Physics 106 Midterm Exam

Physics 106 - How Things Work - Spring, 2000

Midterm Examination - Solutions

Given Friday, March 3, from 1:00 PM to 1:50 PM

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 the midterm examination.

Problem 1:

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: You push upward on the backpack but move it horizontally. Since your force and the direction it moves are perpendicular to one another, you do zero work on the backpack.

Problem 2:

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

(A) A stationary, constant magnetic field.

(B) A stationary, constant electric field.

(D) A stationary wire containing a constant electric current.

Answer: (B) A stationary, constant electric field.

Why: Electric fields push on electric charges; that’s just what they do. The others do not have necessarily have electric fields around them.

Problem 3:

You install a diode in one of the two wires connecting a desk lamp to the electric outlet’s alternating current. Any current passing through the bulb’s filament must also pass through the diode. With the diode in place, the bulb will glow only about half as bright as usual because the diode

(A) turns half the current into voltage, which has no effect on the bulb.

(B) turns half the voltage into current, which has no effect on the bulb.

(D) only allows half as much current to flow at any given time.

Answer: (C) only allows current to flow half the time.

Why: A diode only allows current to flow in one direction. As the alternating current from the power company reverses directions, back and forth, the diode only allows current to flow half of the time.

Problem 4:

The split iron ring of a tape recorder’s playback head is made of a magnetically soft material so that

(A) it doesn’t scratch the tape.

(B) its ends can become electrically charged easily.

(D) a large current can flow through it easily.

Answer: (C) its magnetization follows the tape’s magnetization easily.

Why: During playback, the tape’s magnetic fields magnetizes the split ring. If the ring weren’t made of a soft magnetic material, it wouldn’t be able to magnetize easily in response to the tape’s magnetization.

Problem 5:

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

(A) your velocity remains constant because your acceleration is constant.

(B) your velocity remains constant because your acceleration is zero.

(D) your velocity increases because your acceleration increases.

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

Why: Since your weight doesn’t change as you fall, your downward acceleration remains constant. But you do fall faster and faster, so your velocity increases in the downward direction.

Problem 6:

When you put positive charge on the gate of an n-channel MOSFET, it conducts current well. Its three pieces of semiconductor are then effectively

(A) p-type, n-type, and p-type semiconductor respectively.

(B) pure, n-type, and pure semiconductor respectively.

(D) all n-type semiconductor.

Answer: (D) all n-type semiconductor.

Why: The positive charge on the gate of the n-channel MOSFET attracts extra negative charge into the channel. It goes from being chemically p-type to electrically n-type. It also becomes negatively charged, but that’s not particularly important. The MOSFET then consists of an n-type source, an n-type channel, and an n-type drain. Current flows easily through this all n-type structure.

Problem 7:

When you drop the north pole of a permanent magnet onto an aluminum sheet, it falls slightly slower than normal. The magnet is being repelled by the aluminum because

(A) aluminum is positively charged and repels approaching magnetic poles.

(B) aluminum has a net north magnetic pole that repels any approaching north poles.

(D) current induced in the aluminum by the approaching north pole produces a repelling north pole on the aluminum’s surface.

Answer: (D) current induced in the aluminum by the approaching north pole produces a repelling north pole on the aluminum’s surface.

Why: The approaching north pole develops an electric field because it’s moving and causes currents to flow through the aluminum. These currents are magnetic and, in accordance with Lenz’s law, they oppose the field change that causes them—they repel the approaching north pole.

Problem 8:

You are playing Frisbee with a friend when the Frisbee gets caught in a tree. You throw a rock at the Frisbee to dislodge it. When the rock hits the Frisbee, knocking it loose,

(A) both energy and momentum are transferred to the Frisbee.

(B) momentum is transferred to the Frisbee, but no energy is transferred.

(D) neither momentum nor energy are transferred to the Frisbee since both must be conserved.

Answer: (A) both energy and momentum are transferred to the Frisbee.

Why: The rock pushes the Frisbee and the Frisbee moves in the direction of the push, so work is done and energy is transferred to the Frisbee. Moreover, the rock pushes on the Frisbee for a length of time, so an impulse occurs and momentum is transferred to the Frisbee.

Problem 9:

A photoconductor’s electrical properties go from insulating to conducting when it is exposed to light because,

(A) light allows extra electrons to move out of the valence band giving the semiconductor a positive charge.

(B) light allows extra electrons to move into the conduction band giving the semiconductor a negative charge.

(D) light lowers the energy of the conduction levels eliminating the energy gap.

Answer: (C) light supplies the energy needed to move electrons from the valence band to the conduction band.

Why: A photoconductor is insulating in the dark because its valence band is full and its conduction band is empty. No electrons can move in response to an electric field. However, when you shine light on the photoconductor, light energy promotes some of the valence level electrons to conduction levels and suddenly the electrons can move about.

Problem 10:

A step-down transformer transfers power from the 120 volt alternating current passing through its primary coil to the 12 volt alternating current passing through its secondary coil. If you interchange the primary and secondary coil, and send the 120 volt alternating current through the new primary coil,

(A) a 12 volt alternating current will pass through its new secondary coil.

(B) a 12 volt direct current will pass through its new secondary coil.

(D) a 1200 volt alternating current will pass through its new secondary coil.

Answer: (D) a 1200 volt alternating current will pass through its new secondary coil.

Why: When you reverse the primary and secondary coils, the transformer stops being a step-down transformer and becomes a step-up transformer. With 10 times as many turns in its new secondary coil as in its new primary coil, the transformer draws power from the 120 volt current in its primary circuit and delivers it to the 1200 volt current in its secondary circuit.

Problem 11:

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 drop across the bulb will be

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

Why: As current passes through the long wires, energy is lost and the current loses voltage. The voltage drop available to the bulb is no longer 120 V, it is something less than that. Since the bulb’s filament is roughly ohmic in behavior, as the voltage drop across it diminishes, the current passing through it also diminishes. Thus both the voltage across and current through the bulb are reduced.

Problem 12:

The surface of a photoconductor has been coated with electric charge. This charge will remain in place until you expose the surface to

(A) an electric field.

(B) a magnetic field.

(D) light.

Answer: (D) light.

Why: Light turns the photoconductor from an insulator (with immobile charges) to a conductor (with mobile charges).

Problem 13:

After running a plastic comb through you hair several times you hold it above a small scrap of paper. The paper jumps off the table and sticks to the comb because the paper becomes

(A) magnetic.

(B) electrically charged.

(D) electrically polarized.

Answer: (D) electrically polarized.

Why: The paper doesn’t acquire a net charge because it can’t simply make or destroy charge. Instead, it redistributes its positive and negative charges in such a way as to put opposite charge nearest the comb. It is then attracted to the comb.

Problem 14:

You charge a capacitor by connecting its terminals to opposite ends of a battery. After disconnecting the battery,

(A) there are both electric and magnetic fields between the conducting plates of the capacitor.

(B) there is a magnetic field between the conducting plates of the capacitor.

(D) there is an electric field between the conducting plates of the capacitor.

Answer: (D) there is an electric field between the conducting plates of the capacitor.

Why: With stationary, separated electric charge on its plate, the capacitor has an electric field around it but no magnetic field.

Problem 15:

If your bicycle tires were made of solid rubber rather than being filled with air, it would be harder to start them spinning because they would have

(A) a larger angular momentum.

(B) a larger moment of inertia.

(D) a larger kinetic energy.

Answer: (B) a larger moment of inertia.

Why: The solid tire would have more rotational inertia than a hollow tire. The measure of rotational inertia is moment of inertia.

Problem 16:

The north pole of a permanent magnet is clinging to the front surface of your steel refrigerator, so the refrigerator clearly has a south pole at its surface. If you flip the permanent magnet over, so that its south pole faces the refrigerator, the refrigerator will

(A) keep a south pole at its surface and repel the permanent magnet.

(B) keep a south pole at its surface and attract the permanent magnet.

(D) place a north pole at its surface and attract the permanent magnet.

Answer: (D) place a north pole at its surface and attract the permanent magnet.

Why: The magnetic domains in the steel will rearrange to place an opposite pole near whatever magnetic pole you put nearby. That’s why steel always attracts a nearby magnet.

Problem 17:

You have just pulled your clothes from the dryer and find that a sock is clinging to your jeans with static electricity. You hold the jeans in one hand and the sock in the other and pull the two apart. As jeans and sock move apart, the forces between them become weaker because the

(A) electric charge on each garment increases as they move apart.

(B) electric current passing through each garment diminishes as they move apart.

(D) forces between electric charges become weaker with increasing distance.

Answer: (D) forces between electric charges become weaker with increasing distance.

Why: The charges can’t escape from the insulating fabric. However, as they get farther from one another, the forces become weaker as the inverse square of their separation.

Problem 18:

A person playing Frisbee golf on a windless day throws a Frisbee at a distant target. When the Frisbee is flying forward but has left the hands of the thrower, it experiences

(A) a forward force that diminishes steadily and reaches zero just as the Frisbee strikes the target.

(B) no forward force.

(C) a forward force that increases in strength for the first half of the flight and then decreases in strength for the second half of the flight.

(D) a constant forward force.

Answer: (B) no forward force.

Why: The Frisbee is coasting forward. It has forward momentum and is not being pushed forward by anything at all.

Problem 19:

You are carrying a spinning toy top around your dorm on the surface of a dining hall tray. It continues to spin almost indefinitely because nothing can exchange any

(A) force with it.

(B) angular momentum with it.

(D) momentum with it.

Answer: (B) angular momentum with it.

Why: One way to look at why a toy top spins so long is that it has angular momentum and can’t get rid of it easily. Since it’s only contact with the outside world is at its point and that point can’t exert much torque on the surface that supports the top, the top can’t receive much torque in return. It keeps spinning until its angular momentum gradually leaks out through that tip.

Problem 20:

Your new toaster has two separate toasting units, each of which consumes 600 watts of power when it's in use. When you operate one unit, a current of 5 amperes flows through the wiring in your home and the wires waste about 1 watt of power handling that current. If you operate both toasting units at once, your toaster consumes 1200 watts and the current flowing through the wiring in your home doubles to 10 amperes. How much power will the wires in your home waste now?

(A) about 1 watt.

(B) about 0.5 watts.

(D) about 4 watts.

Answer: (D) about 4 watts.

Why: With twice the current flowing through the home wires, they will waste four times as much power as before. They’re experiencing twice the voltage drop and twice the current, which leads to four times as much energy wasted each second.

Problem 21:

You are watching children play a game of tug-o-war with an old plastic clothesline. The two teams are pulling at opposite ends of the cord and each team is trying to drag the other team into a mud puddle that lies between them. After a few minutes without progress, the team on the right suddenly pulls hard toward the right. The team on the left has anticipated this threat and is able to keep their end of the rope from moving at all. The right end of the rope stretches toward the right and the rope breaks. It took energy to breaking the rope and that energy was provided by

(A) both teams.

(B) the team on the left.

(D) the team on the right.

Answer: (D) the team on the right.

Why: The team on the right pulls the rope right and it move right. Therefore, they do work on the rope and are responsible for the energy that breaks it.

Problem 22:

Which one of the following objects can erase the information stored on the magnetic strip of your student ID card?

(A) A large battery.

(B) A capacitor with lots of separated charge on its two plates.

(D) A coil of wire with a large current flowing through it.

Answer: (D) A coil of wire with a large current flowing through it.

Why: Erasing the magnetic strip requires a strong magnetic field and only the coil of wire with current in it is strongly magnetic.

Problem 23:

Around high tension power lines there are

(A) electric, but no magnetic fields.

(B) neither electric nor magnetic fields.

(D) magnetic, but no electric fields.

Answer: (C) both electric and magnetic fields.

Why: As current flows through the lines, they develop a magnetic field. As the voltage of each line changes with the alternating current flow, the amount of charge on the line and its voltage change. With charges on the lines, there is an electric field present as well.

Problem 24:

A battery in an operating flashlight

(A) does work while transferring positive charge from its negative terminal to its positive terminal.

(B) does work while transferring positive charge from its positive terminal to its negative terminal.

(D) has work done on it when positive charge flows from its positive terminal to its negative terminal.

Answer: (A) does work while transferring positive charge from its negative terminal to its positive terminal.

Why: Batteries pump positive charge against its natural direction of flow, from the negative terminal to the positive terminal.

Problem 25:

One use of a resistor in an audio amplifier is to

(A) amplify currents.

(B) restrict the flow of current to one direction.

(D) store charge.

Answer: (C) limit current.

Why: Resistors can’t store charge, control the direction of current flow, or amplify currents. All they can do is limit a current’s flow by extract energy from it.

PART II: SHORT ANSWER QUESTIONS

Please give a brief answer in the space provided. Part II is worth 33% of the grade on the midterm examination.

Problem 1:

Electrical power is supplied to your house as an alternating current because it is easy to change the voltage of an alternating current without wasting much energy.

(A) The same amount of power can be delivered to your house using a large voltage and a small current or a small voltage and a large current. Why is a large voltage and small current used to transfer power over long distances?

Answer: The power lines waste power in proportion to current squared so minimizing current is energy efficient.

Why: The power carried by a power line is the product of its voltage times its current. If you minimize the current end of that product, you reduce the power wasted in the power lines themselves.

(B) Having high voltages in your house can be dangerous so the power company uses a step-down transformer to reduce the voltage of the power supplied to your house. Compare the number of turns in the primary coil in this transformer to the number of turns in the secondary coil.

Answer: The primary coil has more turns than the secondary coil.

Why: The fewer turns there are in the secondary coil, the less energy each charge gets when passing through the coil and the lower the voltage the current has when it leaves the secondary coil.

Answer: The primary coil creates a changing magnetic field, which creates an electric field, which does work on charges passing through the secondary coil.

Why: The changing magnetic field produced by the primary coil of the transformer induces a current in the secondary coil and passes power to it.

(D) Some electronic devices require a direct rather than alternating current. Why is a diode useful for converting an alternating current into a direct current?

Answer: A diode prevents current from flowing in one direction and ensures that the current in a wire always heads in the other direction, like a direct current.

Why: An alternating current changes directions periodically while a direct current moves steadily in one direction. Since a diode blocks the current reversals, it makes an alternating current source behave more like a direct current source—pushing current only in one direction.

Problem 2:

You have a little lamp for reading books in bed. This lamp requires 6 volt electricity. You can power it either with four 1.5 volt batteries in a battery pack or with a little step-down transformer that plugs into the electric outlet and produces 6 volt alternating current.

(A) There are two wires connecting the battery pack to the lamp. Why isn’t one wire sufficient?

Answer: One wire carries current to the lamp and the other wire returns that current to the batteries (or, equivalently, one wire doesn’t form a complete circuit).

Why: The lamp can’t simply accumulate charges. It must extract their energy and then send them back to the battery pack to obtain more energy.

(B) If one of the four batteries is inserted backward, the lamp will glow dimly because

Answer: The reversed battery lowers the voltage of the current rather than raising it (or, equivalently, the battery pack then only produces 3 volt electricity).

Why: The reversed battery extracts energy from the passing current rather than adding energy to it. This reversed battery recharges by stealing energy from the other batteries.

(C) When you use the transformer to reduce 120 volt alternating current to 6 volt alternating current, what fraction of the electric charges passing through the electric outlet also pass through the lamp?

Answer: Zero percent.

Why: Charges passing through the primary coil of the transformer give their energy to charges passing through the secondary coil. However, the two coils are electrically isolated from one another and do not exchange charges at all. The current in the primary coil is entirely separate from the current in the secondary coil.

(D) When you operate the lamp from the transformer, there are moments when the lamp receives no electric power. Why is that?

Answer:During the reversals of the power line, there is no current flowing through the lamp.

Why: Whenever the power line reverses directions, there is a moment when no current is flowing. During that moment, no power is moving anywhere.

Problem 3:

Ensuring fair play at the Olympics has never been easy, both on the field and off. With your tremendous understanding of physics, you've received many lucrative offers to help the scoundrels, but you've held fast to the traditions of the UVa honor system and refused them all. Instead, you have become the world's foremost authority on sneaky Olympic tricks and have foiled dozens of evil plots. Here are a few of your most famous cases:

(A) The Tomanian cycling team once placed a series of strong magnets beneath the bicycle track and slowed the progress of any athlete riding an aluminum alloy bicycle. You discovered the magnets and fingered the Tomanian team because they were the only people riding bicycles made entirely of plastics. Why did the magnets slow the aluminum bicycles but not the plastic ones?

Answer: Only the aluminum bicycles can conduct currents and become magnetic when they move past the track's magnets.

Why: Conducting objects that move past strong magnets experience electric fields and have currents induced in them. These currents render the objects magnetic and they experience magnetic drag forces that slow their motions.

(B) The Freedonian track team once tried to lower their times in the 5000 meter run by installing air jets all the way around the track. These jets were aimed so that they would always blow each runner forward with a force of 100 newtons. Minutes before the race, you spoiled their plans by turning half the jets around so that they blow each runner backward. As the result of your efforts, the runners traveled exactly the same distance with air jets pushing them forward at 100 newtons as they did with air jets pushing them backward at 100 newtons. Overall, how much work did the air jets do on each runner?

Answer: Zero work.

Why: Work is force times distance. Since the runners are pushed forward for half the distance and backward for half the distance, the work done on them when pushed forward is exactly cancelled by the negative work done on them when pushed backward.

(C) One of the Lilliputian high jumpers decided to give himself an advantage by putting huge negative charges on both himself and on the landing mat under the bar. You caught him in time to remove the negative charge from the mat. The jumper experienced no repulsion from the mat and failed to clear the bar. Instead, the plastic bar stuck to him and the audience laughed as he fought to get it off. Why did the uncharged plastic bar stick to the negatively charged jumper?

Answer: The negative charge polarizes the plastic bar and the two attract

Why: The proximity of the jumper's negative charge shifts the charges inside the plastic bar. The positive charges in the bar move slightly toward the jumper and the negative charges in the bar move slightly away from him. Since the positive charges are closer to the jumper, the attraction they experience is stronger than the repulsion experienced by the negative charges on the bar.

(D) In a misguided attempt to win the 100 meter dash, a runner from the Duchy of Grand Fenwick coated the bottoms of her shoes with Superslide™, the "ultimate in frictionless lubrication." Her shoes experienced exactly zero friction. When the gun went off, the runner found herself unable to move forward and remained at the starting point with her legs churning furiously. What force or other physical effect kept her from moving forward?

Answer: Inertia.

Why: Without friction, the runner experienced no horizontal forces. Her inertia kept her motionless.