window. Sunlight is reflected from this window because

(A) the glass of the rear window is tempered.

(B) sunlight is polarized.

(D) light travels slower in glass than in air.

Answer: (D) light travels slower in glass than in air.

Why: When light tries to enter the window, it slows down and part of the light (about 4%) reflects. There is a second reflection as light speeds up upon reentering the air on the far side of the window glass. The glair that you see is these two reflections, a total of about 8% of the light striking the window’s surface.

Problem 33:

When two pieces of semiconductor touch to form a p-n junction, a depletion region forms around that junction. In the depletion region, all the valence levels are filled and all the conduction levels are empty. The depletion region is

(A) electrically conducting.

(B) filled only with spin-up electrons.

(D) magnetic.

Answer: (C) electrically insulating.

Why: With no partially filled bands of levels, the electrons are unable to move in response to electric fields and no current can flow through the semiconductor. The depletion region behaves like pure semiconductor and is insulating.

Problem 34:

In a nuclear weapon, a chain reaction occurs when each fission

(A) produces an energy equal to the mass times the speed of light squared.

(B) produces at least one more fission.

(D) produces at least one neutron.

Answer: (B) produces at least one more fission.

Why: To continue the chain reaction, each fission must beget another fission, at the very least. Otherwise, the fission rate will gradually decline to zero.

Problem 35:

A softball weighs about twice as much as a baseball. Suppose that a softball and a baseball roll off a horizontal table at the same speed and soon hit the horizontal floor. In that case, the

(A) lighter baseball will land about half as far from the edge of the table as will the heavier softball.

(B) heavier softball will land much, much closer to the edge of the table than will the lighter baseball.

(D) two balls will land at about the same distance from the edge of the table.

Answer: (D) two balls will land at about the same distance from the edge of the table.

Why: Since all objects fall at the same rate and the two balls have equal horizontal speeds, they follow identical arcs and strike the ground together at the same distance from the edge of the table.

Problem 36:

Ordinary iodine atoms (iodine-127) and radioactive iodine atoms (iodine-131) are chemically indistinguishable because both have

(A) virtually identical masses.

(B) virtually identical arrangements of electrons.

(D) the same gamma rays in their nuclei.

Answer: (B) virtually identical arrangements of electrons.

Why: Iodine atoms all have the same electronic structures—that’s what makes them iodine atoms. Chemically, they behave the same way. However, the different isotopes have slightly different masses and one is radioactive.

Problem 37:

An inexpensive microwave oven may heat food unevenly because

(A) the microwaves bouncing around inside the oven can interfere, producing regions where the electric field oscillations are large and regions where the oscillations are small.

(B) low power microwaves are only absorbed in the densest parts of the food.

(D) the metal mesh on the front of cheap microwave ovens is not as efficient at keeping the microwaves in.

Answer: (A) the microwaves bouncing around inside the oven can interfere, producing regions where the electric field oscillations are large and regions where the oscillations are small.

Why: The microwaves bouncing around inside the microwave oven often experience strong interference effects. At some places, the microwave electric fields arriving from various directions sum to an enormous field and the microwave intensity there is unusually large (constructive interference). At other places, the fields nearly cancel one another and the intensity is unusually weak (destructive interference).

Problem 38:

In a xerographic copier, charge is sprinkled uniformly over the surface of a photoconductor. The charge is then removed in some places by illuminating the photoconductor with a pattern of light. The charge is removed when light

(A) causes the photoconductor to become insulating.

(B) causes the photoconductor to become conducting.

(D) ionizes atoms.

Answer: (B) causes the photoconductor to become conducting.

Why: Exposure to light promotes some electrons from the valence band levels to the conduction band levels. With two partially filled bands of levels, the photoconductor becomes electrically conducting and charge can leave its surface.

Problem 39:

When an X-ray photon is absorbed in your body it can damage cells because

(A) its oscillating electric field accelerates atoms and heats them.

(B) X-ray photons carry enough energy to ionize atoms.

(D) cells act as almost perfect antennas, which absorb the X rays.

Answer: (B) X-ray photons carry enough energy to ionize atoms.

Why: X ray photons do chemical damage by rearranging the atoms in molecules. By ejecting electrons from atoms, they break bonds and allow new chemical structures to form.

Problem 40:

The oscillating electric field inside a microwave oven heats food by

(A) accelerating charged water molecules back and forth and causing them to bump into each other.

(B) twisting polar water molecules and causing them to rub against each other.

(D) breaking molecular bonds and releasing chemical potential energy as thermal energy.

Answer: (B) twisting polar water molecules and causing them to rub against each other.

Why: The electric field of a microwave can exert a torque on a polar molecule such as water. When many touching water molecules are exposed to a changing electric field, those water molecules twist and slide across one another, converting energy from the electric field into thermal energy in the rubbing molecules.

Problem 41:

The side window of a car is made of tempered glass that crumbles into thousands of tiny pieces when it breaks. In addition to exhibiting this “dicing fracture,” tempered glass is also very difficult to break because

(A) its surface is compressed by the glass beneath the surface.

(B) it is made of relatively small quartz crystals.

(D) it is made of relatively large quartz crystals.

Answer: (A) its surface is compressed by the glass beneath the surface.

Why: The outer surface of a tempered glass window is squeezed inward by the window’s subsurface material. Starting a tear in such compress glass is hard because you must first overcome the compression forces and then begin to produce a tear..

Problem 42:

Light emitted from a neon lamp appears red because

(A) the charges in the neon gas discharge are only accelerated with enough energy to produce red photons.

(B) the inside of the lamp is coated with phosphors that emit red light.

(D) the lamp runs at a cooler temperature than an incandescent light bulb and cooler objects emit redder light.

Answer: (C) the strongest radiative transitions in neon atoms emit red photons.

Why: The orbitals of neon dictate the colors of light it emits when a current passes through it. The red light that neon emits comes from a particular group of transitions that are strong and common occur during electric discharges.

Problem 43:

The purpose of the graphite (carbon) in the Chernobyl nuclear reactor was to

(A) lubricate the control rods, so that they would experience less sliding friction.

(B) slow down fission neutrons.

(D) prevent the cooling water from boiling.

Answer: (B) slow down fission neutrons.

Why: The Chernobyl reactor, like most reactors, was a thermal fission reactor. It used slow moving neutrons to fission uranium-235 while ignoring uranium-238 in the nuclear fuel. The fast neutrons produced by fissions were slowed down via collisions with the moderator nuclei, in this case carbon nuclei.

Problem 44:

Charged particles travel from the sun to the earth in what is known as “the solar wind.” When these particles encounter the earth’s magnetic field, they spiral in toward the earth’s magnetic poles because

(A) negative charges are attracted to north magnetic poles while positive charges are attracted to south magnetic poles.

(B) electric charges are attracted to the nearest magnetic pole, regardless of whether that pole is north or south.

(D) magnetic fields push on moving charges.

Answer: (D) magnetic fields push on moving charges.

Why: The earth’s magnetic field pushes the fast moving charged particles at right angles to both the particles’ velocities and the magnetic field.

Problem 45:

A 60-watt, 120 volt light bulb is designed to reduce the voltage of a 1/2 amp current by 120 volts. If you screw this bulb into a fixture that is powered by very long thin wires, it will glow more dimly than intended because the voltage that the current through the bulb loses will be

(A) 120 V and the current through the bulb will be 1/2 A.

(B) 120 V, but the current through the bulb will be less than 1/2 A.

(D) less than 120 V, but the current will still be 1/2 A.

Answer: (C) less than 120 V and the current through the bulb will be less than 1/2 A.

Why: As it passes through the long thin wires, the current will lose some of its 120 volts and the voltage drop through the bulb itself will be less than 120 volts. With less of a voltage drop to push the charges through the bulb’s filament, the amount of current that actually flows will be reduced and will not be the full 1/2 A that the bulb is designed to handle.

Problem 46:

A television contains a small step-up transformer that produces the very high voltages needed to accelerate electrons toward the front of the picture tube. When low voltage alternating current passes through the primary coil of this transformer, power is extracted from that current and passed to an alternating current flowing through the secondary coil of the transformer. Each charge passing through the secondary coil receives a relatively large amount of energy because the secondary coil

(A) is wound in the opposite direction from the primary coil. Charges passing through the two coils push apart as they circle the transformer's magnetic core so that charges in the secondary coil accelerate to very high speeds.

(B) uses thinner wire than is used in the primary coil, so that a smaller current flows through the secondary coil and a charge picks up more energy each time it circles the transformer's magnetic core.

(C) has many more turns than the primary coil, so that the charges in the secondary coil circle the transformer's magnetic core many times.

(D) is made from a magnetic wire that repels charges and pushes them to very high energies as they pass through it.

Answer: (C) has many more turns than the primary coil, so that the charges in the secondary coil circle the transformer's magnetic core many times.

Why: In a step-up transformer, the secondary coil circles the magnetic field many times so that each charge travels a long distance in the direction of the transformer’s electric field.

Problem 47:

Someone hands you a capacitor and asks you to find out whether it has separated electric charge on its two plates. To do this successfully, you would determine if

(A) there is a difference between the voltages of the two plates.

(B) there is a current flowing on either one of the two plates.

(D) the capacitor emits infrared light.

Answer: (A) there is a difference between the voltages of the two plates.

Why: If the capacitor’s plates are storing separated charge, then the negatively charged plate will have a voltage that is lower than that of the positively charged plate. After all, a positive charge located on the positively charged plate has more electrostatic potential energy than a positive charge located on the negatively charged plate.

Problem 48:

Nuclear weapons can’t be built from natural uranium because uranium-238

(A) absorbs fission neutrons without fissioning itself.

(B) emits too many neutrons when it fissions.

(D) is below the critical mass required for a chain reaction.

Answer: (A) absorbs fission neutrons without fissioning itself.

Why: Uranium-238 does undergo nuclear processes after absorbing a fission neutron, but it does not fission. Instead, it soon undergoes a series of transformations that eventually convert it into plutonium-239.

Problem 49:

You are observing a distant ship with a telescope but you can't quite read the ship's name. To increase the magnification of the telescope, you replace the current eyepiece with one that

(A) contains a less highly curved lens (a longer focal length).

(B) has a smaller aperture (smaller diameter).

(D) contains a more highly curved lens (a shorter focal length).

Answer: (D) contains a more highly curved lens (a shorter focal length).

Why: The eyepiece lens is acting as a magnifying glass, allowing you to observe the real image that’s projected by the objective lens. To enlarge your view of that real image, you need a shorter focal length lens, a more highly curved converging lens that allows you to move your eye close to the real image.

Problem 50:

In a nuclear reactor, which uses natural uranium, a moderator is used to slow the fast neutrons resulting from the fission of uranium-235 nuclei. These neutrons are slowed in order to

(A) keep the reactor from reaching critical mass.

(B) keep uranium-238 nuclei from absorbing them.

(D) reduce the radioactivity of the waste products.

Answer: (B) keep uranium-238 nuclei from absorbing them.

Why: At low speeds (thermal speeds), neutrons can pass by uranium-238 nuclei without being absorbed. At higher speeds (fission neutron speeds), uranium-238 nuclei tend to absorb neutrons and then convert slowly to plutonium-239. Only at extremely high speeds (fusion bomb speeds) are neutrons able to cause uranium-238 to fission.

PART II: SHORT ANSWER QUESTIONS

Please give a brief answer in the space provided. Words written outside of the allotted space will not be read during grading. Part II is worth 33% of the grade on this examination.

Problem 1:

Before boarding an airplane, you must go through a screening process to make sure that you don't carry on any dangerous objects. The two principal screening devices are a metal detector for your person and an X-ray machine for your carry-on bags.

(A) As you walk through the metal detector, you are exposed to the rapidly varying magnetic field of an AC-powered electromagnet. The current passing through the coil of this electromagnet reverses directions thousands of times each second. You have an aluminum pen in your pocket and it becomes magnetic while you are in the metal detector. What occurs inside the pen to make it become magnetic?

Answer: A current begins to flow in the pen.

Why: The fluctuating magnetic field of the AC-powered electromagnet is changing with time, so it produces an electric field as well. This electric field pushes charges around inside the pen and causes the pen to become magnetic.

(B) Because of its magnetization, your pen causes currents to flow through a second coil of wire in the metal detector. The metal detector beeps to alert the operators that you are carrying a metal object. How does the pen cause currents to flow through that second coil?

Answer: The pen’s magnetic field changes with time, so it produces an electric field. This electric field pushes charges around the second coil.

Why: The pen’s magnetization reverses frequently because it is responding to an AC-powered electromagnet. The pens rapidly reversing magnetic field produces an electric field and this electric field is what propels current through the second coil.

(C) As your carry-on bag goes through the X-ray machine, it is exposed to a weak stream of X rays. These X rays are produced by a vacuum tube in which electrons collide with a tungsten metal surface and emit X rays. The tube uses a small current of high voltage electrons to produce these X rays. Why can't it use a large current of low voltage electrons to produce X rays?

Answer: Each electron must have enough energy to produce one X-ray photon. Since an X-ray photon has an enormous energy, the electron that produces it must have an enormous energy, too.

Why: Each X-ray wave is emitted when a single electron in the X-ray machine interacts with an atom or the atom’s nucleus. Since an X-ray photon has a huge amount of energy, the electron that makes it must also have a huge amount of energy. The electrons in the machine must therefore have huge voltages (energy per unit of charge) and only a small number of these electrons are needed each second, a small current.

Problem 2:

After taking pictures of the mountains far in the distance, you decide to take a close-up picture of a friend.

(A) To shift the camera’s focus to a closer object, which way should you move the camera’s lens relative to its film?

Answer: Move the lens away from the film.

Why: The light reaching the lens from a closer object is diverging more. The lens bends this light inward, but that light converges slowly (because of its original strong divergence). As a result, the real image forms relatively far from the lens and the film must be relatively far from the lens, too.

(B) When you hold the camera as close to your friend as you would like, you find that the camera can’t quite focus the real image on the film. Your friend is just a little closer than the camera can handle. However, you can get around this problem by increasing the camera’s depth of focus by playing with its aperture. How should you change the lens’s aperture to get a sharp picture of your too-close friend?

Answer: Reduce the diameter of the lens’s aperture (or increase the f-number).

Why: A narrower lens (smaller diameter lens) allows only the most closely arranged light rays to pass through it. These light rays are already so near to one another that they are pretty close long before and long after they actually focus to a point. The exactly location of the real image, either in front of the film, on the film, or behind the film doesn’t matter much. The depth of focus is therefore quite large; i.e. almost everything is in focus, regardless of how far it is from the lens.

(C) If you try to take a photograph of an object that’s closer to the lens than that lens’s own focal length, you can’t get a real image to form on the film at all. Explain why no real image forms.

Answer: Light reaching the lens from the too-close object is diverging so strongly that the lens is unable to make it converge at all (or the image distance becomes negative).

Why: The converging lens can only bend light so much. When the extremely divergent rays from the too-close object reach the lens, the lens simply isn’t able to bend those rays enough to make them converge. The rays continue to diverge, although not as strongly as before.

Problem 3:

Most of you have probably ridden on bumper cars at an amusement park. These cars use electrically powered motors.

(A) A metal rod sticks up, out of the back of each car and at the top of this rod is a flat piece of metal, which rubs against the metal ceiling. This is the wire through which the current enters from the ceiling to the motor of the car. A second wire connects the motor to the floor. Why is this second wire necessary?

Answer: Current flows to the car through one wire and leaves through the second wire.

Why: Current travels best in complete circuits. There must be a continuous looping path between power source and power consumer. In this case, the bumper car is the power consumer. Electric current flows to the car through one wire and leaves through the second. That current then effectively flows to the power company to pick up more energy and then returns to the car through the first wire.

(B) The motor has a large electromagnet in it. If the conductor on the ceiling briefly loses contact while a large current is flowing through the electromagnet, a spark will form between the two. Why is there a spark?

Answer: The electromagnet acts as an inductor and opposes changes in current (or the vanishing magnetic field transfers its energy to the current passing through it, producing a spark through the air).

Why: An electromagnet opposes changes in the current passing through it. When the wire loses contact with the ceiling, the current begins to decrease and the electromagnet’s magnetic field begins to collapse. The energy in that magnetic field goes into the current, trying to keep the current flowing. The only way to continue the current, given the lost contact between car and ceiling, is to push a spark through the air from the car to the ceiling.

(C) Your friend's car is stopped directly in front of you. You smash into him from behind. After the collision, your car is stopped. Explain what happens to your friend’s car using the concept of conservation of momentum.

Answer: Your car lost its forward momentum by transferring it to your friend’s car. Your friend’s car must now move forward because it has your original momentum.

Why: Momentum can’t be created or destroyed. Since you were moving forward originally, you had forward momentum. When you bumped into your friend, you gave your friend your original momentum. Your car stopped and your friend’s car began moving forward with your original momentum.

Problem 4:

You’re tired of sitting in restaurants, listening to people talk on their cell phones. To solve the problem, you build a small device that emits a strong radio wave at a frequency you can select. You wait for a talker to pull out a cell phone and then turn on your little transmitter.

(A) Your device has a short antenna and you carefully align that antenna parallel to the talker’s antenna. Why is this important in trying to affect the talker’s cell phone?

Answer: The electric field in the wave emitted by your antenna is parallel to your antenna. It will push on charges in the talker’s antenna best if that electric field is parallel to the talker’s antenna.

Why: A transmitting antenna emits a radio wave that is polarized parallel to that antenna; e.g. a vertical antenna emits vertically polarized radio waves (a vertical electric field). A receiving antenna works best when it is aligned with the polarization of the waves it is receiving; e.g. a vertical antenna responds well to vertically polarized radio waves (the wave’s vertical electric field pushes charges along the length of the receiving antenna).

(B) You adjust the frequency of your transmitter until it matches that of the talker’s cell phone. Now it’s time to get the talker’s attention! The talker’s cell phone is using the amplitude modulation technique to communicate with the telephone company. What should you do to your transmitter to make noise in the talker’s ear?

Answer: Change the power or amplitude of the transmission (or turn your transmitter on and off).

Why: Since sound information is being sent using the amplitude modulation technique, any changes in radio wave amplitude are interpreted by the talker’s cell phone as commands to move its speaker to create sound. By creating amplitude changes with your little transmitter, you can cause the talker’s cell phone to make noise.

(C) The police frown on your little trick, so you decide to use passive gadgets instead. You purchase several large metal sheets and find that if you position them just right around a talker, the radio wave that reaches the talker’s cell phone is surprisingly weak. You aren’t blocking the radio wave entirely, merely reflecting pieces of it toward the cell phone from different directions. The pieces of the radio wave are all reaching the cell phone, so why do they result in such poor reception?

Answer: The pieces are experiencing destructive interference (or the pieces are canceling one another at the cell phone’s antenna).

Why: The pieces of the radio wave don’t necessarily have their electric fields pointing in the same directions at the same times. By carefully controlling the reflections, you can make it so that the electric fields from those pieces cancel one another and yield poor reception.

Problem 5:

Many of the laboratories in this building make use of "dye lasers". In this type of laser, the laser medium is a solution of fluorescent dye molecules. These dye molecules behave similarly to the phosphor used in a fluorescent lamp.

(A) Energy is usually supplied to the dye molecules by light from another laser, the pump laser. If you are using dye molecules that emit yellow laser light at 590 nanometers, what wavelength should the pump laser have (please give a descriptive comparison with the laser wavelength)?

Answer: The pump laser should have a shorter wavelength than the laser wavelength (or at least not longer than the laser wavelength).

Why: Each dye molecule is absorbing a photon of light from the pump laser and emitting a photon of new light. Since the new photon of light can’t have more energy than the pump photon provided, the wavelength of the new photon must be longer than the wavelength of the pump photon. In principle, the pump photon and the laser photon can be the same in certain circumstances, but that’s unlikely.

(B) In order to build a laser, a pair of mirrors must be placed on either side of the laser medium. Briefly explain how these mirrors allow a single, spontaneously emitted photon to be duplicated many times.

Answer: These mirrors reflect the photons back and forth through the laser medium and they are amplified with each passage through that medium.

Why: One mirror reflects the spontaneous photon back through the laser medium for amplification. The other mirror returns this amplified light for another pass through the laser medium. This process repeats over and over again as light bounces back and forth between the mirrors.

(C) Dye molecules contain bands of levels that allow them to emit a continuous range of colors of laser light across this band. In order to select the color that the laser emits, a prism (a wedge shaped piece of glass) can be used. What property of the prism allows it to separate the colors?

Answer: Dispersion (and refraction).

Why: Violet light travels more slowly in glass than does red light. On entry or exit from the prism, the light refracts. However, the violet light bends more than red light and the colors separate.

Problem 6:

On September 30, 1999, an accident occurred in a uranium processing plant in Tokaimura, Japan. About 35 pounds of somewhat enriched uranium (about 19% uranium-235 and 81% uranium-238) were dissolved in nitric acid in a tank surrounded by cooling water. A nuclear chain reaction occurred. For the purposes of this question, you can think of the uranium as being dissolved in water and surrounded by water.

(A) By itself, 35 pounds of this type of uranium would not constitute a critical mass. In fact, it would probably take hundreds of pounds or more to form a critical mass. Why is it so hard to form a critical mass of this type of uranium?

Answer: The uranium-238 nuclei absorb fission neutrons and hinder the chain reaction.

Why: Uranium-238 nuclei don’t fission easily. Instead, they absorb neutrons and spoil any chain reactions that might occur among the uranium-235 nuclei.

(B) Mixing the uranium with water made a huge difference. In a water environment, 35 pounds was enough to form a critical mass. What role did the water play and why did it lead to a critical mass?

Answer: The water slowed down the fission neutrons so that uranium-238 nuclei could no longer absorb them (the water acted as a moderator).

Why: The small nuclei in water slow down the fast fission neutrons and reduce them to thermal velocities. At these slow velocities, the neutrons stop interacting with the uranium-238 nuclei and are able to fission the uranium-235 nuclei unimpeded. As long as the uranium-235 nuclei are close enough and abundant enough, a chain reaction can begin. The surrounding water helped bounce neutrons back into the solution so that they could continue to help with the chain reaction.

(C) The chain reaction in the mixing tank emitted lots of neutrons, which then stuck to the nuclei of atoms throughout the building. Why are atoms with extra neutrons in their nuclei dangerous to people?

Answer: These atoms a radioactive and they are incorporated into people’s bodies just like their non-radioactive siblings.

Why: The extra neutrons don’t change the atoms’ chemical natures, so our bodies incorporate those radioactive isotopes just as though they were normal atoms. But once inside us, the eventually decay and release dangerous energies that damage molecules and cause trouble.

Problem 7:

You have just stepped out of a drenching spring rainstorm. You plug your hairdryer into the upper socket of a 120-volt electric outlet and begin to dry your hair. The hairdryer carries a current of 10 amperes, weighs 10 newtons, and produces air with a temperature of 70° C.

(A) How could you calculate how much electric power the hairdryer is using (you don't have to do this calculation; just describe how to calculate it)?

Answer: Multiply the current (passing through the hairdryer) times the voltage (drop across the hairdryer).

Why: The voltage drop across the hairdryer indicates how much energy each unit of charge deposits in the hairdryer. The current through the hairdryer indicates how many units of charge flow through the hairdryer per unit of time. If you multiply these two quantities together, you obtain the amount of energy deposited in the hairdryer per unit of time, which is the power delivered to the hairdryer.

(B) As your hair dries out, it gradually becomes stiffer. Your hair is a polymer that dissolves lots of water. Why does getting your hair wet make it softer?

Answer: The water (dissolves in your hair and) acts as a plasticizer (or the water lubricates the hair molecules).

Why: Chemicals that dissolve in plastics and lubricate their molecules tend to soften those plastics.

(C) You are brushing your hair with a cheap metal comb. The comb gets tangled in your hair and you pull hard, permanently bending several of the comb's teeth. What happened to the arrangement of atoms in the teeth as the teeth bent?

Answer: The (planes of) atoms (in the metal crystals) slipped across one another.

Why: In a typical metal, the crystals can deform by sliding one sheet of atoms across another. This process is known as slip.

Problem 8:

An induction stove uses an electromagnet to heat a pan rather than burning gas or a hot element.

(A) Alternating current is supplied to an electromagnet, which is beneath a glass or ceramic surface. When a metal pan is place above this electromagnet, current will flow in the pan. Explain how the alternating magnetic field can cause this current to flow.

Answer: The changing magnetic field produces an electric field, which pushes on charges in the metal pan.

Why: Changing or moving magnetic fields produce electric fields. Since electric fields push charges, the mobile charges in the metal pan begin to flow as currents.

(B) Why should the pan be made of a metal that conducts electricity poorly?

Answer: Current flowing in the poorly conducting metal loses energy and produces thermal energy.

Why: The pan is heated by energy wasted by the currents flowing in its surface. If it conducts electricity too well, the pan won’t heat much because the currents in it won’t waste much energy.

(C) Assume that the magnetic field produced by the stove alternates between pointing up and pointing down. The induced current in the pan produces a second magnetic field. What is the direction of the force on the pan resulting from these two fields?

Answer: The pan will be pushed away from the stove’s electromagnet (the pan will be pushed upward).

Why: As noted by Lenz’s law, an induced magnetic field opposes the change in magnetic field that induced the magnetism. In this case, the pan’s magnetic field opposes the stove’s magnetic field. If the stove creates a north pole on its top, then the pan tries to cancel that magnetic pole by creating a south pole on top (and a north pole on its bottom). Since the two north poles are pointed toward one another, the pan is pushed upward, away from the stove.