Physics 106 - How Things Work - Spring, 1998

Final Examination


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:

A rubber car tire cannot be melted for recycling because

Problem 2:

One way to thicken a sauce that you are cooking is to add starch to it. The added starch prevents the sauce from flowing easily because starch molecules

Problem 3:

For a nuclear weapon to explode normally, the fissionable material in its core must be assembled very quickly. For technical reasons, a nuclear bomb developed by a terrorist group would probably not achieve such rapid assembly. As a result of its slow assembly, such a bomb would

Problem 4:

A bright beam of light from a laser passes through a tiny pinhole on its way to a projection screen on the other side of the room. Since the beam was several millimeters in diameter, the pinhole blocks most of the beam's light. After passing through this pinhole, the remaining light

Problem 5:

You are hosting a romantic candlelight dinner in your room, but you forgot to buy the candles and all the stores are closed. Your desk lamp is too white and too bright to provide the right ambience, so you modify it by inserting a diode between one of the power wires and the bulb. As the result of this change, the lamp emits a reddish glow that's roughly half a bright as without the diode. Just for fun, you reverse the diode so that the end that used to connect to the AC power wire is now connected to the bulb and vice versa. As the result of this reversal, the lamp

Problem 6:

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

Problem 7:

While low pressure sodium vapor lamps are the most energy efficient light sources commonly available, producing a pure orange-yellow light with a wavelength of 590 nanometers, high pressure sodium vapor lamps produce a richer spectrum of light that is more pleasing to the eye. One effect that contributes to this richer spectrum is

Problem 8:

Increasing the diameter of a camera lens, while keeping its focal length unchanged, does more than just brighten the image on the film so that you can use a shorter exposure. It also

Problem 9:

You are pushing a file cabinet across the floor in a straight line at a steady speed. Which of the following statements about the forces acting on the file cabinet is correct?

Problem 10:

You drop your boom box and one of the two wires that connects the batteries to the electronics is severed. While you might hope that the device would continue working at half its normal volume, you find that it doesn't work at all. That's because both wires are necessary for the boom box to operate. One wire carries

Problem 11:

The energy that is released by a nuclear weapon was put into the weapon's fissionable core in the process of

Problem 12:

In which one of the following situations are you doing (positive) work on a sack of flour?

Problem 13:

Many simple forms of stainless steel cannot be hardened by heat treatment, even though they contain significant amounts of carbon. Regardless of temperature, these simple stainless steels have an austenite crystal structure, the same crystal structure that normal steel has when it is very hot. Carbon doesn't harden austenitic steels because

Problem 14:

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?

Problem 15:

A good refracting telescope must use more than one glass lens element to form a real image because

Problem 16:

If you put an egg in a microwave oven, it will become very hot. But if you put a dehydrated egg (a dried egg containing no water) in the microwave oven, the egg won't be affected because

Problem 17:

The large sugar crystals found in rock candy are essentially clear. However granulated sugar looks white because

Problem 18:

A makeup mirror is concave, meaning that it is shaped like a round-bottomed soup bowl that is being viewed from above the dinner table. When you hold the makeup mirror a few inches from your face and look at your reflection, you see an enlarged virtual image of your face. Because of its curved shape, the mirror is bending the reflected light rays so that they diverge

Problem 19:

The tubes in fluorescent lamps have a white powder on their inner surfaces. This powder

Problem 20:

At present, a compact disc can only hold about 1 hour of music. This limit is due in large part to the fact that

Problem 21:

Even when the core of a nuclear reactor exceeds critical mass by a small amount, it doesn't overheat immediately. The fission chain reactions build slowly because

Problem 22:

Three different lasers are emitting steady beams of light. Each beam consists of countless copies a single original photon of light. However, not all colors can be emitted by a laser. Which of the following choices is possible for these three lasers?

Problem 23:

The colors that you see when sunlight strikes a cut crystal wineglass or a cut diamond are a result of the fact that two light waves with

Problem 24:

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

Problem 25:

Cotton fibers are essentially pure cellulose, a glassy, crystalline polymer formed from sugar molecules. One reason for spraying water on a cotton shirt just before you iron that shirt is that the water

Problem 26:

Compared to the radio waves used in normal radio broadcasts, the microwaves used for satellite transmissions have

Problem 27:

Electricity produced in a generating plant passes through a large step-up transformer. This step-up transformer produces the high voltages needed to send electric power long distances across the countryside. Which of the following is transferred from the transformer's primary coil to its secondary coil while the transformer is operating?

Problem 28:

The power company uses a step-up transformer to prepare electric power for delivery to a distant city. The secondary coil of this transformer has many more turns than its primary coil. As a result, the transformer's secondary circuit

Problem 29:

Which of the following can cause a stationary charged particle to accelerate?

Problem 30:

A battery

Problem 31:

The fallout from a nuclear explosion and the waste from a nuclear reactor contain radioactive isotopes. The atoms of these isotopes differ from stable atoms in that

Problem 32:

There is a metal screen on the front window of a microwave oven. This screen is essential because it

Problem 33:

Two identical spaceships are travelling through deep, empty space and are not experiencing any forces from their surroundings. Their velocities are both constant, but one ship is moving twice as fast as the other. Each ship has a large rocket engine that can be used to push it forward. From this information, it's clear that

Problem 34:

A gymnast is bouncing on a trampoline, rising 2 meters above its surface on every bounce. After the rising gymnast has left the surface of the trampoline but is still heading upward,

Problem 35:

When laser light reflects from a soap bubble, its photons can interfere with one another. In contrast, when sunlight reflects from a soap bubble, each photon can interfere only with itself. The reason for this difference is that

Problem 36:

Most nuclear reactors in the United States are thermal fission reactors, reactors that slow their fission neutrons by sending those neutrons through materials known as moderators. Water is a common moderator. When a fast moving neutron enters water, it usually slows down because it

Problem 37:

You place an aluminum soda can on a hard floor and step on it with your foot, crushing it flat. The act of crushing the can

Problem 38:

Vegetable oil and Pyrex glass have almost exactly the same indices of refraction-the speed of light is the same in both materials. If you submerge a clear Pyrex dish in vegetable oil,

Problem 39:

The microscopic structure of quartz glass (amorphous quartz) closely resembles that of

Problem 40:

An engineer at the company you're working for has just reported finding an unusual electromagnetic wave. This wave consists only of an electric field, with no magnetic field accompanying it. You are certain that the engineer is mistaken because

Problem 41:

Some of the X-rays emitted by an X-ray imaging machine are fluorescence X-rays and are formed when individual atoms in the machine undergo radiative transitions. While the mercury atoms in a fluorescent lamp also undergo radiative transitions, those mercury atoms emit ultraviolet light, not X-rays. The reason for this difference is that

Problem 42:

If you float an aluminum pie plate on the surface of a pond and move the north pole of a strong magnet in a clockwise circle just above that plate, the plate will

Problem 43:

A glass fiber can act as a pipe for light-light that enters the fiber at its end follows the fiber almost indefinitely without escaping through the fiber's surface. The light follows the fiber because

Problem 44:

The rear windows of some cars have holes in them so that motors inside the cars can operate wiper blades outside the cars. These holes were diamond drilled at the factory before the glass was tempered. If a local car glass company were to try to drill a hole in a car window that had already been tempered,

Problem 45:

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 eyepiece with one having a

Problem 46:

You have just put fresh batteries in your flashlight and it's working nicely. Now suppose that you remove all of the batteries and reinsert them backward. Despite the fact that their positive and negative terminals are reversed, the batteries connect properly to one another and to the flashlight, so that there are no connection problems in the flashlight. As the result of this battery reversal, the flashlight will

Problem 47:

An expert archer is firing arrows at a target roughly 50 meters away. Each arrow travels almost horizontally and hits the target at over 100 mph. Once an arrow has left the archer's bow, that arrow experiences

Problem 48:

If you melt quartz (also known as silica or silicon dioxide), it becomes a thick, gooey liquid. If you cool this liquid quickly, it forms a clear solid but if you cool it too slowly, the resulting solid is cloudy. The cloudy solid forms because slow cooling

Problem 49:

The X-rays used in medical imaging travel through tissue relatively easily but are mostly absorbed by bone. That's because

Problem 50:

A glass window pane reflects about 4% of the light striking its front surface because


Please give a brief answer in the space provided. Part II is worth 33% of the grade on this examination.
Answer: (A) light slows down upon entering the glass and the resulting impedance mismatch causes some of that light to reflect.

Problem 1:

Modern audio amplifiers usually contain at least four important electronic components: resistors, capacitors, diodes, and MOSFETs. Let's take a brief look at each of these devices.

(A) A resistor behaves like a wire, except that its electric resistance has been adjusted to a particular value. Like a wire, a resistor wastes power when current flows through it so that the resistor becomes warm. If you double the amount of current passing through a particular resistor, by how much does the power being wasted by that resistor change?
Answer: The power increases by a factor of four (it quadruples).
Why: When double the current passing through a resistor or wire, the voltage (energy per unit of charge) lost by that current doubles. Since you are now sending twice as many units of charge through the resistor or wire each second, and each unit of charge is losing twice as much energy, the current is losing 2 x 2 or 4 times as much energy per second--four times as much power.

(B) A capacitor stores energy when it has positive charge on one plate and negative charge on the other. The voltage difference between those two plates is equal to the energy that would be released in letting a unit of positive charge return from the positive plate to the negative plate. How would this voltage different be affected if you were to move the two capacitor plates farther apart without changing their charges?
Answer: The voltage difference would increase.
Why: Voltage difference is a measure of the energy that would be released by a unit of positive charge that flows from the high voltage side to the low voltage side. If you take a charged capacitor--one with positive charge on one plate and negative charge on the other plate--and pull those plates apart, you do work on the charges. After all, the oppositely charge plates attract one another and you must push them apart as they move apart. This work ends up as energy in those separated charges. The energy that would be released when a unit of positive charge flows from one plate to the other would increase, so the voltage difference between the plates also increases.

(C) A diode conducts current only in one direction. Most diodes are constructed out of two different pieces of modified semiconductor: p-type and n-type semiconductors. If you assembled a diode out of two pieces of n-type semiconductor, omitting the p-type semiconductor altogether, would the new device conduct current and, if so, in which direction(s)?
Answer: Yes, it would conduct current in both directions.
Why: The combined system would be all n-type semiconductor. No p-n junction would form and there would be no "one-way" character to the system. Since n-type semiconductor is itself an electric conductor, the system would conductor electricity in either direction.

(D) An MOSFET makes it possible for a small amount of charge on the MOSFET's gate to turn on or off a substantial current flowing through the rest of the MOSFET. In a typical n-channel MOSFET, a modest positive charge on the gate will allow current to flow through the MOSFET from the drain to the source. What will happen if you instead put a modest negative charge on the gate of this same MOSFET?
Answer: The MOSFET would not allow current to flow.
Why: Putting negative charge on the gate of the MOSFET would push more negatively charged electrons out of the nearby p-type segment of the "n-channel MOSFET". That p-type segment, rather than becoming n-type and forming the "n-channel" that allows current to flow through the MOSFET, would become still more p-type. The p-n junctions in the device that prevent current flow through it would simply become stronger and further inhibit current flow. Problem 2:

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.

(D) You put down the bent metal comb and pick up another comb that's made of a hard, glassy plastic. This time when you pull on the comb after it becomes tangled in your hair, several of its teeth break off. Why doesn't this plastic comb bend the way the metal comb did?
Answer: The atoms and molecules in the glassy plastic aren't mobile and can't slip across one another, so that the molecules break apart (when overstressed).
Why: While some plastics can deform permanently, glassy plastics cannot. They have so little mobility at the atomic and molecular level that the break before they experience plastic deformation. Problem 3:

Sir Lancelittle headed off to seek his fortune, riding on his noble horse Fleabag and armed only with the legendary sword Whycaliber. Unfortunately, Whycaliber was made of pure lead because it was given to him by the Lady of the Pond and she was into heavy metal.

(A) As Sir Lancelittle sat under a tree that evening, he noticed that Whycaliber was already bent out of shape. He silently wished that the Lady of the Pond had been a little less obsessed with purity and had mixed a few other elements into the lead when she formed the blade. How would adding other elements to the lead have made the blade stiffer?
Answer: The other elements would have impeded slip (so that sheets of atoms would not have been able to slide across one another as easily).
Why: The lead sword deforms when its individual crystals experience slip. By inhibiting slip, alloying elements would harden the metal.

(B) During his travels, Sir Lancelittle was introduced to Plick and Plack, twin brothers whose swords were made of pure uranium 235. A few weeks after their meeting, Plick and Plack got into a heated argument over who's turn it was to empty the garbage. They drew their swords and began to fight but the moment those two swords struck one another, the brothers disappeared in a flash, along with much of the surrounding forest. Why were two separated swords safe, but two very nearby swords unsafe?
Answer: The separated swords are each below the critical mass, but together they exceed the critical mass.
Why: To experience a chain reaction, fissionable materials must be assembled in such a way that they use their fission neutrons efficiently. The separated swords waste too many neutrons to maintain a chain reaction, but the combined swords give each fission neutron more opportunity to cause a subsequent fission and thus use the neutrons more efficiently. Evidently, they exceeded the critcal mass and caused an explosion.

(C) To idle away his free hours, Sir Lancelittle often tossed Whycaliber into the air and tried to have it slice point first into the soft ground at his feet. He was only hospitalized twice as the result of this game. Each time Whycaliber left his hands, it would rise to a peak and then descend. Neglecting air resistance, in which direction was the net force on Whycaliber as it rose (after leaving his hands) and as it descended?
Answer: The forces was downward in both cases.
Why: Whether the sword is rising or descending, it is in free fall. The only force it is experiencing (apart from air resistance) is gravity and that force is in the downward direction. The sword is thus accelerating downward throughout its flight.

(D) Astonishingly enough, Whycaliber proved a valuable defensive tool when Sir Lancelittle was attacked by a band of outlaws armed with a wind-powered X-ray machine. What aspect of the sword's lead caused it to absorb the deadly X-rays before they could harm Sir Lancelittle?
Answer: Lead atoms have many tightly-bounce electrons that can absorb the X-ray photons (via photoemission).
Why: To absorb X-rays effective, an atom must have tightly bound electrons that can absorb an X-ray photon's energy and end up leaving the atom slowly. The electrons in small atoms are too easy to remove and therefore can't absorb all of the X-ray photon's energy easily. A lead atom is so huge that its tightly bound electrons can easily handle the X-ray photon's energy. Problem 4:

One way to detect an art forgery is to look for chemical elements in the paint that are not found in other paintings done by the artist. Many modern paint pigments contain elements that aren't present in old paintings, so finding one of these elements in a supposedly old painting is a sure sign that the painting is a fake. A common way to discover these inappropriate elements is to use a technique called "neutron activation." In this technique, the painting is exposed to neutrons from a nuclear reactor and the neutrons stick to the nuclei of some of the painting's atoms.

(A) What causes the neutrons to stick to the nuclei of the atoms?
Answer: The nuclear (or strong) force.
Why: When nucleons touch, they exert strong attractive forces on one another--the nuclear force.

(B) Once a neutron sticks to the nucleus of an atom, that atom may become radioactive. Since most nuclei contain neutrons without being radioactive, why does adding extra neutrons cause some nuclei to become radioactive?
Answer: Isolated (or "lonely") neutrons are unstable and fall apart.
Why: Isolated neutrons fall apart spontaneously with a half-life of about 17 minutes. Even in a nucleus, an isolated neutron can be unstable if there are too many other neutrons around. Nuclei with excessive numbers of neutrons are radioactive because their neutrons fall apart.

(C) These radioactive nuclei often decay by emitting an electron and a neutrino (actually an anti-neutrino). As the electron and neutrino leave the nucleus, one of the neutrons in the nucleus becomes a proton. How does this additional proton affect the atom that contains the nucleus?
Answer: The atom changes into a different element (and its chemical properties change).
Why: The number of protons in an atom determines the number of electrons that atom has (one electron for each proton). By adding a proton to the nucleus of an atom, you change the number of electrons that atom ends up with. The atom becomes a different element, with different chemical properties.

(D) The remaining nucleus is often left with extra energy-it's in an excited state. It soon emits a gamma ray that is characteristic of that nucleus. By studying the gamma rays coming from the neutron-activated painting, scientists can determine exactly which elements it contains and whether or not the distribution of elements is consist with those used by the artist. Once the neutron-activation test is over, the painting must be stored while its radioactivity diminishes. While most of its radioactivity vanishes within days, it remains slightly radioactive for a very long time. If it loses half of its radioactivity in one day, why doesn't it lose the other half in one more day?
Answer: It only loses about half its remaining radioactivity with each passing day.
Why: Radioactive decay is a random process. If a half of a collection of radioactive nuclei survive a day without decaying, then the clock starts all over for them and you can expect that only half of the remaining half will decay on the second day. By the third day, a quarter of the original nuclei will remain and the clock will again start over for them. Half of these will survive the third day, and so on. Problem 5:

You are outdoors on a sunny day, playing with a magnifying glass that is 10 centimeters in diameter, 1.0 centimeter thick, and has a focal length of 20 centimeters.

(A) You decide to use this glass lens to burn a piece of wood. You hold it above the wood so that a bright circle of sunlight forms of the wood's surface. To make the circle's edges sharp and clear, how high above the wood should you hold the lens?
Answer: 20 centimeters.
Why: The lens has a focal length of 20 centimeters. Since one way to determine a lens' focal length is to find the distance from the lens to the real image it forms of a distant object, distant objects will form real images 20 centimenters from this lens.

(B) How would you have to change the lens to make the sharp circle of sunlight it forms appear the same size as before, but brighter?
Answer: You would increase the diameter of the lens.
Why: The larger the lens is in diameter, the more light it captures and works with. Increasing its diameter won't change the location of its real image, but will increase the brightness of that image.

(C) How would you have to change the lens to make the sharp circle of sunlight it forms appear larger than before?
Answer: You would increase the focal length of the lens (or, equivalently, decrease the curvature of the lens).
Why: The farther from the lens the real image forms, the larger that real image will be. By delaying the focus, a less curved lens--one with a longer focal length--will have room to create a larger real image.

(D) You've tired of burning wood, so you begin using the lens as a magnifying glass to inspect a leaf. What's the farthest from the leaf you can hold the magnifying glass and still see a virtual image of the leaf?
Answer: (Almost) 20 centimeters.
Why: As you move the lens away from the leaf, the virtual image you see gradually drifts farther away (it's always on the far side of the lens) and becomes larger. But as the distance from the leaf to the lens approaches the focal length of the lens, the virtual image reaches becomes huge and infinitely far away. That huge image is so distorted you can't really tell what you're looking at, so you do best to stay just a little closer to the leaf. Problem 6:

Your eye is similar to a camera lens. A camera lens forms a real image of the scene in front of it on a sheet of film. Your eye forms a real image of the scene in front of it on your retina.

(A) To form a sharp image of a particular object on the film, the distance between the camera lens and the film must be carefully adjusted. Suppose that the camera is focused on an object 3 m (10 feet) away. If the object moves farther from the camera, which way must the lens move so that a real image of that object forms on the film-toward the film or away from it?
Answer: The lens must move toward the film.
Why: Light from a more distant object diverges less when it strikes the lens and focuses more easily. It forms a real image nearer to the lens and thus the lens must move toward the film.

(B) The lens in your eye can't move toward or away from your retina. Instead, it changes its curvature. Its middle can either bulge outward to make it more curved or it can squeeze inward to make it flatter. As the object you are watching moves away from you, how should the lens of your eye change so that a real image of the object forms on your retina-should its middle bulge outward more or squeeze inward more?
Answer: It should squeeze inward more (to make it flatter).
Why: To keep the real image at its same distance from the lens, you must decrease the focusing ability of the lens in your eye. You do this by making the lens less curved.

(C) When a person is farsighted, the light rays from a nearby object focus after the retina and the person's vision is blurry. With the help of eyeglasses, this person's vision can be corrected so that the person sees a sharp image of the nearby object. To correct the person's vision of nearby objects, should those eyeglasses contain converging lenses or diverging lenses?
Answer: The eyeglasses should contain converging lenses.
Why: To focus light from a nearby object into a real image on your retina, the lens in your eye must become highly curved. If you cannot do this and can only focus light from more distant objects, you evidently don't have enough converging strength in your lens. To assist your lens in converging the rays, you must wear converging lens eyeglasses.

(D) When you select eyeglasses, you have the choice of buying high index of refraction plastic lenses. A high index of refraction means that the plastic in the lenses slows light more than normal plastic. These lenses are 40% thinner than normal plastic lenses because the high index of refraction plastic bends light more than normal plastic. How does this increased index of refraction affect the amount of light that these lenses reflect?
Answer: They reflect more light (because the impedance mismatch between air and the plastic is more severe than normal).
Why: The more light slows down or speeds up in going between air and plastic, the worse the impedence mismatch and stronger the reflections. High index plastic lenses reflect more light than low index plastic lenses.