Physics 105 - How Things Work

Problem 1:

The outside temperature is 0 °F (-18 °C) and there is snow on the ground. Oddly enough, the snow is gradually disappearing into the air. The snow is disappearing because

(A) while water molecules are both landing on and leaving the snow's surface, they are landing more often than they are leaving.

(B) water molecules release potential energy as they separate into a gas, so the need to reduce total potential energy causes the snow to convert into water vapor.

(C) there is always liquid water present when both solid ice and gaseous water vapor exist. The ice is becoming water and the water is evaporating as water vapor.

(D) while water molecules are both landing on and leaving the snow's surface, they are leaving more often than they are landing.

Answer: (D) while water molecules are both landing on and leaving the snow's surface, they are leaving more often than they are landing.

Why: When two phases of matter are present, the action at the interface between the two is very important. If molecules depart one phase for the other more often than they return, the first phase will shrink and the other will grow.

Problem 2:

Copper is a much better conductor of heat than glass because copper

(A) contains mobile electrons while glass does not.

(B) has a reddish color while glass is transparent.

(C) is much softer than glass.

(D) is shiny and reflective while glass is not.

Answer: (A) contains mobile electrons while glass does not.

Why: The same electrons that make copper a good electrical conductor also make it a goo thermal conductor.

Problem 3:

As the wind blows past one of the entry doors to a modern office building, the wind is bending inward—toward the building's surface. This entry door can swing either inward (into the building) or outward (out of the building). The effect of the wind is to make it

(A) easy to open the door outward and hard to open it inward.

(B) hard to open the door outward and easy to open it inward.

(C) easy to open the door both outward and inward.

(D) hard to open the door both outward and inward.

Answer: (A) easy to open the door outward and hard to open it inward.

Why: The pressure outside the door is below atmospheric because the air is bending toward it. Air accelerates toward low pressure, so the air near the door must be lower than the atmospheric pressure far from the door (atmospheric pressure). With low pressure outside the door and atmospheric pressure inside the building, the door experiences an outward push from the pressure imbalance.

Problem 4:

A stream is flowing gently under a bridge and past a cylindrical support post. The flow around this vertical post is smooth and laminar, so the water separates in front of the post, arcs around its sides, and rejoins behind the post before continuing down the stream. Compared with the average water level in the stream, the water level is

(A) high in front of the post and low on the sides and behind the post.

(B) high in front of and behind the post, and low on the sides of the post.

(C) low in front of the post and high on the sides and behind the post.

(D) low in front of and behind the post, and high on the sides of the post.

Answer: (B) high in front of and behind the post, and low on the sides of the post.

Why: With laminar flow around the post, the water's total energy will be constant along a streamline. If we look at the water in a horizontal slice in the stream, the water will be bending away from the post at its front and back and toward the post on its sides. As with laminar flow around a ball, the pressure will rise in front of and behind the post and will drop on the sides of the post. The elevated pressure in front of and behind the post will support more water, so the level there will be high. The decreases pressure on the sides of the post will support less water, so the level there will be low.

Problem 5:

Two cars are heading northward on a highway. The red car is in front and the blue car is behind it. The blue car gently bumps the red car and the two cars push on one another and exchange momentum. The force that the blue car exerts on the red car is

(A) equal in amount to the force the red car exerts on the blue car and the momentum lost by the blue car is equal to the momentum gained by the red car.

(B) larger in amount than the force the red car exerts on the blue car, but the momentum lost by the blue car is equal to the momentum gained by the red car.

(C) equal in amount to the force the red car exerts on the blue car, but the momentum lost by the blue car is greater than the momentum gained by the red car.

(D) smaller in amount than the force the red car exerts on the blue car, but the momentum lost by the blue car is equal to the momentum gained by the red car.

Answer: (A) equal in amount to the force the red car exerts on the blue car and the momentum lost by the blue car is equal to the momentum gained by the red car.

Why: The two must push on one another with equal but oppositely directed forces, in agreement with Newton's third law. They will therefore give one another equal but oppositely directed impulses and the momentum will be transferred perfectly... no lost or gained momentum.

Problem 6:

While the strings of a violin or guitar are all the same length, the strings in a piano get shorter as their pitch (frequency) increases. The highest frequency strings of a piano are only a few inches long. But suppose the strings of a piano were all the same long length. To compensate from their dramatic increase in length, those highest frequency strings would have to have

(A) more tension and less mass per inch.

(B) more tension and more mass per inch.

(C) less tension and less mass per inch.

(D) less tension and more mass per inch.

Answer: (A) more tension and less mass per inch.

Why: Lengthing the strings will effectively reduce their stiffness and slow their periods. To compensate, the strings must be stiffened by increasing their tensions and the strings' masses must be decreased to lessen their inertia.

Problem 7:

A rocket is heading upward quickly and a plume of exhaust is streaming downward from its tail. The amount of force that the rocket is exerting on the plume of exhaust is

(A) less than the amount of force the plume is exerting on the rocket, but not zero.

(B) greater than the amount of force the plume is exerting on the rocket.

(C) equal to the amount of force the plume is exerting on the rocket.

(D) zero.

Answer: (C) equal to the amount of force the plume is exerting on the rocket.

Why: In accordance with Newton's third law, the force that the plume exerts on the rocket must be equal and opposite to the force that the rocket is exerting on the plume.

Problem 8:

It's a cold winter day and you are in an unheated cabin in the woods. Everything in the cabin is at the same cold temperature. You find that when you stand in front of a full-length mirror in the bedroom that you feel warmer. That is because the mirror

(A) emits more of its own thermal radiation at you than any other surface in the house.

(B) concentrates the thermal radiation from the rest of the bedroom and focuses it on you.

(C) reflects your own thermal radiation back at you, so you lose heat more slowly.

(D) emits less of its own thermal radiation at you than any other surface in the house.

Answer: (C) reflects your own thermal radiation back at you, so you lose heat more slowly.

Why: The whole room has a single, cold temperature so its thermal radiation is relatively cold. The mirror is particularly bad at emitting its own thermal radiation and mostly reflects the thermal radiation that hits it. When you stand in front of the mirror, your own thermal radiation bounces back at you. Since you're the warmest thing around, having your own radiation come back it you is a welcome treat and helps keep you warmer.

Problem 9:

A single violin string can vibrate in several different ways, as though it were several separate harmonic oscillators. Each of these vibrational modes has its own frequency. If the frequency of the fundamental (lowest frequency) vibrational mode is 440 Hz (Hertz or cycles-per-second), then the frequencies of the string's overtones are

(A) 880 Hz, 1320 Hz, 1760 Hz, and so on.

(B) 880 Hz, 1760 Hz, 3520 Hz, and so on.

(C) 550 Hz, 660 Hz, 770 Hz, and so on.

(D) 660 Hz, 880 Hz, 1100 Hz, and so on.

Answer: (A) 880 Hz, 1320 Hz, 1760 Hz, and so on.

Why: A string has harmonics at all the integer multiples of the fundamental frequency. The fundamental's frequency is 440 Hz, so the second harmonic's frequency is 2 * 440 Hz or 880 Hz. The third harmonic's frequency is 3 * 440 Hz or 1320 Hz, and so on.

Problem 10:

Gliders often have very long wings so that they contact lots of air each second. These long wings enable the glider to stay aloft longer because it can then give the air it contacts

(A) large amounts of downward momentum and energy.

(B) a large amount of downward momentum but a small amount of energy.

(C) small amounts of downward momentum and energy.

(D) a small amount of downward momentum but a large amount of energy.

Answer: (B) a large amount of downward momentum but a small amount of energy.

Why: The glider needs to tranfer downward momentum into something else. The last thing it wants to do is transfer energy at the same time because energy is precious. If the glider could transfer downward momentum into a mountain peak, that would be great because the mountain peak wouldn't move and the glider would do no work on it and transfer no energy to it. Since there is no mountain peak to touch, the glider's next best choice is to transfer downward momentum to as much air as it can touch. The air will move and have work done on it and take away the glider's precious energy. But by pushing on lots of air, the glider minimizes the distance that air travels during the downward push and therefore the amount of energy the air receives.

Problem 11:

When a sport utility vehicle (SUV) makes a sudden left turn on the highway, it is in danger of flipping over. One valid explanation for this effect is:

(A) the SUV's angular mass increases as it turns and its angular momentum decreases. A transfer of angular momentum from its wheels to its frame then causes it to begin rotating so that it flips over.

(B) the centrifugal force on the SUV as it goes around the turn pushes outward on the top of the SUV. The wheels are held in place by friction, so only the top of the SUV accelerates outward and it flips over.

(C) the leftward frictional force that causes the SUV to accelerate leftward during the turn also exerts a torque on the SUV about its center of mass and can cause the SUV to undergo angular acceleration and flip over.

(D) the force of the SUV's momentum pushes it forward while the road pushes it to the left and these two forces twist the SUV so that it undergoes angular acceleration and flips over.

Answer: (C) the leftward frictional force that causes the SUV to accelerate leftward during the turn also exerts a torque on the SUV about its center of mass and can cause the SUV to undergo angular acceleration and flip over.

Why: The SUV's problem is that its static stability is poor. It's just too tall for its base and its center of gravity is too high above that small base. While it can recover from a modest tip, it cannot survive tips that would not put lower lying automobiles in jeopardy. So an SUV is an accident waiting to happen. During a high-speed turn, the frictional forces exert low on the car (on its wheels, in fact) can rotate the SUV pretty far from verticle during the turn and may take it beyond the limits of its static stability.

Problem 12:

As an incandescent light bulb ages, it develops a dark spot on the glass directly above the filament. This dark spot indicates that the bulb has gas inside it because the spot is produced by

(A) plasma.

(B) conduction.

(C) convection.

(D) radiation.

Answer: (C) convection.

Why: The tungsten atoms that form the dark spot were carried there in the convection fluid flow that develops inside the bulb. The presence of gas is bad for energy efficiency because convection does carry heat upward from the filament and wastes that heat on the surface of the bulb and the air above it. But the gas does help the filament's life by bouncing many of the tungsten atoms that try to leave the filament back onto the filament.

Problem 13:

You're a passenger in a car and you have your eyes closed. The car is traveling at a constant speed on a level road that is turning toward the left. You feel a gravity-like sensation toward your right, but you remain in your car seat. The net force acting on you during this turn

(A) is zero.

(B) points toward your left.

(C) points toward your right.

(D) points forward.

Answer: (B) points toward your left.

Why: You always feel a gravity-like sensation in the direction opposite your acceleration. It's your inertia trying to make you go straight. In this case, you are accelerating to your left so you feel this gravity-like sensation toward your right.

Problem 14:

A plastic bottle, partly full of water, has been sitting on the kitchen counter for the past hour. Some of the water molecules in the bottle are gaseous and some are liquid. To increase the amount of liquid water in the bottle, you could (note: neglect any effect squeezing has on the temperatures in the bottle)

(A) cool the bottle down, but you must not squeeze it to increase the density of its gas.

(B) open the bottle to the kitchen air.

(C) cool the bottle down and/or squeeze it to increase the density of its gas.

(D) warm the bottle up and/or squeeze it to increase the density of its gas.

Answer: (C) cool the bottle down and/or squeeze it to increase the density of its gas.

Why: You can shift the balance between the liquid and gaseous phases of water by either slowing the leaving process (molecules leave the liquid less often) or speeding up the landing process (molecules land on the liquid more often). Cooling the bottle will slow the leaving process and making the gas above the water more dense will speed up the landing process.

Problem 15:

To make a large surface wave on the ocean travel faster, you could

(A) increase its amplitude (the height difference between its crests and troughs).

(B) decrease its amplitude (the height difference between its crests and troughs).

(C) decrease its wavelength (the distance between adjacent crests).

(D) increase its wavelength (the distance between adjacent crests).

Answer: (D) increase its wavelength (the distance between adjacent crests).

Why: Surface waves on water travel with a speed that depends on their wavelengths. Longer wavelength waves simply travel faster.

Problem 16:

To catch a football successfully, you should allow the ball to push your hands in the direction of its travel. Allowing your hands to move with the football is crucial because it allows you to

(A) add energy to the football.

(B) add momentum to the football.

(C) extract momentum from the football.

(D) extract energy from the football.

Answer: (D) extract energy from the football.

Why: It's easy to exchange momentum with the football, but getting it to stop and stay stopped requires that you extract all of its energy. By letting it do work on your hands, you help it lose energy so that it stays put in your hands.

Problem 17:

As you are going around the loop-the-loop on a roller coaster, you are basically traveling in a vertical circle. For simplicity, let's imagine that you are traveling around and around that circle. When during this circular motion do you feel the heaviest?

(A) When you are at the bottom of the circle.

(B) When you are going down the descending side of the circle.

(C) When you are going up the rising side of the circle.

(D) When you are at the top of the circle.

Answer: (A) When you are at the bottom of the circle.

Why: You're traveling in something like uniform circular motion, although you're actually going fastest when you're lowest (at the bottom of the circle). Since acceleration is toward the center of the circle in uniform circular motion, you are accelerating upward most rapidly when you are at the bottom of the circle. That's when you feel the strongest gravity-like sensation due to acceleration and it points in the same direction as your real weight. You feel extremely heavy at the bottom of the loop.

Problem 18:

You drop a bouncy ball from rest and it bounces off a granite floor. The ball rebounds to its original height. During the bounce, the ball transferred

(A) both energy and momentum to the floor.

(B) neither energy nor momentum to the floor.

(C) energy but not momentum to the floor.

(D) momentum but not energy to the floor.

Answer: (D) momentum but not energy to the floor.

Why: It's easy to transfer momentum to the floor and the ball actually transfers twice as much downward momentum to the floor as it had before it hit. The result is that the ball has a negative amount of downward momentum, which is a positive amount of upward momentum. All it takes to transfer momentum is an impulse: a force exerted on the floor for a time. But transferring energy to the floor requires that the floor move so that the ball can do work on the floor. Since the granite floor won't move, the ball does not work on it and there is no transfer of energy.

Problem 19:

You are standing still in the basket of a hot air balloon and you are wearing a backpack. As the hot air balloon rises upward, you are doing

(A) (positive) work on the backpack and the hot air balloon is doing zero work on you.

(B) (positive) work on the backpack and the hot air balloon is doing (positive) work on you.

(C) zero work on the backpack and the hot air balloon is doing zero work on you.

(D) zero work on the backpack and the hot air balloon is doing (positive) work on you.

Answer: (B) (positive) work on the backpack and the hot air balloon is doing (positive) work on you.

Why: The balloon is pushing up on you, supporting your weight, and you move upward. Therefore, the balloon is doing work on you. You are pushing up on your backpack, supporting its weight, and it moves upward. Therefore, you are doing work on the backpack.

Problem 20:

You are swinging a bucket full of water around you in a big horizontal circle at a constant speed. You are at the center of its circular path. The net force on the bucket points directly

(A) toward you.

(B) downward.

(C) along the bucket's velocity (along its direction of travel).

(D) away from you.

Answer: (A) toward you.

Why: You are providing the centripetal force that causes the bucket to travel around in a large horizontal circle. You are also keeping the bucket from falling by balancing its weight. However, the observation is the bucket is simply traveling in a circle at a constant speed. Therefore, it is experiencing a net force directly toward the center of the circle: you.

Problem 21:

A guitar string vibrating in its fundamental mode (as a single arc) behaves as a harmonic oscillator, which means that the restoring force acting on the string is

(A) proportional to how far it is from equilibrium and that its pitch (frequency) can vary but its volume (amplitude) cannot.

(B) proportional to how far it is from equilibrium and that its volume (amplitude) can vary but its pitch (frequency) cannot.

(C) independent of how far it is from equilibrium and that its volume (amplitude) can vary but its pitch (frequency) cannot.

(D) independent of how far it is from equilibrium and that its pitch (frequency) can vary but its volume (amplitude) cannot.

Answer: (B) proportional to how far it is from equilibrium and that its volume (amplitude) can vary but its pitch (frequency) cannot.

Why: Harmonic oscillators must have restoring forces that are proportional to displacement, and the result is that their vibrations are independent of their amplitudes.

Problem 22:

You are at a campfire in an open field. It is a cool, windless evening and you are sitting 10 feet from the fire. The fire is keeping you warm by transferring heat to you via

(A) radiation alone.

(B) conduction alone.

(C) conduction and convection.

(D) radiation and convection.

Answer: (A) radiation alone.

Why: There is very little conduction of heat through air and convection lifts hot air upward from the fire. That leaves just radation to carry heat to you.

Problem 23:

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 turbulent flow can fully combine the ingredients.

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

(C) viscosity 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 laminar flow can fully combine the ingredients.

Answer: (A) inertia to dominate the flow of batter in the mixer, so that the resulting turbulent flow can fully combine the ingredients.

Why: Turbulent flow involves microscopic eddies and swirls that mix stuff up. To encourage turbulence, you need high Reynolds numbers so that inertia dominates the flow and rips it apart.

Problem 24:

If you use a microwave oven to heat clean water in a smooth glass container, you can sometimes superheat the water—that is, raise its temperature well above water's boiling temperature without it boiling. In that case, the very hot water fails to boil because

(A) even though bubbles of pure steam are stable at such high temperatures, they cannot form without help.

(B) bubbles of pure steam must stick to the surface of a container in order to grow in size, but slick glass surfaces won't hold these bubbles in place long enough for boiling to occur.

(C) bubbles of pure steam are not stable in clean water that is uniformly heated, even at such high temperatures.

(D) bubbles of pure steam shrink quickly when they are exposed to atmospheric pressure, even at such high temperatures.

Answer: (A) even though bubbles of pure steam are stable at such high temperatures, they cannot form without help.

Why: It's often hard to start the steam bubbles of boiling. Without some piece of crude to trap an initial gas bubble, there is a chance that bubbles won't form at all.

Problem 25:

You and your best friend are trying to pull one another toward your respective dorm rooms. You're the stronger of the two and, with a mighty tug, you drag your friend into your room. As you are pulling your friend toward your room, the force you exert on your friend is

(A) equal in amount to the force your friend exerts on you.

(B) definitely equal to three times the weight of Spongebob Squarepants.

(C) less in amount than the force your friend exerts on you.

(D) greater in amount than the force your friend exerts on you.

Answer: (A) equal in amount to the force your friend exerts on you.

Why: This is simply Newton's third law: if you pull on your friend, your friend pulls on you equally hard in the opposite direction.

Problem 26:

A steam engine manages to do real work using only hot steam and cold air. It needs both the steam and the air because

(A) there is order present in their difference in temperature.

(B) total entropy decreases when heat flows spontaneously from hot steam to cold air.

(C) work is released when heat flows from cold air to hot steam.

(D) there is order present in the hot steam and energy present in the cold air.

Answer: (A) there is order present in their difference in temperature.

Why: Even though thermal energy is itself disordered energy, there is still order present in the uneven distribution of that thermal energy.

Problem 27:

At the heart of a quartz watch is a tiny

(A) quartz sphere that bounces about like a ball in a box.

(B) container of quartz powder that emits electrical pulses because of thermal energy.

(C) quartz sphere that spins with constant angular acceleration.

(D) quartz tuning fork that vibrates like a pair of masses on a spring.

Answer: (D) quartz tuning fork that vibrates like a pair of masses on a spring.

Why: Modern quartz watches contain such a tiny tuning fork, laser trimmed to vibrate at just the right frequency.

Problem 28:

Because of bad planning during the design and construction of a high-rise apartment building, all 50 floors of the building receive their water from a single pipe. That pipe is fed from a water tank located on the building's roof. On opening day, residents on various floors begin taking showers and have different experiences. They quickly discover that the total energy per liter in the spraying water is (neglecting any effects of viscosity and friction)

(A) less on higher floors

(B) greater on higher floors.

(C) the same on all floors, but the speed of the spraying water is slower on higher floors.

(D) the same on all floors, but the speed of the spraying water is higher on higher floors.

Answer: (C) the same on all floors, but the speed of the spraying water is slower on higher floors.

Why: The higher the water is, the more of its energy is in the form of gravitational potential energy and the less is available to become kinetic energy.

Problem 29:

Tides are caused by the moon's gravity acting on the earth and its oceans. The moon reshapes the earth's oceans so that they bulge slightly outward

(A) only on the side of the earth closest to the moon.

(B) all the way around the earth, from north pole to south pole.

(C) on the side of the earth closest to the moon and the side of the earth farthest from the moon.

(D) all the way around the earth's equator.

Answer: (C) on the side of the earth closest to the moon and the side of the earth farthest from the moon.

Why: The water nearest the moon tries to fall toward it more rapidly than the earth while the water farthest from the moon tries to fall toward it less rapidly than the earth. The result is two bulges, one on each side of the earth.

Problem 30:

Before it burns the fuel and air mixture, the piston and cylinder of an automobile engine compress that mixture to high density. During this compression, the temperature of the mixture rises because

(A) the piston does work on the mixture during the compression process.

(B) friction between the piston and cylinder heats the mixture.

(C) high density gases are hotter than low density gases.

(D) high pressure gases are hotter than low pressure gases.

Answer: (A) the piston does work on the mixture during the compression process.

Why: When you do work on a gas by compressing it, the gas stores that work in the only form it has available to it: thermal energy. It gets hotter.

Problem 31:

You cannot cool room air simply by converting its thermal energy into electrical energy because

(A) that would be a statistically unlikely event.

(B) that would violate Newton's third law of motion.

(C) that would violate Newton's second law of motion.

(D) thermal energy and electrical energy are different conserved quantities and one cannot be converted into the other.

Answer: (A) that would be a statistically unlikely event.

Why: Thermal energy is extraordinarily unlikely to reorder itself to become electrical energy.

Problem 32:

You are bouncing gently up and down at the end of a springy diving board, with your feet never leaving its surface. If you double the overall height of the bounce, the time it takes to complete each bounce (the period of the bounce) will

(A) increase by a factor of 4.

(B) decrease by a factor of 2.

(C) stay the same.

(D) increase by a factor of 2.

Answer: (C) stay the same.

Why: You are a harmonic oscillator, with a restoring force that is proportional to your displacement from equilibrium. The period of a harmonic oscillator is independent of the amplitude of motion.

Problem 33:

The pendulum of a grandfather clock gradually loses energy because of air drag and friction. To keep its pendulum swinging, the clock has to add a tiny amount of energy to it every swing. In essence, the clock gently pushes the pendulum in the

(A) same direction as its acceleration.

(B) same direction as its velocity.

(C) direction opposite its acceleration.

(D) direction opposite its velocity.

Answer: (B) same direction as its velocity.

Why: To do work on the pendulum, you must push it in the direction that it moves.

Problem 34:

The air emerging from the nozzle of a leaf blower is traveling fast but its pressure is atmospheric pressure. Before that same air passed through the nozzle it was traveling

(A) faster but its pressure was above atmospheric pressure.

(B) slower but its pressure was below atmospheric pressure.

(C) slower but its pressure was above atmospheric pressure.

(D) faster but its pressure was below atmospheric pressure.

Answer: (C) slower but its pressure was above atmospheric pressure.

Why: Upstream of the nozzle, the air's total energy was mostly in the form of pressure potential energy. That pressure potential energy converts into kinetic energy during the air's trip through the nozzle.

Problem 35:

A huge abstract iron sculpture has been installed in front of the local art museum. It sits there motionless, "guarding" the main doorway. The sculpture is experiencing its weight downward and an equally strong force upward from the brick courtyard beneath it. We know that these two forces on the sculpture are equal in amount but oppositely directed because

(A) for every action, there is an equal but oppositely directed reaction.

(B) the sculpture is not accelerating so the two forces must sum to zero.

(C) the sculpture has zero velocity.

(D) Newton's third law requires that forces always appear in equal but oppositely directed pairs.

Answer: (B) the sculpture is not accelerating so the two forces must sum to zero.

Why: Only an object experiencing zero net force can remain motionless for more than an instant. All the forces on an endlessly stationary object must cancel.

Problem 36:

You drop a bouncy ball straight down from your friend's 30th floor balcony. It is spinning rapidly so that its northern side is turning upward (toward you). As a result of this spin, the ball does not continue falling straight downward, but instead deflects horizontally as it falls. The ball deflects the passing airstream

(A) northward and the ball accelerates northward.

(B) southward and the ball accelerates southward.

(C) southward and the ball accelerates northward.

(D) northward and the ball accelerates southward.

Answer: (C) southward and the ball accelerates northward.

Why: The Magnus force deflects an airstream toward the side of the ball that is moving against onrushing air. The ball deflects toward the side of it that is moving with the passing air.

Problem 37:

When a large wave travels across the ocean, water at the ocean's surface moves

(A) steadily forward at the wave's velocity.

(B) steadily forward at half the wave's velocity.

(C) directly up and down and returns to its starting point.

(D) in a circular path and returns to its starting point.

Answer: (D) in a circular path and returns to its starting point.

Why: The wavecrests are all built from local water and that local water simply moves in a circle to form the crests and troughs.

Problem 38:

You toss a quarter straight up into the air. It rises to a peak and then descends. After it leaves your hand and neglecting air resistance, the quarter experiences

(A) a downward net force that is proportional to the quarter's speed.

(B) a constant downward net force.

(C) an upward net force that gradually diminishes to zero at its peak height and then becomes a downward net force.

(D) a constant upward net force on the way up and a constant downward net force on the way down.

Answer: (B) a constant downward net force.

Why: While it's in the air, the only non-air force, is gravity. The coin experiences its weight. Even if you include buoyancy, the net force on the coin is still downward and constant.

Problem 39:

The light from an incandescent light bulb is redder than sunlight and photographs taken in incandescent lighting often have a reddish cast to them. There is a practical reason why an incandescent light bulb cannot produce a larger fraction of blue light. To shift its light spectrum toward the blue, the bulb would have to

(A) shorten the distance between coils in its spiral filament and no one knows how to wind these tiny spirals any tighter.

(B) use a blue metal filament and all known metals are either shiny, yellow, orange, or red.

(C) increase the length of its filament and the filament would consume too much electricity to be cost effective.

(D) operate its filament at a higher temperature and the filament would die quickly.

Answer: (D) operate its filament at a higher temperature and the filament would die quickly.

Why: The filament is a black body and the color of its light is characteristic of its temperature. If you heat it hotter, it will emit more bluish light but its filament won't live long.

Problem 40:

You roll a marble down the side of a round bowl—a bowl with a spherical bottom. The marble rolls back and forth between the front and back of the bowl, passing right through the bottom of the bowl on each trip. At this exact moment, the marble has just rolled down your side of the bowl and is exactly at the bottom of the bowl. It is about to begin rolling up the far side of the bowl. It is accelerating

(A) away from you.

(B) upward.

(C) downward.

(D) toward you.

Answer: (B) upward.

Why: At the exact bottom of the bowl, the marble is essentially moving in a circle about the center of the bowl's curvature. It is experience a pure centripetal acceleration upward.

This question is the hardest question on the entire exam. If the marble were moving back and forth in a straight line, It would not be accelerating at the equalibrium point, that is, at the effective bottom of the bowl . But the marble is moving in an arc and even at the midpoint (which is no longer a true equilibrium), its direction of travel is still bending. So while it is not gaining or losing speed at that midpoint, it is still accelerating to one side.

Problem 41:

Two marbles are in a large bowl and the system is completely isolated from its surroundings. Each of the four arrangements listed below as possible answers contains exactly the same amount of total energy, although that energy may be in different forms in the different arrangements. Which arrangement has the most entropy:

(A) the marbles high up on the same side of the bowl, but not touching.

(B) the marbles both rolling quickly through the bottom of the bowl, but not touching.

(C) the marbles resting motionless in the bottom of the bowl.

(D) the marbles high up on opposite sides of the bowl.

Answer: (C) the marbles resting motionless in the bottom of the bowl.

Why: Whatever situation is the final situation is certain to be the highest in entropy. Since the marbles sitting motionless in the bottom of the bowl is clearly the end point for all the motions, that must be the high-entropy state.

Problem 42:

If you throw a ball straight forward at high speed with no spin at all, the air pressure at its surface will not be uniform. The location of the highest air pressure on the ball's surface will be at its

(A) front (the side farthest from you).

(B) bottom.

(C) top.

(D) back (the side nearest to you).

Answer: (A) front (the side farthest from you).

Why: The airflow around the ball reaches its highest pressure at the front of the ball. The pressure is low on the sides and the back of the ball has a turbulent wake.

Problem 43:

When you blow gently across the top of a soda bottle, the air inside it vibrates as a harmonic oscillator and it emits a clear tone. If you replace the air in the bottle with helium, the bottle's new tone will definitely occur at a

(A) lower pitch (a lower frequency).

(B) lower volume (a smaller amplitude).

(C) higher pitch (a higher frequency).

(D) higher volume (a larger amplitude).

Answer: (C) higher pitch (a higher frequency).

Why: Helium has less mass per liter than air, so it vibrates faster (less inertia for the same restoring forces).

Problem 44:

A liquid pours smoothly down a channel and into a basin, experiencing only laminar flow. To make this flow become turbulent, you should

(A) decrease the speed of the flow and/or decrease the viscosity of the liquid.

(B) increase the speed of the flow and/or increase the viscosity of the liquid.

(C) increase the speed of the flow and/or decrease the viscosity of the liquid.

(D) decrease the speed of the flow and/or increase the viscosity of the liquid.

Answer: (C) increase the speed of the flow and/or decrease the viscosity of the liquid.

Why: Turbulence occurs when inertia dominates over viscosity. Inertia becomes more dominant when you either move the liquid faster or reduce its viscosity.

Problem 45:

Two children are trying to lift toys using identical-looking helium balloons. However, one child is located in Norfolk, where the altitude is roughly sea level, and the other child is located in Denver, where the altitude is about 5,000 feet above sea level. Which balloon, if any, can lift more weight?

(A) I am just randomly picking answers and do not deserve credit for this problem.

(B) The Denver balloon can lift more weight.

(C) They can both lift equal weights.

(D) The Norfolk balloon can lift more weight.

Answer: (D) The Norfolk balloon can lift more weight.

Why: With denser air around it, the Norfolk balloon is displacing more weight of air and therefore experiences a greater buoyant force.

Problem 46:

A wooden sculpture weighs exactly 1 pound. You very gently float this sculpture in a pot that was perfectly full of water, so some of that water overflows. The pot is again perfectly full of water, but now the sculpture is floating in it. If you weigh the water that overflowed, you'll find that it weighs

(A) slightly less than 1 pound.

(B) much less than 1 pound.

(C) exactly 1 pound.

(D) more than 1 pound.

Answer: (C) exactly 1 pound.

Why: This is simply Archemede's principle: the floating pot will displace its weight in water. We're neglecting the complications of air here.

Problem 47:

You're standing at the top of a tall lighthouse. You are holding two balls, one twice as heavy as the other, and you throw them together horizontally with one hand. They leave your hand at the same time and the same speed. Both balls soon hit the water. Neglecting any air resistance, the heavier ball reaches the water

(A) at the same time but half as far from the lighthouse as the lighter ball.

(B) in half the time and half as far from the lighthouse as the lighter ball.

(C) in half the time but at the same place as the lighter ball.

(D) at the same time and at the same place as the lighter ball.

Answer: (D) at the same time and at the same place as the lighter ball.

Why: Everything falls at the same rate. Since these balls start from the same height and have the same vertical component of velocity (zero), they plummet together.

Problem 48:

An air conditioner is most effective at cooling a room on a warm summer day when the work done while operating its compressor ends up as

(A) thermal energy split evenly between the outside air and the indoor air.

(B) thermal energy in the indoor air.

(C) work back at the power company.

(D) thermal energy in the outside air.

Answer: (D) thermal energy in the outside air.

Why: The compressor must consume electric power and convert that power into thermal power. The thermal power has to go somewhere, so putting it into the outside air is the best choice.

Problem 49:

A high-speed chase ends when the robbers drive their car into the concrete base of a bridge. The car is badly crumpled and the robbers are dazed, but the bridge is unscathed. When the car collided with the bridge, it transferred

(A) both momentum and energy to the bridge.

(B) momentum to the bridge but did not transfer energy to the bridge.

(C) neither momentum nor energy to the bridge.

(D) energy to the bridge but did not transfer momentum to the bridge.

Answer: (B) momentum to the bridge but did not transfer energy to the bridge.

Why: You can easily transfer momentum to a stationary object: just push it forward for a time. But you can't do work on a stationary object because it will not move a distance in the direction of your force.

Problem 50:

A kiln is used to fire pottery—to heat it red or even yellow hot so that it fuses into a hard, finished ceramic. You have four pots to fire, each with its own surface color. One is black, one is white, one is shiny aluminum-like, and one is essentially transparent. You place the four pots in a kiln and heat them to the same yellow-hot temperature. When you look inside the kiln, the one that is glowing most brightly is the one that is

(A) white.

(B) shiny aluminum-like.

(C) black.

(D) essentially transparent.

Answer: (C) black.

Why: Black objects are both the best absorbers of light and the best emitters of their own 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 examination.

Problem 1:

You are trying to learn how to walk on a tightrope. The rope stretches between two rigid supports and has a net below it to catch you each time you fall of the rope. Needless to say, you and the net have encountered each other a great many times.

(A) When you are standing exactly upright on the rope, you are in equilibrium. And when you hang from the rope with your hands, you are also in equilibrium. Why is it so much easier to stay in the hanging equilibrium than the standing equilibrium?

Answer: The hanging equilibrium is stable while the standing equilibrium is unstable.

Why: When you're disturbed from the hanging equilibrium, you experience a restoring force/torque that pushes you back toward equilibrium. When you're disturbed from the standing equilibrium, the forces/torques that develop actually push you away from the equilibrium and you tend to fall over.

(B) What happens to your total potential energy whenever you begin to tip away from the standing equilibrium?

Answer: It decreases.

Why: As you tip away from the standing (unstable) equilibrium, your center of gravity descends and your total potential energy (which is only gravitational potential) decreases. Since you accelerate in the direction that reduces your total potential energy as quickly as possible, you accelerate away from the standing equilibrium, which is why it's unstable.

(C) To help you stay in the standing equilibrium, you hold a long massive rod by its middle. Each time you begin to tip over toward the right, you twist the rod hard so that its right end drops and its left end rises. The rod responds by twisting you back toward the standing equilibrium. What conserved physical quantity are you exchanging with the rod when you use it in this manner?

Answer: Angular momentum.

Why: You twist the rod, giving it an angular impulse in one direction, and it twists you back. Your goal in this unconscious exercise is to return yourself to upright. The rod ends up spinning, but you recover your balance and then can go on to worry about stopping the rod from spinning.

(D) After a while, you get so good at tightrope walking that you start bouncing as you walk. As long as you stay in contact with the rope, the period of each bounce is independent of how far you bounce. But when you start bouncing so high that your feet lose contact with the rope, the period starts to get longer. Why is the period dependent on how far you bounce once your feet begin to leave the rope? [NOTE: Wording is flawed. I should have specified that it is YOUR PERIOD of motion that gets longer. See NOTE below for more details.]

Answer: Once your feet leave the rope, the restoring force becomes constant and you're not a harmonic oscillator. The period now increases with amplitude.

Why: Only while your feet are touching the rope is the force on you proportional to your distance from equilibrium (along the rope's bouncing direction). Once you're in the air, you experience a constant downward force--your weight--and you are not a harmonic oscillator anymore.

NOTE: We will not be grading this question because its language is flawed. I did not specify which period I meant when I asked "Why is the period dependent on how far you bounce...". Once you and the rope are no longer touching, the two of you move separately and have different periods. The rope now vibrates more quickly than before because it has less mass, so the rope's period decreases. You vibrate more slowly because the restoring force on you becomes less than proportional to your displacement from equilibrium, so your period increases. It's a mess and grading the answers is impossible.

Problem 2:

When you look out your apartment window, you can see a power line that stretches between two utility poles. On a windy day, you notice that the line is bouncing up and down rhythmically as a single arc, once per second—its fundamental period.

(A) A flock of birds settles on the line. Do these birds affect the fundamental period and, if so, does that period increase or decrease?

Answer: Yes, they increase the period.

Why: The birds add mass to the line and slow down its accelerations. It takes longer to bounce.

(B) The birds have left and you continue to watch the power line. You notice that it sometimes bounces as a single arc and sometimes bounces as two halves—half the line arcs upward as the other half arcs downward. What is the period of this second mode of bouncing—its overtone period? Be specific.

Answer: 0.5 seconds.

Why: The second harmonic mode of a string (two half-strings) occurs at exactly twice the frequency of the fundamental mode. It has a period that is half that of the fundamental mode.

(C) The utility company arrives and tightens the power line. Does this increase in the line's tension affect its fundamental period and, if so, does that period increase or decrease?

Answer: Yes, the period decreases.

Why: The line's tension contributes to its stiffness. By tightening the line, they stiffen it and it goes through its motions faster.

(D) Finally, the utility company clips a large mass to the power line, exactly midway between the two utility poles, while leaving the line's tension unchanged. Does the presence of this mass affect either period (fundamental and/or overtone) and, if so, does that period(s) increase or decrease?

Answer: The mass affects only its fundamental period and increases it.

Why: The mass sits at the node of the second harmonic mode (two half-strings). As a result, it has no affect on that mode at all--the string doesn't move at the location of the mass, so the mass does nothing. However, the mass adds inertia to the fundament mode and slows it down, increasing its period.

Problem 3:

There's nothing like skydiving to get the adrenaline running! You have just jumped out of a plane at 15,000 feet and you're plummeting toward the ground.

(A) Your friend pushed on your shoulder as you left the plane and set you spinning about a vertical axis. You are having trouble stopping the spin. What conserved quantity are you trying to transfer to the air in order to stop spinning?

Answer: Angular momentum

Why: Once you have been given angular momentum by your friend, you have it until you transfer it elsewhere. Your friend gave you vertical angular momentum in one direction, so you will keep spinning in that direction until you give it to the air.

(B) You have stopped spinning and have reached terminal velocity: you are descending in a straight vertical line at a constant velocity. The only significant upward force you are experience is pressure drag. What is the amount of that drag force?

Answer: Equal to your weight.

Why: The net force on you is zero, so the upward force you are experiencing (the drag force) must be equal to the downward force you are experiencing (your weight).

(C) You are now trying to get together with your friends, who are above you and to your north. To join your friends in the vertical direction, you spread out your arms and increase the drag force you experience. Why does that help reduce your vertical separation from your friends?

Answer: Increasing your drag causes you to accelerate upward and your friends overtake you.

Why: To let your friends catch up with you (in the downward direction), you need to reduce your speed. You do this by increasing the upward force on you so that the net force you are experiencing is upward and you accelerate upward.

(D) To join your friends in the horizontal direction, you begin to push the passing air toward the south. Why does that help reduce your horizontal separation from your friends?

Answer: The air pushes back on you and you accelerate toward the north.

Why: To head northward, you must push something southward. You shove the air toward the south and it shoves you toward the north. You accelerate toward the north and your friends.

Problem 4:

When an air conditioner is operating properly, its working fluid converts back and forth between a gas and a liquid. The fluid converts from a gas to a liquid in the condenser located outside. The fluid converts from a liquid to a gas in the evaporator located inside.

(A) Both liquid and gaseous working fluid are present in the condenser. However, to encourage the working fluid to convert from a gas to a liquid there, the air conditioner increases the density of that gas. Why does increasing the density of the gas favor the formation of liquid working fluid?

Answer: Molecules in the denser gas land more often and the balance between gas and liquid shifts toward liquid.

Why: The phase balance between liquid and gas depends on the landing and leaving of the working fluid molecules. The leaving rate from the liquid to the gas is determined primarily by temperature. The landing rate from the gas to the liquid is determined primarily by how often the working fluid molecules hit the liquid surface. By packing the gas molecules more tightly, the air conditioner ensures that they will hit the liquid surface more often. The landing/leaving balance will shift in favor of landing and the liquid phase will grow at the expense of the gaseous phase.

(B) As the working fluid condenses from a gas to a liquid, it releases an enormous amount of thermal energy even when its temperature doesn't change. What form of energy was it that was converted into this thermal energy?

Answer: Chemical potential energy

Why: The working fluid molecules have chemical potential energy that they release when they bond together to form a liquid. In the air conditioner, they release this chemical potential energy as thermal energy.

(C) As the liquid working fluid evaporates into the vast, nearly empty chamber of the evaporator, its temperature drops. The working fluid and chamber therefore lose thermal energy so the entropy associated with thermal energy in the evaporator decreases. Nonetheless, the second law of thermodynamics is not being violated because entropy associated with something else is being created during the evaporation. What order is being lost as the liquid evaporates?

Answer: There is order in have all the molecules in one small part of the chamber.

Why: The most disordered arrangement of the molecules is having them spread out throughout the chamber. Because the situation is originally not uniform, it has some order in it.

(D) Both the indoor air and the outdoor air experience changes in their entropies while the air conditioner is operating. (1) Does the entropy of the indoor air increase or decrease? (2) Does the entropy of the outdoor air increase or decrease? (3) Which of the two experiences the larger change in entropy, or are they equal in amount?

Answer: (1) (indoor air's entropy) decreases, (2) (outdoor air's entropy) increases, (3) outdoor's increase is greater than indoor's decrease.

Why: There is disorder associated with thermal energy, so removing thermal energy from the indoor air definitely decreases that air's entropy. Similarly, adding thermal energy to the outdoor air definitely increases that air's entropy. But to operate properly, the air conditioner cannot have the total entropy decrease. Therefore, it has to dump extra thermal energy into the outdoor air and raise the entropy there more than enough to balance the entropy lost by the indoor air.

Problem 5:

A bird is flying at constant velocity in a straight, horizontal path at an altitude of 1,000 feet.

(A) What is the net force on the bird?

Answer: Zero.

Why: The bird is at constant velocity, so it is not accelerating and the net force it is experiencing is zero.

(B) Gravity is transferring a certain amount of downward momentum to the bird every second. How do we know this?

Answer: Gravity exerts a steady downward force on the bird, giving it the same downward impulse each second.

Why: Each second, gravity gives the bird and impulse equal to the bird's weight times one second. That's an amount of downward momentum.

(C) The bird is not accumulating any net downward momentum. What is it doing with the downward momentum that gravity is transferring to it?

Answer: It is transferring this downward momentum to the air.

Why: The only thing that the bird has nearby to transfer momentum to is the air. So it pushes the air down and obtains an upward force in response. This upward force gives the bird an upward impulse that balances gravity's downward impulse.

(D) The bird is experiencing pressure drag as it flies forward. This pressure drag pushes the bird backward. What does the bird do to keep from slowing down? (No details, just the basic physics please… a dozen words should be enough.)

Answer: The bird pushes air backward and air pushes the bird forward.

Why: Air drag is extracting forward momentum from the bird. To replace this lost momentum, the bird must obtain some forward momentum from the air. It pushes the air backward and the air pushes it forward, replacing the lost forward momentum.

Problem 6:

A tall flagpole sits motionless and perfectly upright on a calm summer day. Suddenly, a flying Frisbee hits the flagpole hard near its top and it begins swaying back and forth rhythmically, toward you and away from you. Let's neglect air resistance or any forms of friction, so the flagpole will sway like this forever.

(A) When during its swaying is the flagpole accelerating toward you the fastest?

Answer: It is accelerating toward you fastest when it is farthest away from you.

Why: Accelerations are caused by forces and the force experienced by the springy flagpole is strongest when it is bent the farthest. The moment when the flagpole is experiencing the strongest force toward you is when it is bent the farthest away from you. That is also the moment of maximum acceleration toward you.

(B) When during its swaying is the flagpole moving toward you the fastest? (i.e. has its maximum velocity toward you.)

Answer: It is moving toward you fastest when it is passing through equilibrium on its way toward you.

Why: When it's bent, the flagpole always accelerates toward the equilibrium point. While heading toward you from its most distant point, it accelerates forward and speeds up until it reaches equilibrium. After passing through equilibrium, it accelerates backward and slows down. Since it reaches its highest speed just as it stops accelerating forward, its velocity toward you is greatest just as it passes through the equilibrium point on its way toward you.

(C) When during its swaying does the flagpole have its lowest amount of total potential energy?

Answer: It has the lowest total potential energy when it is at equilibrium

Why: The flagpole is moving about its stable equilibrium. Since it accelerates toward the lowest total potential energy, that equilibrium point is also the point of lowest total potential energy. In fact, this minimum of total potential energy is why that point is a stable equilibrium point.

(D) When during its swaying does the flagpole have its largest amount of momentum toward you?

Answer: It has its largest momentum toward you when it is passing through equilibrium on its its way toward you.

Why: Since its momentum is proportional to its velocity, it reaches maximum momentum toward you at the same moment it reaches maximum velocity toward you.