Physics 105 - How Things Work - Fall, 2002

Final Examination - Solutions

Given Wednesday, December 11, from 9:00 AM to 12:00 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 final examination.

Problem 1:

The temperature of a glass of ice water (a mixture of ice and water)
(A) is proportional to the ratio of water to ice.
(B) depends on the total volume of ice and water in the glass.
(C) is 0 °C.
(D) is proportional to the ratio of ice to water.
Answer: (C) is 0 °C.
Why: Ice and water can only coexist at one temperature: the freezing/melting temperature of 0 °C.

Problem 2:

You live in a cylindrical high-rise apartment building. It looks like a giant upright can with windows. Your apartment has a window on the south side of the building and you have noticed that the air pressure outside that window varies according to the direction of the wind. That pressure affects airflow into or out of your window. When the wind blows from west to east, the air pressure outside your window is
(A) above atmospheric pressure and air flows out of your window.
(B) above atmospheric pressure and air flows into your window.
(C) below atmospheric pressure and air flows out of your window.
(D) below atmospheric pressure and air flows into your window.
Answer: (C) below atmospheric pressure and air flows out of your window.
Why: The wind is undergoing an inward bend as it flows around your side of the building and so the pressure at the surface of the building is lower than atmospheric pressure. Since air accelerates toward lower pressure, the air in your room flows out the window.

Problem 3:

The frequencies of the modes of vibration in a single violin string are related to one another. If the string's fundamental frequency is 440 Hz (440 cycles-per-second), then the next 3 consecutive frequencies are
(A) 550 Hz, 660 Hz, and 770 Hz.
(B) 880 Hz, 1320 Hz, and 1760 Hz.
(C) 660 Hz, 880 Hz, and 1100 Hz.
(D) 880 Hz, 1760 Hz, and 3520 Hz.
Answer: (B) 880 Hz, 1320 Hz, and 1760 Hz.
Why: The harmonics of a string occur at 2, 3, 4, ... times the fundamental frequency, which is 880 Hz, 1320 Hz, 1760 Hz, ... when the fundamental frequency is 440 Hz.

Problem 4:

Burning fuel in an engine turns the ordered chemical potential energy in gasoline into disordered thermal energy in the hot burned gases. The engine's ability to extract some work from this thermal energy reflects the fact that
(A) there is remaining order in an unequal distribution of temperatures: a hot region and a cold region.
(B) about 25% of thermal energy is actually ordered and can be extracted as work.
(C) about 10% of thermal energy is actually ordered and can be extracted as work.
(D) the second law of thermodynamics is only a statistical law and doesn't always hold true.
Answer: (A) there is remaining order in an unequal distribution of temperatures: a hot region and a cold region.
Why: Even though the car engine is working with only thermal energy, the fact that this thermal energy is unequally distributed allows it to extract some disordered energy as ordered energy while destroying the remaining order in the situation.

Problem 5:

Which of the following will encourage ice to melt into water (by making liquid water more stable relative to solid ice)?
(A) salt, sugar, but not sand.
(B) salt, sugar, and sand.
(C) salt, but not sugar or sand.
(D) salt, sand, but not sugar.
Answer: (A) salt, sugar, but not sand.
Why: Anything that dissolves in water will keep the water molecules in the liquid occupied and will slow the landing of liquid water molecules in the surface of ice. That effect will destabilize ice relative to water and typically will melt some of the ice. Sugar dissolves in water, so it melts ice. Sand doesn't.

Problem 6:

Two jet engines obtain the same amount of thrust by pushing air backward. One engine, a turbojet, pushes a small amount of air backward at very high speed. The other engine, a turbofan, pushes a large amount of air back at a slower speed. Both engines transfer the same amount of backward momentum each second to the air they push on. During this process, the energy they transfer to the air is
(A) greater for the turbofan than for the turbojet.
(B) zero for both jet engines.
(C) greater for the turbojet than for the turbofan.
(D) equal for both jet engines, but more than zero.
Answer: (C) greater for the turbojet than for the turbofan.
Why: Ejecting gases at high speeds gives them lots of kinetic energy. Since kinetic energy is proportional to speed squared, minimizing speed is key to reducing energy transfer to the air.

Problem 7:

When a log is floating on water, much of the log is above the water and is actually surrounded by air. If that surrounding air were to suddenly be replaced by an oil that is less dense than the log, the log would
(A) float at the same height as before the air left.
(B) move upward slightly and float somewhat higher (less deep) in the water.
(C) sink to the bottom of the water.
(D) move downward slightly and float somewhat lower (deeper) in the water.
Answer: (B) move upward slightly and float somewhat higher (less deep) in the water.
Why: The buoyant force on the log is equal to the weight of the fluid or fluids it displaces. If it begins to displace denser fluids all of a sudden, the buoyant force on it will increase. Since the log had been floating at equilibrium before the air was change to oil, the buoyant force had been exactly equal in amount to the log's weight. But now that it is displacing oil, the buoyant force on the log increases and it accelerates upward in response.

Problem 8:

A steady, horizontal stream of water from a hose strikes a wall. As the water hits the wall, its velocity is forward, its acceleration is
(A) forward, and its pressure is increasing.
(B) backward, and its pressure is increasing.
(C) backward, and its pressure is decreasing.
(D) forward, and its pressure is decreasing.
Answer: (B) backward, and its pressure is increasing.
Why: The wall stops the water's forward motion, so the water has to accelerate backward. That backward acceleration is caused by a pressure imbalance, so the pressure in front of the water must be higher than the pressure behind it.

Problem 9:

A piece of driftwood floats on the sea in the passing waves. There is no wind and the sea has no current. When the wood is exactly on the top of a wave crest, the wood's velocity is
(A) zero (the wood is not moving).
(B) horizontal and points in the wave's direction of travel.
(C) vertical.
(D) horizontal and points opposite to the wave's direction of travel.
Answer: (B) horizontal and points in the wave's direction of travel.
Why: Local water travels in a circle as a wave passes. The direction of the circle is such that the water travels forward (in the wave's direction) when it reaches the top of the circle and forms the crest.

Problem 10:

A springboard diver leaps upward from the springboard, rises dramatically to a peak height, and than drops impressively into the water below the board. Neglect any influences of air or the atmosphere. During this trip, the diver experiences
(A) an upward net force that gradually diminishes to zero at the peak height and then becomes a downward net force.
(B) a constant upward net force on the way up and a constant downward net force on the way down.
(C) a downward net force that is proportional to the diver's height above the water.
(D) a constant downward net force.
Answer: (D) a constant downward net force.
Why: The only force acting on the diver is gravity, so the diver is falling.

Problem 11:

You are flying a kite in a steady, horizontal breeze and the kite is maintaining a steady position in the sky. After it passes the kite, the air in the breeze
(A) has separated into two streams, with the top stream deflected upward and the bottom stream deflected downward.
(B) is still moving horizontally.
(C) has been deflected upward somewhat.
(D) has been deflected downward somewhat.
Answer: (D) has been deflected downward somewhat.
Why: The kite is obtaining upward lift from the air, so it must be pushing the air downward (the air pushes back on the kite and provides the lift force). The formerly horizontal wind has been deflected downward.

Problem 12:

A single pipe delivers water to all 4 floors of a house. Compared to water flowing to the basement bathroom, water flowing to the attic bathroom has
(A) less total energy per liter, but the same pressure.
(B) the same total energy per liter, but less pressure.
(C) less total energy per liter and less pressure.
(D) the same total energy per liter and the same pressure.
Answer: (B) the same total energy per liter, but less pressure.
Why: Water in the pipe tends to have the same energy per liter, regardless of where it is in the pipe. But at great height, that water has much of its energy in the form of gravitational potential energy and less in pressure potential energy.

Problem 13:

A stream of water travels essentially horizontally through the air from a nozzle to a flower. While it is traveling freely through the air, this stream of water experiences
(A) a constant forward horizontal force.
(B) a forward horizontal force that diminishes in proportion to the distance from the nozzle.
(C) a forward horizontal force that increases steadily to the midpoint of the flight and then decreases steadily to zero at the flower.
(D) zero forward horizontal force.
Answer: (D) zero forward horizontal force.
Why: The water is coasting forward because of inertia. Nothing is pushing it forward.

Problem 14:

The strings of an acoustic guitar are each attached at one end to a flexible surface so that the surface can move as a string vibrates. This arrangement is crucial to the volume of the guitar because
(A) a rigid surface would keep the string from vibrating.
(B) the surface does work on the vibrating string, adding energy to the string and increasing the string's volume.
(C) the vibrating string does work on the surface and that surface does work on the air to create sound.
(D) a flexible surface prolongs the string vibration time so that each tone lasts longer.
Answer: (C) the vibrating string does work on the surface and that surface does work on the air to create sound.
Why: The string shakes the surface back and forth, pushing and pulling it in the direction that it moves. That shaking involves doing work on the surface and the string transfers energy to it. The surface then does work on the air and sound is created.

Problem 15:

Airports often provide you with moving sidewalks to help you get from one place to another quickly and easily. Suppose you are riding one of these sidewalks up a gentle hill to your departure gate. You are traveling at a constant velocity, forward and slightly upward. Neglect any air resistance. During this time, the sidewalk is pushing you
(A) in the direction you are moving (up the hill) and you are doing work on the sidewalk.
(B) upward and forward, but it is not doing any work on you.
(C) in the direction you are moving (up the hill) and it is doing work on you.
(D) straight up and it is doing work on you.
Answer: (D) straight up and it is doing work on you.
Why: You are being carried up a ramp at constant velocity, so the net force on you is zero. The ramp must be balancing your weight by pushing you straight up with a force equal to your weight. Since you are moving upward (as well as sideways), the sidewalk is doing work on you.

Problem 16:

Steam at 100 °C is much more effective for cooking broccoli than air at 100 °C because steam
(A) undergoes convection much better than does air.
(B) at 100 °C water is much hotter than air at 100 °C.
(C) is an electric conductor and thus a much better conductor of heat than is air.
(D) condenses to water on the broccoli and releases chemical potential energy.
Answer: (D) condenses to water on the broccoli and releases chemical potential energy.
Why: The 100 °C steam has too high a density of molecules to remain purely gaseous when it comes in contact with the colder broccoli. Some of the water molecules in the steam land on and stick to the broccoli and there is a net transfer of water molecules from the gas to the liquid. This transfer, which is called condensation, releases lots of chemical potential energy. The water molecules bind reasonably strongly to one another and release chemical potential energy as thermal energy in the process.

Problem 17:

You have an indoor swimming pool in one room of your 87-room mansion. The ventilation is turned off in that room and the air and water are at the same temperature. You observe that the amount of water in the pool remains precisely constant—water is neither evaporating nor condensing. If you were to examine the water's surface microscopically to see if any water molecules were landing on the water's surface or leaving that surface, you would find that
(A) both landing and leaving are occurring, but that landing takes place more often than leaving.
(B) both landing and leaving are occurring, but at exactly equal rates.
(C) both landing and leaving are occurring, but that leaving takes place more often than landing.
(D) both landing and leaving are absent—no molecules are landing or leaving the water.
Answer: (B) both landing and leaving are occurring, but at exactly equal rates.
Why: Although there is no net movement of water molecules between the liquid and the gas, that doesn't mean that the surface of the water is totally static. Instead, water molecules are landing and leaving all the time, but at equal rates.

Problem 18:

A bicycle automatically steers so as to return you to an unstable equilibrium. That unstable equilibrium occurs when your center of gravity is
(A) at its maximum possible height.
(B) behind the rear wheel.
(C) at its minimum possible height.
(D) in front of the front wheel.
Answer: (A) at its maximum possible height.
Why: An unstable equilibrium requires that the system experience zero net force at the equilibrium point and a potential energy that decreases when the system is displaced from that equilibrium. In the case of the bicycle, the unstable equilibrium occurs when the center of gravity (and therefore the gravitational potential energy) is a high as possible. Any tip from that point will cause the potential energy to decrease.

Problem 19:

To accelerate to the left, an airplane
(A) pivots horizontally so that is nose is to the left of its tail.
(B) tips so that its right wing is lower than its left wing.
(C) tips so that its left wing is lower than its right wing.
(D) pivots horizontally so that its nose is to the right of its tail.
Answer: (C) tips so that its left wing is lower than its right wing.
Why: The plane uses lift force from its wings to accelerate to the left. It does this by tipping its left wing low, so that the lift force from the wings is not purely vertical. Instead, that lift force points upward and to the left. The leftward component of lift causes the plane to accelerate to the left.

Problem 20:

A flutist in the symphony drank too much root beer before the concert and burps noiselessly during his flute solo. The carbon dioxide gas in his stomach emerges from his mouth and fills the flute. Carbon dioxide gas is denser than air. As a result of this change in the flute, the flute's
(A) volume becomes softer than normal, but its pitch stays the same.
(B) pitch becomes lower than normal but its volume stays the same.
(C) volume becomes louder than normal, but its pitch stays the same.
(D) pitch becomes higher than normal, but its volume stays the same.
Answer: (B) pitch becomes lower than normal but its volume stays the same.
Why: The denser carbon dioxide resists accelerations more strongly than air does. As a result, it moves through its vibration cycle more slowly and has a lower frequency (and pitch) than air.

Problem 21:

The upright bar of a football goalpost is basically a spring. If you bend it, it experiences a restoring force that is proportional to its displacement from equilibrium. During a football game, the ball hits the upright bar and bends it 1 foot away from equilibrium. The bar vibrates back and forth with a period of 1 second. If the football had bent the bar 2 feet away from equilibrium, the bar would have vibrated back and forth with a period of
(A) 4 seconds.
(B) 2 seconds.
(C) 0.5 seconds.
(D) 1 second.
Answer: (D) 1 second.
Why: The goalpost is acting as a harmonic oscillator. Like all harmonic oscillators, the period of its vibrational motion is independent of the amplitude of that motion. Whether the post vibrates a little or a lot, the time it takes to complete a vibration cycle is the same.

Problem 22:

A taut (tightly stretched) string can experience
(A) standing waves but not traveling waves.
(B) neither standing waves nor traveling waves.
(C) traveling waves but not standing waves.
(D) both standing waves and traveling waves.
Answer: (D) both standing waves and traveling waves.
Why: The string easily vibrates with standing waves (like in a violin) or traveling waves (like a plucked kite string that sends a ripple up to the kite).

Problem 23:

When a home air conditioner is working properly, its working fluid is
(A) evaporating to a gas inside the home and condensing to a liquid outside the home.
(B) condensing to a liquid both inside and outside the home.
(C) evaporating to a gas both inside and outside the home.
(D) evaporating to a gas outside the home and condensing to a liquid inside the home.
Answer: (A) evaporating to a gas inside the home and condensing to a liquid outside the home.
Why: Evaporation occurs inside the house (albeit in a sealed pipe inside the house) and that evaporation soaks up thermal energy (it takes energy to separate the molecules and let them turn into a gas). Condensation occurs outside the house (again in a sealed pipe) and that condensation releases energy as thermal energy (chemical potential energy is released as thermal energy as the molecules bind together to form a liquid).

Problem 24:

You wander into the kitchen on a dark, moonless night and open the refrigerator door. Sadly, the light bulb in the refrigerator has burned out and the kitchen remains pitch black. Just as you are about to reach for the carton of chocolate milk, your pet squirrel leaps onto your back and you twirl around several times before the squirrel heads off for some other part of the house. You have no idea which way you are facing. Fortunately, the refrigerator door is still open and you can feel the cold on your face as you turn in its direction. The physics explanation for this feeling of cold that you get when you face the refrigerator is that
(A) heat is flowing from the rest of the kitchen into the refrigerator and the pressure of this heat flow causes coldness to accumulate on the side of your body that's facing the refrigerator.
(B) the cold contents of the refrigerator do a much better job of absorbing your thermal radiation than do the warmer contents of the rest of the kitchen.
(C) you are radiating far more heat toward the cold contents of the refrigerator than they are radiating toward you.
(D) the cold contents of the refrigerator radiate coldness toward your skin and lower your skin's temperature.
Answer: (C) you are radiating far more heat toward the cold contents of the refrigerator than they are radiating toward you.
Why: Radiation only transfers heat (not cold) and the cooling effect described here is the result of an unbalanced exchange of radiation. You radiate nicely at the refrigerator, but it doesn't return the favor very well. With so little radiant heat coming toward you, you are experience a net loss of heat through radiation and feel cold.

Problem 25:

The second law of thermodynamics allows you to transfer heat from a colder object to a hotter object, but only if you accompany that transfer by a destruction of
(A) momentum from some other source.
(B) angular momentum from some other source.
(C) energy from some other source.
(D) order from some other source.
Answer: (D) order from some other source.
Why: Ordering the world by moving heat against its natural direction of flow requires that you disorder the world somewhere else. Though this usually involves turning ordered energy into disordered energy, but it can actually be done by turning any sort of ordered system into a less ordered one.

Problem 26:

You have invented a new variation of bowling in which you send the ball down the lane by hitting it with a mallet. The ball is stationary and you pound it forward to give it momentum. You have two mallets with identical masses: one with a head full of sand and one with a head made of highly elastic rubber. The sand mallet doesn't bounce off the ball, while the rubber mallet bounces almost perfectly. If you swing both mallets exactly the same way, you will find that
(A) the two mallets give the ball about the same forward momentum.
(B) the sand mallet will give the ball about twice as much forward momentum as the rubber mallet.
(C) only the rubber mallet gives the ball any forward momentum.
(D) the rubber mallet will give the ball about twice as much forward momentum as the sand mallet.
Answer: (D) the rubber mallet will give the ball about twice as much forward momentum as the sand mallet.
Why: The rubber mallet pushes the ball forward twice: once as it comes to a stop and once as it rebounds backward. In each case, it gives the ball forward momentum in the amount of the mallet's initial forward momentum. The sand mallet gives only its forward momentum and then stops pushing.

Problem 27:

You brought home a toy helium balloon this afternoon and already it has lost some of its helium. It is now hovering motionless at a constant height and is touching neither the ceiling nor the floor. The weight of air that the balloon is displacing is
(A) more than the weight of the balloon.
(B) zero.
(C) less than the weight of the balloon.
(D) exactly equal to the weight of the balloon.
Answer: (D) exactly equal to the weight of the balloon.
Why: The balloon is in equilibrium: zero net force. Thus the buoyant force upward on it must exactly balance the downward weight of the balloon.

Problem 28:

Cars that have trouble with "knocking" may require premium gasoline to run smoothly. The characteristic of premium gasoline that suppresses "knocking" is that premium gasoline is relatively
(A) hard to ignite.
(B) slippery and acts as a better lubricant.
(C) viscous and flows without turbulence.
(D) easy to ignite.
Answer: (A) hard to ignite.
Why: During the compression stroke, the temperature of the fuel and air mixture leaps upward. That's because the engine is doing work on this gas mixture and the gas mixture handles that added energy as thermal energy. If the fuel ignites too easily, it will do so and won't wait for the sparkplug to fire. To prevent or reduce this knocking, some cars use fuel that is hard to ignite: premium or "high-test" gasolines.

Problem 29:

For your art class, you are building a complicated kinetic structure with a single moving part. That moving part will have a stable equilibrium if there is an arrangement in which
(A) the net force (and net torque) is zero and from which any displacement will cause a decrease in total potential energy.
(B) the net force (and net torque) is zero and from which any displacement will cause a rise in total potential energy.
(C) the net force (and net torque) is minimum and from which any displacement will cause a rise in that net force (and net torque).
(D) the net force (and net torque) is maximum and from which any displacement will cause a decrease in that net force (and net torque).
Answer: (B) the net force (and net torque) is zero and from which any displacement will cause a rise in total potential energy.
Why: To be in a stable equilibrium, the system has to have a position at which it experiences zero net force and it has to have its total potential energy rise when it is displaced from that equilbrlium point. Because of the rising potential, it will naturally accelerate back toward the equilibrium point. That's what creates the stable aspect of the equilibrium point.

Problem 30:

It's a windy day and you are standing in an enormous, open plaza. It's hard to keep your hat from blowing away. You find that when you stand just downwind of a huge, rigid abstract sculpture located at the center of the plaza, that you feel only a gentle swirling breeze instead of the overall wind. That's because the statue
(A) deflects the wind so that it misses you.
(B) creates a turbulent wake and you are standing in that wake.
(C) causes the air to experience laminar flow and you are standing in that flow.
(D) is extracting energy from the wind so that it is only barely moving.
Answer: (B) creates a turbulent wake and you are standing in that wake.
Why: As the air moves swiftly around the huge statue, its Reynolds number becomes enormous and inertia dominates its dynamics. The flow becomes turbulent and creates a wake of swirling air behind the statue. That swirling wake travels at about the same speed as the statue: that is it is approximately stationary on average. When you stand in this wake, there isn't much wind... just some swirling.

Problem 31:

You throw a ball at the wall in front of you and the ball bounces directly back at you. While the ball is touching the wall, the horizontal force(s) the ball is experiencing is (are)
(A) the support force from the wall plus a forward force from the ball's momentum while it's coming to a stop.
(B) the support force from the wall plus a force from the ball's momentum that initially points forward, gradually reduces to zero as the ball stops, and then begins to point backward as the ball rebounds.
(C) only the support force from the wall.
(D) the support force from the wall plus a forward force from the ball's momentum throughout the bounce.
Answer: (C) only the support force from the wall.
Why: Momentum isn't a force and does have any intrinsic force associated with it. Instead, forces are associated with transfers of momentum. When the ball hits the wall, it transfers momentum to the wall via a support force and the wall pushes back, action & reaction, with its own support force. That support, the wall pushing back on the ball, is the only horizontal force on the ball.

Problem 32:

An earthquake in the countryside can produce more than one distinct shaking motion at a distant city. These shaking motions are associated with different types of waves and may arrive at the city at slightly different times. Of these types of waves,
(A) 1 is a transverse wave and 2 are longitudinal waves.
(B) 2 are transverse waves and 1 is a longitudinal wave.
(C) 1 is a transverse wave and 1 is a longitudinal wave.
(D) 2 are transverse waves and 2 are longitudinal waves.
Answer: (B) 2 are transverse waves and 1 is a longitudinal wave.
Why: The ground can shake up-and-down or side-to-side, both of which are transverse waves (motion at right angles to the wave's direction of travel). The ground can also shake toward-and-away from the distant city, which is a longitudinal wave (motion in the direction of the wave's travel).

Problem 33:

The pendulum of a clock swings through its stable equilibrium rather than stopping at that equilibrium. To stop abruptly at the equilibrium point, the pendulum would have to get rid of what conserved quantity or quantities?
(A) Energy, but not momentum.
(B) Energy and momentum.
(C) Momentum, but not energy.
(D) Acceleration and velocity.
Answer: (B) Energy and momentum.
Why: The pendulum could not stop immediately at the equilibrium point because that would require destroying or somehow transferring away both of those conserved quantities. The pendulum has horizontal momentum that will keep it moving right through the equilibrium. It also has energy that it cannot have while remaining stationary at its lowest point.

Problem 34:

The atoms in a sugar molecule are bound together, meaning that
(A) acceleration would be required to separate them.
(B) inertia would be required to separate them.
(C) momentum would be required to separate them.
(D) work would be required to separate them.
Answer: (D) work would be required to separate them.
Why: The atoms pulled together as they assembled into the sugar molecule and they did work on something in the process. That energy is now missing from the sugar molecule and would have to be returned in order to separate the atoms once again.

Problem 35:

You've missed a turn on a go-cart track and you're headed for disaster. You can crash into either a brick wall or a haystack. After a rapid review of all the physics you know, you decided to aim for the haystack. Good choice. Although either obstacle would have brought you to a complete stop, the haystack extracted
(A) the same amount of momentum from you that the brick wall would have, but while exerting less force on you.
(B) more momentum from you than the brick wall would have.
(C) less momentum from you than the brick wall would have.
(D) almost no momentum from you and thereby exerted less force on you than the brick wall would have.
Answer: (A) the same amount of momentum from you that the brick wall would have, but while exerting less force on you.
Why: In coming to a stop, you will lose all your momentum. Therefore, the amount of momentum you transfer to the object you hit is always the same. What changes when you hit something soft is the time over which that momentum transfer occurs. The haystack takes away your momentum gradually with a gentle force.

Problem 36:

Mike and Johnny are in trouble for scuffling in the school cafeteria. While Mike admits that he pushed Johnny, who immediately fell over backward, Mike claims that Johnny pushed back and is thus just as guilty. From the perspective of physics,
(A) Johnny pushed back on Mike, but with less force than Mike exerted on him.
(B) Johnny pushed back on Mike, but with more force than Mike exerted on him.
(C) Johnny did push back on Mike, with exactly the same amount of force as Mike exerted on him.
(D) Johnny didn't push back on Mike.
Answer: (C) Johnny did push back on Mike, with exactly the same amount of force as Mike exerted on him.
Why: The force that Johnny exerts on Mike and the force that Mike exerts on Johnny are a Newton's third law pair and must be equal and opposite.

Problem 37:

If your car didn't have shock absorbers, it would bounce up and down wonderfully on its spring suspension whenever you drove onto a curb. If you put more passengers into your car before driving onto that curb, the car would
(A) bounce at the same rate (same period).
(B) bounce faster (shorter period).
(C) bounce more slowly (longer period).
(D) become a taxi and you would have to apply for a taxi license and a cab medallion.
Answer: (C) bounce more slowly (longer period).
Why: The car acts as a harmonic oscillator, with the spring suspension driving the passengers up and down as those passengers' masses resist the accelerations. By increasing the mass of the passengers, you slow the accelerations and length the period of oscillation.

Problem 38:

A long-life bulb operates with its filament at a lower temperature than that of a standard light bulb. As a result of this low operating temperature, the long-life bulb
(A) emits redder light and is less energy efficient than a standard bulb.
(B) emits bluer light and is more energy efficient than a standard bulb.
(C) emits bluer light and is less energy efficient than a standard bulb.
(D) emits redder light and is more energy efficient than a standard bulb.
Answer: (A) emits redder light and is less energy efficient than a standard bulb.
Why: The filament of a bulb emits thermal radiation with a spectrum determined by its temperature. Lowering the temperature shifts the spectrum of light toward the red and infrared. As more of the thermal radiation becomes invisible, the bulb's energy efficiency--the fraction of its electric power it converts to visible light power--decreases.

Problem 39:

Two separate pipes head to a bathroom sink side-by-side. One carries hot water and the other carries cold water. Hot water has more thermal energy per liter than cold water. Water is flowing at the same speed in each pipe and
(A) the pressure of the hot water is greater than that of the cold water.
(B) the pressure of the hot water is less than that of the cold water.
(C) the pressures in the two pipes do not have any relationship to one another.
(D) the pressure of the hot water is the same as that of the cold water.
Answer: (C) the pressures in the two pipes do not have any relationship to one another.
Why: The flows in the two pipes are entirely separate and have no streamlines in common. Therefore, the total energies of the flows can be completely different and there is no relationship between their pressures.

Problem 40:

You are less likely to burn your hand on a pot with a stainless steel handle than on one with an aluminum handle. That's because stainless steel is
(A) a poorer thermal conductor than aluminum.
(B) hotter than aluminum.
(C) less dense than aluminum.
(D) shinier than aluminum.
Answer: (A) a poorer thermal conductor than aluminum.
Why: When you put two pots on the stove, one with a stainless steel handle and one with an aluminum handle, heat flows out through each handle at a rate determined in large part by the thermal conductivity of the metal. Though the processes the establish the exact temperature distributions along each handle are complicated, the aluminum handle is a better conductor of heat and will draw more heat from the pot and send it farther down the handle than the stainless steel handle will.

Problem 41:

The water rising upward in a fountain has an upward velocity
(A) and an acceleration that is upward for the first half of the rise and downward for the second half of the rise.
(B) and an upward acceleration.
(C) and a downward acceleration.
(D) and a zero acceleration.
Answer: (C) and a downward acceleration.
Why: Like any falling object, the water has a weight and is accelerating downward as a result. Other minor forces, such as the water's buoyancy and air resistance complicate the situation, but the water clearly doesn't go up forever and thus the acceleration must be downward.

Problem 42:

Which of the following is not a harmonic oscillator:
(A) A person bouncing gently up and down on a stretched bungee cord.
(B) A car antenna bending back and forth.
(C) A bowling ball bouncing gently up and down on a trampoline.
(D) A yoyo going up and down on its string.
Answer: (D) A yoyo going up and down on its string.
Why: The force acting to pull the yoyo down its string is roughly constant -- the weight of the yoyo -- regardless of how high up the string the yoyo is. Since it doesn't vary with displacement from equilibrium (the bottom of the string), the yoyo can't be a harmonic oscillator.

Problem 43:

A 100-watt light bulb has been operating for hours in a quiet, calm room and consumes 100 watts of electric power. The rate at which heat is flowing out of the bulb is
(A) about 100 watts.
(B) zero watts.
(C) significantly more than 100 watts.
(D) significantly less than 100 watts, but more than zero watts.
Answer: (A) about 100 watts.
Why: The light bulb can't create or destroy energy, nor can it store energy without limit. Therefore, it must be releasing energy as heat at the same rate that energy arrives as electric energy. Since it receives 100 watts of electric power, it must release 100 watts of thermal power or heat.

Problem 44:

Superheated water fails to boil because it is
(A) unable to form the initial bubbles needed for boiling.
(B) too hot to boil at atmospheric pressure.
(C) too viscous to boil at atmospheric pressure.
(D) too dense to boil at atmospheric pressure.
Answer: (A) unable to form the initial bubbles needed for boiling.
Why: While steam bubbles become stable against the crush of atmospheric pressure at water's boiling point, that is no guarantee that those bubbles will form in the first place. If no steam bubbles ever form, then boiling never starts and the water simply evaporates from its surface faster than at lower temperatures. Something has to start the bubbling and that something is usually trapped gases at defects.

Problem 45:

To catch a ball well, you do best to let the ball push your hands backward as it hits. This motion of your hands lets the ball transfer more of its
(A) energy to your hands.
(B) force to your hands.
(C) acceleration to your hands.
(D) momentum to your hands.
Answer: (A) energy to your hands.
Why: If you give when the ball hits your hand, the ball will push your hand and your hand will move in the direction of that push, so that the ball does work on your hand. You therefore take energy out of the ball and let it settle better in your grip. If you don't let the ball do work on you, it may well bounce out of your hand because of its inability to get rid of its energy.

Problem 46:

Your pendulum clock is running slow and you are arriving late to appointments. To speed up the pendulum and shorten its period, you should
(A) lengthen the pendulum.
(B) remove weight uniformly from the pendulum, while keeping its length the same.
(C) shorten the pendulum.
(D) add weight uniformly to the pendulum, while keeping its length the same.
Answer: (C) shorten the pendulum.
Why: The period of a pendulum depends on its length and on the strength of gravity. Shorting the length decreases the period. It's a matter of stiffness: the shorter pendulum has a stiffer restoring force and goes through its motions (specifically, its accelerations) faster.

Problem 47:

A kitchen mixer combines the ingredients best when its blades turn fairly rapidly through the batter you are making. If the blades turn too slowly, the various ingredients don't mix thoroughly, even if you wait a considerable amount of time. The advantage of rapid motion of the mixer blades reflects the need for
(A) viscosity to dominate the flow of batter in the mixer, so that the resulting laminar flow can fully combine the ingredients.
(B) viscosity to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.
(C) inertia to dominate the flow of batter in the mixer, so that the resulting laminar flow can fully combine the ingredients.
(D) inertia to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.
Answer: (D) inertia to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.
Why: The mixer works best when regions of batter that began close to one another are separated to great distances very quickly. That separation requires turbulence and is encouraged by inertial effects in the batter.

Problem 48:

The gas in the neck of a sealed champagne bottle is clear. It is essentially humid air at 100% relative humidity. After the cork pops out of a champagne bottle and flies across the room, this gas turns suddenly into a foggy mist. The gas transformed from clear to foggy because
(A) evaporation began to occur once the bottle was opened.
(B) it did work on the outgoing cork and experienced a drop in temperature. Water droplets condensed as a result of this temperature drop.
(C) tiny particles of cork were left behind in the air due to sliding friction with the bottle's walls.
(D) the cork's violent flight out of the bottle atomized some of the liquid champagne into a mist.
Answer: (B) it did work on the outgoing cork and experienced a drop in temperature. Water droplets condensed as a result of this temperature drop.
Why: Pushing out the cork takes energy and the gas provides that energy. Since the energy comes out of the gas's thermal energy, the gas cools as it does work on the cork. The sudden drop in temperature made the liquid phase of water more stable relative to the gasous phase, so water vapor began condensing into droplets of liquid water.

Problem 49:

Natural convection is used to heat food in a conventional electric oven. That convection is most efficient at conveying heat to the food when the oven's heating element is located
(A) above the food.
(B) below the food.
(C) beside the food.
(D) behind the food.
Answer: (B) below the food.
Why: Natural convection lifts heat upward in buoyant hot air. The heating element warms the air it touches and that hotter air is lifted upward by buoyant forces from the surrounding colder air. Food directly above the element heats rapidly as this hot air arrives and touches it.

Problem 50:

You have 3 metal coins. They are identical except that one is shiny silver, one is black, and one is white. You put all 3 coins in a fire and heat them red hot. If they are all at the same temperature,

(A) the white one will glow most brightly.
(B) the silver one will glow most brightly.
(C) the black one will glow most brightly.
(D) they will all glow equally brightly.
Answer: (C) the black one will glow most brightly.
Why: Black is not only the best absorber of light, it is also the best emitter of thermal radiation.

PART II: SHORT ANSWER QUESTIONS

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

Problem 1:

Although the U.S. Patents Office tries not to issue patents for things that cannot possibly work, they aren't always successful in weeding out the nonsense. That's why they have hired you: to find the impossible claims and send their inventors packing. You're excited about the position and confident in your ability to distinguish fact from fiction.

(A) An inventor comes to you with a small box that's supposed to make batteries obsolete. The inventor claims that the box can produce electricity forever without having to be recharged. Its mechanical components supposedly twist one another in such a way that they keep each other turning indefinitely without any external help and can even generate electricity at the same time. You can be sure that this claim is nonsense because

Answer: The device would not conserve energy.
Why: This device would be producing work endless without any source for that work. Such a situation would violate the conservation of energy.

(B) Another inventor comes in with a small motor-like device that supposedly soaks up thermal energy from the surrounding air and delivers it as electricity to a small power outlet on its side. Your knowledge of the laws of thermodynamics assures you that this claim, too, is nonsense because

Answer: This device would violate the second law of thermodynamics.
Why: This device would be creating ordered energy from disordered energy at a single temperature or, equivalently, reducing the entropy of the universe.

(C) You can't seem to keep the con-artists and wackos from your door today! In walks another hypster who claims to have a heat pump that can transfer heat out of a can of sardines for as long as you like. The sardines just get colder and colder. Once again, you know that this is impossible because

Answer: The sardines cannot get colder than absolute zero.
Why: There is only so much thermal energy in an object such as a can of sardines. Once it's all gone (and you can't even collect the last bits of it), there is no more to be had.

(D) What a day! You are about to head home to tell your friends about the crazy crew you've been talking with when someone comes in with a glass vase that's supposed to automatically reassemble itself if you accidentally break it. You just have to put the broken vase in a box and wait. In a minute or two, the vase will be as good as new. You agree with the inventor that this reconstruction trick doesn't violate any of the laws of motion. However, you can still be sure that it won't work because

Answer: Reassembly of the vase "by accident" is statistically unlikely.
Why: Entropy never decreases and random chance never fixes broken vases.

Problem 2:

According to all the designers in New York, Paris, and Milan, last year's colors are out and you'll have to repaint your room to match the new fall fashions. After replacing your entire wardrobe, you head off to the hardware store to buy matching paint.

(A) You select a particular can of paint and the salesperson opens it to check that it is still good. You notice that one of the paint's constituents has separated out and is floating on the top of the rest of the paint. What characteristic of that constituent is keeping it at the top of the can, rather than at the bottom?

Answer: Its density is less than that of the liquids beneath it.
Why: The floating constituent is held at the top by the buoyant force. Liquids that don't mix (like oil and water) separate with the lower density liquid floating on top of the higher density liquid.

(B) Many of the pigment particles are resting at the bottom of the can. When the can was first manufactured, those tiny solid particles were distributed evenly throughout the paint. However, as months passed they gradually settled to the bottom. What force slowed the descent of those solid pigment particles through the syrupy paint?

Answer: Drag force.
Why: The tiny particles move extremely slowly through the liquid because they experience severe viscous drag force. They aren't buoyant enough to float, but they fall ever so slowly because they have so much surface area for their weights.

(C) To remix the paint, and make it homogeneous again, the salesperson mounts the sealed can in a shaking machine and lets the can jiggle back and forth violently for about a minute. The can's peak speed is never very high. You could make it go faster simply by dropping it from the store roof onto a foam pillow down below, but that wouldn't mix the paint very well. The paint can's velocity simply isn't important to the mixing process. What related physical quantity is essential to the mixing process?

Answer: Acceleration.
Why: Sloshing the can's contents around inside it requires accelerations. At a steady velocity, everything moves because of inertia alone and the constituents of the paint doesn't push on one another any differently than they do when they are sitting still on the shelf. But when the can accelerates violently back and forth, large forces are needed to accelerate the regions of paint and they begin flowing around within the can whenever they fail to get just the right force to keep them moving with the can.

(D) What type of flow does the paint experience during the mixing process and why does that improve the uniformity of the finished paint?

Answer: Turbulent flow quickly separates formerly nearby regions of paint and spreads them throughout the can.
Why: Mixing is best when every small region of paint is torn apart and mixed wildly with every other region of paint. That happens only when there is turbulence. Laminar flow keeps nearby portions of liquid nearby indefinitely and just doesn't mix them up.

Problem 3:

You are an experienced rock-climber and are attempting to scale the face of a sheer granite cliff by yourself. Free climbing doesn't mean being foolish, so you carefully attach yourself to the rock every few feet as you ascend. Each attachment point is small gadget that you insert into a crack or opening and you bind yourself to that gadget with an elastic rope. If you were to fall, you would drop only about twice the distance between yourself and the nearest attachment point. You have been making steady progress all morning and are about half way up the face. You are standing still when suddenly your footing gives way and you begin to fall.

(A) Since the nearest attachment point is 1 meter below you when you start to fall, you descend 2 meters before the rope begins to pull tight. By the time you have dropped to that point, you have acquired lots of downward momentum. Where did that momentum come from and what transferred it to you?

Answer: The momentum came from the earth and it was transferred to you by gravity (or your weight).
Why: Gravity pours downward momentum into you all the time, but you normally get rid of that downward momentum by transferring it into the objects that support you. But when you fall, you aren't able to get rid of the downward momentum and you begin accumulating it.

(B) The rope is rather elastic and can easily stretch to about 7% more than its normal length. If the rope did not stretch, it might easily pull the attachment point out of the rock. Why is the stretchiness of the rope related to the force exerted on the attachment point during a fall?

Answer: When the rope stops your fall, it takes out your downward momentum via an impulse. If the rope doesn't stretch, the impulse involves a big force for a short time and may pull out the attachment.
Why: When the rope pulls taut, you are going to lose your downward momentum (you hope). You can lose it slowly as the right kind of rope stretches or quickly as the wrong kind of rope pulls tight in an instant. Rapid momentum transfers involve enormous forces and that's no fun for anyone.

(C) The rope successfully breaks your fall, but you end up bouncing around and swinging back and forth for a while. What conserved quantity are you having to get rid of in order to come to a stop?

Answer: Energy.
Why: You exchange momentum often with the rock face and the earth, so conservation of momentum is not much of an issue here. But you can't transfer energy to the rock because it won't move and you can't do work on it. Therefore, you keep all of your energy and have to get rid of it as thermal energy. You bounce around until you've done that.

(D) When you finally come to a stop, hanging there on the somewhat-stretched rope, what force (amount and direction) is the rope exerting on you? (Assume that you are not touching the rock face at all).

Answer: An upward force equal in amount to your weight.
Why: You are remaining motionless, so you are not accelerating and the net force on you must be zero. Since you have two forces acting on you, your weight downward and the rope force upward, they must balance perfectly.

Problem 4:

You love spy movies and the latest Jaymes Bahnd movie is playing at the local theatre. You and your significant other pick up your extra large popcorn and wheel it down the aisle to your seats. The lights dim and you're soon immersed in the world of Jaymes Bahnd, secret agent number 006.95 plus tax. Naturally, Mr. Bahnd has lots of gadgets that do neat things, but some of them violate the laws of physics. Among the bloopers that you notice during this otherwise fabulous show are the following.

(A) To break into a private museum and recover the stolen medieval manuscript, Jaymes must enter the building and defeat all of its security systems. Jaymes decides to break into the building from its penthouse, 100 feet above the ground. He takes a small, lightweight pen from his pocket and clicks the button. A plume of rocket exhaust emerges from the other end of the pen and this midget rocket lifts Jaymes 100 feet in the air so that he lands easily in the penthouse garden. Why is the small weight of this pen incompatible with it lifting Jaymes off the ground?

Answer: A rocket needs stored mass to push against. There isn't enough mass in the lightweight pen for this stunt to work.
Why: A rocket obtains its thrust by throwing its contents backwards. The ejected contents push back on the rocket, action and reaction. With virtually no mass in Bahnd's tiny rocket, it cannot prove the large upward force needed to lift Bahnd off the ground and high into the air.

(B) Bahnd plans to enter the building through its ventilation ducts. They will open when the temperature inside the penthouse apartment drops below 10 °C. Bahnd drills a small hole in the wall and lowers a small air conditioning device into the apartment on the end of its power cord. The unit consists only of a small box and its power cord. Jaymes plugs the cord into an outlet in the garden and the temperature inside the apartment begins to go down. Why can't you make such an air conditioner—one that uses only its connection to the power company to lower the temperature of the room in which it's placed?

Answer: That device would reduce the entropy of the world (or would convert disordered energy into ordered energy).
Why: Thermal energy at a single temperature cannot be destroyed or turned into ordered energy. Regardless of what is going on in the device's power cord, the device would have to getting rid of disorder from the room by some means other than exporting it. That's just not possible. It either violates the conservation of energy or the second law of thermodynamics.

(C) Once inside the building, Bahnd moves swiftly to the museum. He must slip past several sensors that see thermal radiation and can tell when a warmer body is moving through the halls. Bahnd slips on a black velvet robe and becomes impossible to see with your eyes in the darkened hallways. He goes right by the thermal sensors without them noticing. Sadly, the black velvet would not really help Jaymes hide from the thermal radiation sensors. Why not?

Answer: Black is the best emitter of thermal radiation and the sensors would see Bahnd's warmth right away.
Why: Contrary to intuition, black objects glow brightly with their thermal radiation. In Bahnd's case, that would be in the infrared. However, a sensitive infrared sensor will see Bahnd even better when he's wrapped in black.

(D) To break the glass cabinet that contains the manuscript, Jaymes takes out a tiny tuning fork and hammer. He smacks the tuning fork with the hammer and holds the tuning fork to the microphone of the museum's public address system. The high-pitched tone travels briefly through the museum and all of the glass objects in that museum shatter. Why is it extraordinarily unlikely that even one glass object in the museum would shatter, let alone all of them?

Answer: Glass will only break when it is shaken violently by sound at its own resonant frequency. Each piece of glass has its own frequency and Bahnd's tuning fork almost certainly won't match them.
Why: To break glass with sound, you must expose it to intense sound at just the right pitch. The glass has to store up the energy over many cycles of the sound and any mismatch in pitch will spoil the process. Actually, most pieces of glass have such poor resonances that they can't be broken by sound and resonant energy transfer at all.

Problem 5:

Nothing says romance like a candlelight dinner. You have just taken that gourmet tuna-noodle casserole out of the oven and are ready to serve it to your sweetie, but first you must light the candles.

(A) You strike a match by rubbing it across the side of the matchbox. How does this action cause the match to ignite?

Answer: Sliding friction provides thermal energy that acts as the activation energy to initiate the chemical reactions of combustion.
Why: Although molecules in the match head can recombine in new ways to release chemical potential energy, they need some initial energy to get this process started. That activation energy is provided by work done against sliding friction and the resulting thermal energy.

(B) The candle wax begins to burn. Which molecules have stronger chemical bonds: (1) the wax and oxygen molecules before burning or (2) the water and carbon dioxide molecules that are formed as a result of burning?

Answer: The water and carbon dioxide have stronger chemical bonds.
Why: Energy is released when chemical bonds form. The stronger those bonds are, the more energy is released. By rearranging from weakly bound molecules to more strongly bound molecules, wax and oxygen release chemical potential energy and burn.

(C) The candles emit a pleasant reddish-orange glow. The temperature in the candle flame is less than that of a normal light bulb's filament. How can you tell?

Answer: The candle flame is redder (and dimmer) than a bulb's filament.
Why: The candle and the filament are both emitting black body spectra. The cooler candle flame emits a black body spectrum that is farther toward the infrared and thus appears redder in color. The hotter filament emits more green and blue light and appears more yellow-white.

(D) Liquid wax doesn't burn but gaseous wax does. In terms of individual wax molecules at the surface of the liquid wax, how does raising the temperature of the wax increase the density of gaseous wax nearby?

Answer: At higher temperature, wax molecules on the liquid surface are more likely to "take off" from the surface and enter the gas phase. The density of gaseous wax molecules increases.
Why: Wax molecules are constantly leaving and landing on the surface of the liquid wax. The landing rate is determined by the density of wax molecules in the gas phase, but the leaving rate depends on the wax's temperature. By raising that temperature, the leaving rate can be increased and the balance of phases shifts toward the gaseous phase. The density of gas-phase wax molecules increases.

Problem 6:

The movie you were working on at the time of the midterm exam was a tremendous box-office success and you're working on the sequel! Once again, your heroine is going to rescue the hero from an unjust hanging. It's deja-vu all over again, but this time the screenwriters are going to be more careful to get the wording of the script clear. As this scene begins, the hero is standing still on a trapdoor high above the ground and there is what appears to be a rope around his neck. Of course, the heroine has again replaced the rope with an elastic bungee cord.

(A) Consider the exact moment when the trapdoor opens and there is suddenly nothing under the hero's feet. The bungee cord is at its equilibrium length and is not pulling on anything yet. At that exact moment, the instant in time when the trapdoor has vanished, the hero is experiencing what (1) net force, (2) velocity, and (3) acceleration? (report specific values for these three quantities)

Answer: The net force is his weight, his velocity is zero, and his acceleration is 9.8 meters/second2.
Why: He has just entered free fall. He suddenly has only his weight acting on him and is now accelerating downward at the full acceleration of gravity. However, he hasn't had time to acquire any velocity so it remains at zero.

(B) Because it's a bungee cord rather than a rope, the cord tenses gradually as the hero descends for the first time. At what point in this first descent does the hero reach his maximum downward velocity?

Answer: At his equilibrium height (on the bungee)
Why: The equilibrium height, when the upward force from the bungee cord exactly balances his weight, is the point at which his acceleration reverses directions as he falls. While he is above that point and dropping, he is accelerating downward and picking up speed. While he is below that point and dropping, he is accelerating upward and losing speed. He reaches is peak speed just as he passes through equilibrium.

(C) The heroine gallops up on a white horse, passing right under the hero as he descends for the first time. He slows to a stop just as she reaches him and she cuts the cord from his neck. At the moment he stopped descending (and she cut him free), was the hero accelerating vertically and, if so, which way?

Answer: He was accelerating upward.
Why: He is below the equilibrium point, so the net force he is experiencing is upward. He is accelerating upward even though he has zero velocity.

(D) The elastic cord snaps upward violently after being cut and it knocks the evil sheriff off the platform (the judge from the first movie is still in the hospital). Clearly, the cord has enormous kinetic energy at the end of the scene. What form was that energy in at the beginning of the scene—when the hero was standing on the closed trapdoor?

Answer: The energy was gravitational potential energy (in the hero).
Why: It was the hero's gravitational potential energy that became kinetic as he fell and that then stretched the bungee cord. The snapping bungee cord releases this energy.