Physics 105 - How Things Work - Fall, 2001

Final Examination

Given Saturday, December 15, from 9:00 AM to 12:00 PM

PART I: MULTIPLE CHOICE QUESTIONS
Please murk 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:

When a car "knocks," that is because the fuel and air mixture in one of its cylinders is igniting before the spark plug fires. This early ignition occurs because compressing the mixture causes its
(A) temperature to increase, but not its pressure.
(B) density to increase, but not its temperature or pressure.
(C) temperature and pressure to increase.
(D) pressure to increase, but not its temperature.

Problem 2:

Viscous drag is associated with viscose forces within the air, while pressure drag is associated with unbalanced pressures. When a dust particle in the air is experiencing only gravity, it descends very slowly through the air around it. Because of its tiny size and slow motion, the dust particle experiences
(A) turbulent flow and only viscous drag.
(B) turbulent flow and only pressure drag.
(C) laminar flow and only viscous drag.
(D) laminar flow and only pressure drag.

Problem 3:

When you bounce up and down on a springboard, without leaving the board's surface, you are a harmonic oscillator. But as soon as you fly up off the surface, you stop being a harmonic oscillator because
(A) you stop having any mass.
(B) the restoring force on you stops being proportional to your displacement from equilibrium.
(C) harmonic oscillators must have small amplitudes of motion.
(D) you stop having any weight.

Problem 4:

Which action causes the greatest increase in entropy-the measure of disorder?
(A) Adding 1 joule of thermal energy to a cold object.
(B) Adding 1 joule of work to a cold object.
(C) Adding 1 joule of thermal energy to a hot object.
(D) Adding 1 joule of work to a hot object.

Problem 5:

During the power stroke in one cylinder of a car's engine, the burned fuel and air gases push the piston out of the cylinder. In accordance with Newton's third law, the piston pushes back on the burned gases. Overall,
(A) the burned gases do work on the piston and they experience a drop in temperature.
(B) the burned gases do work on the piston and they experience a rise in temperature.
(C) the piston does work on the burned gases and they experience a drop in temperature.
(D) the piston does work on the burned gases and they experience a rise in temperature.

Problem 6:

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) inertia 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 laminar flow can fully combine the ingredients.
(C) inertia to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.
(D) viscosity to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.

Problem 7:

The bottom of a large hot-air balloon is open, yet the hot air doesn't flow out. That is because
(A) the density of air inside the open bottom is the same as the density of air outside the open bottom.
(B) the pressure of air inside the open bottom is the same as the pressure of air outside the open bottom.
(C) the mass of air inside the open bottom is the same as the mass of air outside the open bottom.
(D) the weight of air inside the open bottom is the same as the weight of air outside the open bottom.

Problem 8:

Your company has invented a new rubber ball that bounces perfectly. When you drop it on a hard surface, it rebounds to its original height and continues to bounce that way indefinitely. This phenomenal bounciness indicates that the ball
(A) retains all of its energy and its momentum during each bounce.
(B) retains all of its energy, but not its momentum during each bounce.
(C) retains all of its momentum, but not its energy during each bounce.
(D) converts its energy into momentum and back again during each bounce.

Problem 9:

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.

Problem 10:

You travel quickly around the loop-the-loop of a roller coaster and find that you can't even tell when you are upside-down without looking. At the very top of the loop, you are
(A) accelerating upward.
(B) not accelerating. You are just coasting forward horizontally.
(C) accelerating downward less fast than the acceleration due to gravity.
(D) accelerating downward faster than the acceleration due to gravity.

Problem 11:

A 1-inch (2.5 cm) diameter garden hose will carry far more water than a 1/2-inch (1.25 cm) diameter garden hose, everything else being equal. This phenomenon is explained by the fact that the wider hose
(A) has less inside surface area and therefore exerts less static friction force on the passing water.
(B) has a higher Reynolds number and therefore introduces less turbulence into the flowing stream, so that it can travel faster.
(C) has less inside surface area and therefore exerts less sliding friction force on the passing water.
(D) has more room for the water to pass through and places much of that passing water farther from the walls of the hose, so that it can travel faster.

Problem 12:

When hurricane winds blow horizontally past the peaked or domed roof of a house, they tend to lift that roof upward and pull it off the house. This upward force develops because the airflow bends downward (toward the roof) as it flows over the top of the roof. This downward bend (toward the roof's upper surface) indicates that the air pressure at the roof's upper surface is
(A) equal to normal atmospheric pressure and that there is a strong, unbalanced viscous drag force on the roof that is pushing the roof upward.
(B) lower than normal atmospheric pressure and that there is an unbalanced pressure force on the roof that is pushing the roof upward.
(C) higher than normal atmospheric pressure and that there is an unbalanced pressure force on the roof that is pushing the roof upward.
(D) equal to normal atmospheric pressure and that there is a strong, unbalanced pressure drag force on the roof that is pushing the roof upward.

Problem 13:

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 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.
(B) the support force from the wall plus a forward force from the ball's momentum throughout the bounce.
(C) the support force from the wall plus a forward force from the ball's momentum while it's coming to a stop.
(D) only the support force from the wall.

Problem 14:

You can make water boil at room temperature by
(A) adding enough salt to lower its boiling temperature to room temperature.
(B) blowing air bubbles through it.
(C) putting the water in a very low pressure environment.
(D) adding enough sugar to lower its boiling temperature to room temperature.

Problem 15:

A helium-filled balloon weighs only about 1/7th as much as the air it displaces. If you replace the helium gas in the balloon with hydrogen gas (which is half as dense as helium gas), the upward buoyant force on the balloon would
(A) increase and the net force on the balloon would increase slightly in the upward direction.
(B) increase and the net force on the balloon would roughly double in the upward direction.
(C) stay the same and the net force on the balloon would increase slightly in the upward direction.
(D) decrease and the net force on the balloon would roughly double in the upward direction.

Problem 16:

The houseware store you have just entered has a uniform temperature throughout. You pick up a heavy copper pot and place it on a soft, fabric mat. As a result of this contact, heat
(A) flows from the more massive object to the less massive object, whichever is which.
(B) flows from the fabric mat to the copper pot.
(C) flows from the copper pot to the fabric mat.
(D) does not flow at all.

Problem 17:

A friend suggests that you invest in a new invention that apparently absorbs heat from the room and converts it into electricity. It supposedly sits in the middle of the room, gradually cooling the room air while providing a steady and endless supply of electric power. You wisely choose not to invest because in order to work as described, this device would have to do something impossible-it would have to
(A) violate the conservation of energy.
(B) lower the total entropy of its environment.
(C) turn stored energy into power.
(D) turn work into heat, or more precisely, into thermal energy.

Problem 18:

You are choosing the filament for a light bulb and want it to emit visible light as efficiently as possible when it becomes very hot. You should make that filament
(A) black
(B) white
(C) shiny like a mirror
(D) gray

Problem 19:

A turbofan engine includes a giant ducted fan-a fan that sits inside a duct. The purpose of this huge metal duct is to slow the passing air down so that the fan doesn't have to work with air moving by at the full speed of the airplane. Instead of dealing with air moving at 600 mph, the air passing through the duct may be traveling only 200 mph. The duct slows the passing air primarily by
(A) exposing that air to sliding friction with the surfaces of the duct.
(B) exposing that air to viscous drag with the surfaces of the duct.
(C) sending the air through a reversed nozzle, so that it exchanges its kinetic energy for pressure potential energy.
(D) passing that air through blades that introduce turbulence into the airstream.

Problem 20:

Sound waves in air and surface waves on water differ in the following important respect:

(A) sound waves in air have frequencies, while surface waves on water do not have frequencies.
(B) the speed of sound waves in air doesn't depend on frequency, while the speed of surface waves on water does depend on frequency.
(C) sound waves in air do not have wavelengths, while surface waves on water do have wavelengths.
(D) sound waves in air are standing waves, while surface waves on water are traveling waves.

Problem 21:

Two children are swinging on identical swings. One child is twice as heavy as the other. The period of the lighter child's swing is
(A) about 3/4 the period of the heavier child's swing.
(B) about twice the period of the heavier child's swing.
(C) about half the period of the heavier child's swing.
(D) about the same as the period of the heavier child's swing.

Problem 22:

You are outside the shuttle on a routine satellite repair mission. You are moving at a constant speed at a constant distance of two earth radii above the surface of the earth. Relative to your weight on the surface of the earth, what is the magnitude of the net force on you? Neglect the effects of the satellite and the shuttle.
(A) zero
(B) 1/2
(C) 1/4
(D) 1/9

Problem 23:

Wrapping a hot potato in aluminum foil will help keep the potato warm because the shiny aluminum foil
(A) is a very poor emitter of thermal radiation.
(B) is so thin that it doesn't have enough mass to cool the potato significantly.
(C) is transparent to infrared radiation and allows radiant heat from the room to enter the potato and keep it warm.
(D) is a poor conductor of heat, so the surface temperature of the foil is much less than the surface temperature of the potato.

Problem 24:

You're operating a propane gas grill from a fuel tank that's located below the grill. This tank is half filled with liquid propane. As the grill consumes gaseous propane, the tank's temperature drops below room temperature. This refrigerating effect occurs because
(A) heat naturally flows from a cooler object to a hotter object.
(B) heat is needed to initiate and sustain combustion in the grill.
(C) thermal energy is being used to convert liquid propane into gaseous propane in the tank.
(D) heat naturally rises from the tank to the grill above it.

Problem 25:

The glass envelope of an ordinary incandescent light bulb surrounds a
(A) volume of chemically inert gas, which significantly increases the bulb's energy efficiency but slightly shortens the filament's life expectancy.
(B) region of almost perfect vacuum, which significantly increases the bulb's energy efficiency but slightly shortens the filament's life expectancy.
(C) region of almost perfect vacuum, which significantly increases the filament's life expectancy but slightly reduces the bulb's energy efficiency.
(D) volume of chemically inert gas, which significantly increases the filament's life expectancy but slightly reduces the bulb's energy efficiency.

Problem 26:

Some satellites orbit the earth at such large distances that they are never in the earth's shadow. These satellites are constantly exposed to full sunlight. With no air around them to take away heat, why don't these satellites continue to grow hotter forever?
(A) They use air conditioners (which NASA calls "thermal stabilization units") to eliminate the excess thermal energy as rapidly as it arrives.
(B) They have solar panels that convert the sun's thermal radiation completely into electricity and avoid any need to eliminate heat.
(C) Because they are isolated from the sun by empty space, the sun's heat can't reach them and they don't experience any changes in temperature.
(D) Their temperatures rise until they are able to radiate heat away into space as fast as it arrives from the sun.

Problem 27:

Two equal-sized cars are driving side-by-side down the road. The blue car is a sleek aerodynamic marvel and leaves only a tiny turbulent wake behind it as it moves. The red car is a boxy aerodynamic catastrophe that scrambles the air furiously and leaves a huge swirling wake behind it. As it moves forward, the red car does
(A) the same amount of work on the air it encounters as the blue car does, but transfers more forward momentum to that air than the blue car does.
(B) the same amount of work on the air it encounters as the blue car does, but transfers more energy to that air than the blue car does.
(C) more work on the air it encounters than the blue car does, but transfers the same amount of forward momentum to that air as the blue car does.
(D) more work on the air it encounters than the blue car does and transfers more forward momentum to that air than the blue car does.

Problem 28:

It's a hot summer day and your apartment doesn't have air conditioning. Your roommate decides to cool the room by opening the refrigerator door. A minute passes and then the refrigerator's compressor starts to whirr into action. It continues whirring continuously after that. As a result of opening the refrigerator door, the temperature of the room air
(A) first deceases for about a minute and then begins to rise steadily thereafter.
(B) decreases steadily from the moment the door opens.
(C) remains constant despite the fact that the door is open.
(D) drops quickly at first and then decreases steadily at a smaller rate thereafter.

Problem 29:

Independent, gaseous water molecules can leave the surface of hot water at 212 °F (100 °C)
(A) and the surface of room temperature water at 68 °F (20 °C) but not the surface of ice at 0 °F (-18 °C).
(B) and the surfaces of room temperature water at 68 °F (20 °C) and ice at 0° F (-18 °C).
(C) but not the surfaces of room temperature water at 68 °F (20 °C) or ice at 0° F (-18 °C).
(D) and the surface of ice at 0 °F (-18 °C) but not the surface of room temperature water at 68 °F (20 °C).

Problem 30:

A baseball that is hit well by a bat travels at speeds in excess of 100 mph (160 kilometers per hour) and the boundary layer of air close to its surface is turbulent. Because of this turbulent boundary layer, extra energy flows into the air near the ball's surface and this surface layer has less trouble working its way from the sides of the ball toward the back of the ball. The ball flies better as a result. The reason why the boundary level's flow from the ball's sides to its back is difficult is that
(A) the pressure is rising during this passage (from the sides toward the back) and the air in the flow is actually speeding up.
(B) the pressure is rising during this passage (from the sides toward the back) and the air in the flow is actually slowing down.
(C) the pressure is falling during this passage (from the sides toward the back) and the air in the flow is actually slowing down.
(D) the pressure is falling during this passage (from the sides toward the back) and the air in the flow is actually speeding up.

Problem 31:

You are enjoying an elegant candlelit dinner for two but the waiter has been a little careless with the ice. Your glass of ice water contains 25% water and 75% ice, while your friend's glass contains 75% water and 25% ice. The temperature of your glass of ice water
(A) is higher than that of your friend.
(B) is lower than that of your friend.
(C) is the same as that of your friend.
(D) depends on when it was filled. The glass that was filled first will now be warmer than the glass that was filled second.

Problem 32:

As a prank, you fill a friend's saxophone with helium gas. When she plays the instrument a few seconds later, its pitch
(A) the same as normal, but its volume is abnormally soft.
(B) is higher than normal.
(C) is lower than normal.
(D) the same as normal, but its volume is abnormally loud.

Problem 33:

If you add salt to an insulated container of ice water (a roughly equal mixture of ice and liquid water), the temperature of the mixture will
(A) decrease and some liquid water will convert into ice.
(B) decrease and some ice will convert into liquid water.
(C) increase and some ice will convert into liquid water.
(D) increase and some liquid water will convert into ice.

Problem 34:

An airplane maintains level flight while consuming the least amount of fuel when its wings
(A) separate the airstreams evenly and symmetrically so that both the upper and lower airstreams experience equal changes in speed and pressure and thus satisfy Bernoulli's equation.
(B) change the horizontal momentum of the airstream as much as possible.
(C) allow the airstreams to pass by essentially undeflected and without significant turbulence.
(D) deflect the passing airstream downward without introducing any significant turbulence into that airstream.

Problem 35:

The higher you stand up in a canoe, the higher the overall center of gravity rises. Eventually, the canoe becomes unstable and tips over at the slightest disturbance. That instability develops as soon as
(A) the overall center of gravity no longer rises during a tip and instead descends during a tip.
(B) the buoyant force exceeds your weight.
(C) the canoe's gravitational potential energy exceeds its kinetic energy.
(D) the net force on the canoe stops rising and instead begins to decrease.

Problem 36:

You are riding a skateboard down a gradual incline. In order to waste as little energy as possible while still maintaining control over your direction of motion, the contact between the sidewalk and the wheels should experience
(A) no friction.
(B) only sliding friction.
(C) only static friction.
(D) both static and sliding friction.

Problem 37:

The giant waves or tsunamis created by earthquakes have extremely long wavelengths. They travel
(A) extremely slowly and involve water to great depth in the ocean.
(B) extremely quickly because they involve only the water near the ocean's surface.
(C) extremely quickly and involve water to great depth in the ocean.
(D) extremely slowly because they involve only the water near the ocean's surface.

Problem 38:

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) you are radiating far more heat toward the cold contents of the refrigerator than they are radiating toward you.
(B) the cold contents of the refrigerator radiate coldness toward your skin and lower your skin's temperature.
(C) 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.
(D) 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.

Problem 39:

Your friend's enormous new house has bathrooms with showers on all four floors, including the basement. The spray from the shower in the basement is significantly harder and faster than the spray from the third-floor shower. This difference is explained by the fact that water leaving the third-floor shower has
(A) less of its total energy in the form of gravitational potential energy and more in the form of kinetic energy.
(B) less total energy and can't produce as much kinetic energy.
(C) more of its total energy in the form of gravitational potential energy and less in the form of kinetic energy.
(D) more total energy but its weight slows it down and prevents it from spraying hard.

Problem 40:

The spacecraft used in most science fiction movies never seem to require refueling. Presumably, they have great energy reserves located on-board somewhere. But rockets can't operate on energy alone because
(A) they propel themselves forward by pushing stored mass backward as exhaust.
(B) rockets are heat engines and they need both a hot source of energy and cold region into which they can deposit that energy.
(C) energy itself has momentum in the downward direction and cannot contribute to a rocket's upward motion.
(D) energy doesn't weigh anything and rockets need weight to propel themselves forward.

Problem 41:

You are swimming at the beach. You swim out past the breaking surf so that you can float among the waves. Each time a wave crest passes, you travel
(A) vertically -- directly up and then directly down.
(B) horizontally toward shore for a distance that's proportional to the slope of the wave crest.
(C) in a circle-up, toward shore, down, and away from shore.
(D) horizontally toward shore for a distance equal to one wavelength of the passing wave.

Problem 42:

You're flying a kite on a long kite string. You pluck that string and a wave travels up the string toward the kite. A few minutes later, the wind is blowing much harder and the string is tauter. You again pluck the string and another wave forms. This wave travels
(A) at the same speed as the first wave, even if the string is wet.
(B) slower than the first wave.
(C) at the same speed as the first wave, unless the string is wet.
(D) faster than the first wave.

Problem 43:

You have an inclined plane and two balls that are identical in every respect EXCEPT that one ball (ball A) is frictionless while the other (ball B) experiences significant friction. You release both balls from the top of the inclined plane at exactly the same time. Ball A slides down the plane and ball B rolls down the plane. Which statement is FALSE:
(A) Ball A has more total kinetic energy when it gets to the bottom of the plane than does ball B when it gets to the bottom of the plane.
(B) Ball A has more linear momentum when it gets to the bottom of the plane than does ball B when it gets to the bottom of the plane.
(C) Ball A gets to the bottom of the plane before ball B.
(D) Ball A has a higher speed when it gets to the bottom of the plane than does ball B when it gets to the bottom of the plane.

Problem 44:

A heat engine produces useful work as it transfers heat from a hot region to a cold region. If the cold region's temperature increases and the hot region's temperature stays constant, the heat engine will
(A) need to transfer more heat to produce the same amount of useful work as before.
(B) become more efficient than before at converting heat into useful work.
(C) have the same efficiency as before at converting heat into useful work.
(D) be able to produce more useful work while transferring the same amount of heat as before.

Problem 45:

Which of the following is not a harmonic oscillator?
(A) a superball bouncing on a ceramic tile floor.
(B) a person bouncing gently up and down at the end of a bungee cord, near the end of the ride.
(C) a vertical flagpole swaying back and forth.
(D) a tuning fork with its two tines vibrating rhythmically in opposite directions.

Problem 46:

A sealed propane cylinder contains both liquid and gaseous propane (and no air). You put the cylinder outside on a hot day and its temperature increases. As a result of this rise in temperature, the fraction of propane molecules that are in gaseous form
(A) increases, but the pressure in the cylinder remains constant.
(B) and the pressure remain constant, but the thermal energy in the cylinder increases.
(C) increases and so does the pressure in the cylinder.
(D) remains constant, but the pressure in the cylinder increases.

Problem 47:

A candle won't burn properly onboard the orbiting Space Shuttle because, in the freely falling Shuttle, there are no pressure gradients and no buoyant forces. Without buoyant forces,
(A) there is such strong convection that the flame actually blows itself out.
(B) the candle's flame falls onto the top surface of the candle wax and goes out.
(C) the candle's flame floats away from the wick and the candle spontaneously goes out.
(D) there is no natural convection in the flame to remove burned gases and bring in fresh oxygen.

Problem 48:

You see a television advertisement for a product that can be inserted into a light fixture to reduce the incandescent bulb's power consumption. With this device installed, a 100-watt bulb's filament receives only 50-watts of power on average. As a result, the bulb will cost less to operate, however it will produce
(A) somewhat more than half its normal illumination and the light it emits will be redder than normal.
(B) somewhat less than half its normal illumination and the light it emits will be redder than normal.
(C) half its normal illumination and the light it emits will be redder than normal.
(D) half its normal illumination and the light it emits will be bluer than normal.

Problem 49:

An astronaut is orbiting the earth in a circular path at an altitude of about 187 miles (300 kilometers). Just before takeoff, her weight was measured to be 140 pounds. As she orbits, her weight is
(A) zero, her velocity is horizontal, and her acceleration is horizontal.
(B) slightly less than 140 pounds, her velocity is horizontal, and her acceleration is downward.
(C) much less than 140 pounds, her velocity is zero, and her acceleration is downward.
(D) zero, her velocity is zero, and her acceleration is zero.

Problem 50:

You are delivering pizza to pay your overdue library book fines. Unfortunately, a poorly timed order for 3 double-cheese and anchovies pizzas has trapped you aboard the Space Shuttle during liftoff. Everyone on board is so kind that they agree to let you have a slice yourself once you are all in orbit. However, they require that you figure out which box contains the remaining pizza without opening any of the boxes. You place one box after the next on a scale to weigh it, but each time the scale reads zero. To solve the puzzle and find the pizza, you
(A) you drop each box from a set height in the cabin and open the box that hits the cabin floor in the shortest amount of time.
(B) push each box against the scale with your hands and open the box that reads the highest weight on the scale.
(C) shake each box and open the box that is hardest to shake.
(D) you release each box from the front of the cabin and open the box that hits the rear of the cabin in the shortest amount of time.

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:

For some reason you find yourself sitting in a heavy metal bucket. Together, you and the bucket weigh one thousand Newtons. There is a rope tied to the bucket that loops over a pulley attached to the ceiling. By pulling on the free end of the rope you are able to lift yourself off of the ground. You pull yourself up at a constant rate.

(A) What is the tension in the rope?

(B) What is the net force on you?

(C) How much does your potential energy increase when you lift yourself by one meter?

(D) How much work must you do to get one meter above the ground?

Problem 2:

You slide two shallow ramps together to form a "V" shape and then allow a ball to roll back and forth between the ramps. Throughout this problem, neglect both the ball's rolling motion and friction.

(A) Is the moving ball a harmonic oscillator? Why or why not?

(B) When the ball reaches its highest point on the right-hand ramp, what is its velocity?

(C) When the ball reaches its highest point on the right-hand ramp, what is its acceleration?

(D) Use the conservation of energy to explain why the ball reaches its highest speed at the bottom of the "V".

Problem 3:

The recession has been hard on your job prospects and you've had to settle for a fallback career as a one of the world's foremost pianists. Although you are paid a bundle and have adoring fans throwing themselves at your feet, no one is willing to tune your piano for you. It all dates back to the time you dunked an inferior piano tuner into the fountain in front of you piazza in Florence, but that's another story. You've taken a correspondence course and now do the tuning yourself. You just arrived in Melbourne Australia and your custom-built piano suffered some trauma during its flight from Zurich Switzerland. With a concert coming up in only 4 hours, you are working feverishly to perfect the tune of the piano's strings.

(A) One of the strings is vibrating too slowly and its pitch is too low. You can't change the string's length or mass, so how can you raise the pitch of this string?

(B) Another string broke during shipment and you can't find an identical replacement. You must use a string that is slightly thicker and heavier than the original string. If you install this replacement string and adjust everything as though it were the original string, how would the replacement string sound?

(C) The piano's soundboard has come loose from the rest of the piano, so the vibrating strings aren't able to make the soundboard vibrate properly. As a result, the piano can't produce loud music. Why can't the strings themselves produce loud sound?

(D) You reattached the soundboard, replace and tune all the strings, and prepare to begin your performance. You walk on stage, seat yourself at your piano, and play a long and loud piece that thrills the audience. You find yourself exhausted, as though you had transferred a huge amount of energy to the piano while playing the piece. In fact, you did transfer a huge amount of energy to the piano. Use physics and the concept of work to show that this energy flowed into the piano while you played its keys.

Problem 4:

The serviceperson is fixing your home air conditioner because it doesn't have the correct amount of working fluid in it. Let's take a look at why the total quantity of working fluid in the system matters.

(A) When the air conditioner was working properly, low-pressure liquid working fluid converted to low-pressure gaseous working fluid in its evaporator. Heat flowed into the working fluid as this conversion took place. Why did the low-pressure environment encourage the working fluid to shift from a liquid to a gas? (Hint: describe the movement of working fluid molecules at the surface between the liquid and the gas).

(B) Your air conditioner contained far too much working fluid. Because of that mistake, the density of working fluid molecules in the gas phase was very high, even in the evaporator. Why did that problem discourage the evaporation of liquid working fluid into gaseous working fluid in the evaporator?

(C) When the air conditioner is again working properly, high-pressure gaseous working fluid converts to high-pressure liquid working fluid in its condenser. Heat flows out of the working fluid as this conversion takes place. Where does this out-flowing heat come from?

(D) Use the concept of entropy to explain why the air conditioner must consume ordered energy (e.g. electricity) as it cools your home on a hot day.

Problem 5:

You and your friends are gathered around a campfire on a cold, clear December evening in the Rocky Mountains, at an altitude of about 10,000 feet above sea level.

(A) You were so busy studying for finals that you didn't pay attention to the travel plans. Thinking that your group was headed for the Bahamas, you packed only shorts and T-shirts. Right now, as you stand facing the big campfire at a distance of about 10 feet, your front is feeling quite hot while your back is feeling quite cold. Since the air temperature around you is essentially uniform, why are you feeling cold on one side and hot on the other?

(B) One of your friends is trying to "mull" cider by boiling it gently along with various spices. But even though the cider is boiling, the spices are taking a surprisingly long time to infuse into the cider. Someone brings out a thermometer and discovers that the cider's temperature is only about 90 °C (194 °F), rather than the expected 100 °C (212 °F). What aspect of the situation is responsible for this lower temperature and why?

(C) It's time to roast marshmallows for "smores" (toasted marshmallows, chocolate bars, and graham crackers, in case you've never eaten them before). You place your marshmallows on a stick and hold them near the glowing coals at the side of the fire. You find that your marshmallows cook faster when they are directly above the coals rather than to the sides of the coals. Why do they cook faster when they are directly above the coals?

(D) One of your more foolhardy friends shows off by passing his hand quickly through the flame. His hand emerges unscathed. But he does it a second time and accidentally touches the metal cooking grate for a moment. Although the temperature of the grate is approximately the same as the temperature of the flame, the grate gives him a small burn. Why does the hot grate burn quickly while the hot flame doesn't?

Problem 6:

Since firefighter use water to put out fires, handling that water is half their job. That job becomes particularly difficult when they are fighting a fire in a high-rise building.

(A) The water pressure in a fire hydrant is about 500,000 pascals (about 5 times atmospheric pressure). When the firefighters attached a hose directly to a fire hydrant, they find that water won't flow out of the hose above the 10th floor of the building, located about 50 meters above the sidewalk. Why won't the water flow?

(B) A spectator suggests that the firefighters return to the 8th floor, where water does flow from the hose, and attempt to spray water up the stairwell to the 11th floor. Explain why this strategy will or will not work.

(C) The firefighters find that water leaving a hose with a narrow nozzle on it travels faster than water leaving that same hose with no nozzle. Why does narrowing the opening of the hose speed up the water emerging from it?

(D) When water hits hot material in a fire, it turns to steam. This steam takes up much more space than the water did and displaces air from the room. Without oxygen to sustain it, the fire quickly goes out. But the hot material must be much, much hotter than 100° C, water's boiling temperature, for the water that hits it to turn completely into steam. Why?