Physics 105 - How Things
Work - Fall, 2000
Final
Examination - Solutions
Given Monday, December 11, 2000, from 9:00 AM to 12:00 Noon
PART I: MULTIPLE CHOICE QUESTIONS
Please mark the correct answer for each question on the bubble sheet. Fill in the dot completely with #2 pencil. Part I is worth 67% of the grade on this examination.
Problem 1:
Here in Charlottesville, your friend cooks her eggs in boiling water for exactly 3 minutes. But when she visits Denver, with an altitude almost 1 mile higher than here, she has to cook her eggs for more than 3 minutes in boiling water to reach the same consistency. The eggs cook more slowly in Denver because
(A) more of the water's thermal energy is in the form of pressure potential energy.
(B) water boils at a lower temperature at high altitude.
(C) more of the water's thermal energy is in the form of gravitational potential energy.
(D) the thermal conductivity of water decreases as the altitude increases.
Answer: (B) water boils at a lower temperature at high altitude.
Why: With less pressure on them, steam bubbles are able to form and grow at lower temperatures.
Problem 2:
You have three incandescent light bulbs that are each consuming 50 W (50 watts) of power. Bulb #1 is a 50W halogen bulb operating at its designed power level. Bulb #2 is a three-way bulb, with 50W, 100W, and 150W settings, which is presently operating at its 50W setting. Bulb #3 is an ordinary 100W light bulb that is connected to a dimmer system so that it is only consuming 50 W. Rank these three bulbs from brightest to dimmest (i.e. put the bulb that that emits the most visible light first).
(A) #2 (brightest), #3 (middle), #1 (dimmest).
(B) #2 (brightest), #1 (middle), #3 (dimmest).
(C) #3 (brightest), #1 (middle), #2 (dimmest).
(D) #1 (brightest), #2 (middle), #3 (dimmest).
Answer: (D) #1 (brightest), #2 (middle), #3 (dimmest).
Why: A halogen bulb has a high normal operating temperature and produces visible light relatively efficient. An ordinary bulb has a moderate operating temperature and produces somewhat more invisible infrared than the halogen bulb. It is thus less efficient. But an ordinary bulb at much less than normal power has a low operating temperature and produces far, far more infrared than visible light. It is very inefficient.
Problem 3:
When you casually toss a melon into the hanging basket of spring scale at the grocery store, the basket bounces up and down a couple of times. If you now toss a second melon into that basket, along with the first melon, the basket will begin to bounce again. This time the frequency of that bouncing will
(A) be the same rate as when it contained just one melon.
(B) be slower than when it contained just one melon.
(C) be faster than when it contained just one melon.
(D) depend on whether the second melon was heavier or lighter than the first melon.
Answer: (B) be slower than when it contained just one melon.
Why: With more mass bouncing up and down on the same spring, the larger inertia will slow the period of this harmonic oscillator.
Problem 4:
You are in the kitchen with three mixing bowls in front of you. One bowl is metal, the second is glass, and the third is plastic. All three are at exactly the same temperature: the 68 °F (20 °C) temperature of the room. If you touch the three bowls together,
(A) heat will flow from the plastic bowl to the glass bowl, and from the glass bowl to the metal bowl.
(B) heat will flow from the metal bowl to the glass bowl, and from the glass bowl to the plastic bowl.
(C) no heat will flow between the bowls.
(D) heat will flow from the glass bowl to both the plastic bowl and the metal bowl.
Answer: (C) no heat will flow between the bowls.
Why: Because the three bowls have the same temperature, they are in thermal equilibrium. That situation actually helps define temperature. No heat flows spontaneously between objects that are at thermal equilibrium.
Problem 5:
An ordinary incandescent light bulb contains some inert gas inside its glass enclosure because the gas increases
(A) the filament's life while causing a small decrease in the bulb's energy efficiency.
(B) the bulb's energy efficiency while causing a small decrease in the filament's life.
(C) the filament's temperature by providing it with extra chemical potential energy.
(D) both the filament's life and the bulb's energy efficiency.
Answer: (A) the filament's life while causing a small decrease in the bulb's energy efficiency.
Why: The filament's tungsten sublimes at high temperature. Adding the inert gas slows this sublimation by bouncing the tungsten atoms back onto the filament. But the gas also allows convective heat losses that diminish the bulb's energy efficiency.
Problem 6:
You accidentally bump into a bookcase. It tilts briefly but then returns to upright, and you breathe a sigh of relief. When you first bumped the bookcase, its center of gravity moved
(A) upward and its gravitational potential energy increased.
(B) downward and its gravitational potential energy decreased.
(C) downward and its gravitational potential energy increased.
(D) upward and its gravitational potential energy decreased.
Answer: (A) upward and its gravitational potential energy increased.
Why: The bookcase is in a stable equilibrium, as evidenced by its tendency to return to that equilibrium after being bumped. To obtain this stable equilibrium, the bookcase's potential energy must increase as it tilts so that it accelerates in the direction that reduces its potential energy as quickly as possible--namely back toward equilibrium. That arrangement requires that its center of gravity rise, since gravitational potential energy is the only form of potential energy in this situation.
Problem 7:
A wave travels across the water on a lake, heading northward. As the result of this wave's passage, water on the surface of the lake
(A) moves toward the north by a distance that is proportional to the amplitude (height) of the wave.
(B) returns to its original location and makes no overall movement.
(C) moves toward the north continuously at the speed of the wave.
(D) moves toward the north by a distance equal to one wavelength of the wave.
Answer: (B) returns to its original location and makes no overall movement.
Why: The water at the surface of the lake circles as the crests pass, but never makes any overall progress across the lake. The surface water returns to its original position after the wave is gone.
Problem 8:
The flow of air around a ball can be perfectly laminar only when the ball is traveling extremely slowly through the air. During such laminar flow, the ball experiences
(A) viscous drag but no pressure drag.
(B) neither viscous drag nor pressure drag.
(C) pressure drag but no viscous drag.
(D) both viscous drag and pressure drag.
Answer: (A) viscous drag but no pressure drag.
Why: Pressure drag only occurs when the ball leaves a turbulent wake behind it, not when it has perfectly laminar flow. On the other hand, viscous drag is always present when something moves through air.
Problem 9:
The brass pendulum of a particular grandfather clock has a mass of 2 kilograms and completes its swing once every 2 seconds. If you were to replace the brass pendulum with an identically shaped gold pendulum having a mass of 4 kilograms, it would complete its swing once every
(A) 4 seconds.
(B) 2 seconds.
(C) 16 seconds.
(D) 8 seconds.
Answer: (B) 2 seconds.
Why: A pendulum's period depends only on its length and on the strength of gravity. Altering the pendulum's mass makes no difference to its period. That's because the pendulum's mass increases not only its inertia, but also its weight and therefore the restoring force that swings that mass back and forth. The mass cancels out of the equations of motion.
Problem 10:
When you stand in front of an open refrigerator, trying to decide which flavor of Ben and Jerry's to eat, you feel cold, even though no chilled air actually touches your skin. The reason you feel cold is that
(A) the cold refrigerator is radiating cold toward you and is lowering the temperature of your skin directly.
(B) you are radiating heat toward the refrigerator but receiving relatively little radiated heat in return.
(C) you can sense the presence of nearby cold air, even though it is not exchanging heat with your skin.
(D) you can sense the presence of nearby cold air, even though it is not exchanging cold with your skin.
Answer: (B) you are radiating heat toward the refrigerator but receiving relatively little radiated heat in return.
Why: You and the refrigerator are exchanging heat via radiation. Since your temperature is higher than its temperature, you send more heat toward it as thermal radiation than it sends toward you. Overall, you lose heat and feel cold.
Problem 11:
A stunt pilot flips her plane upside-down and flies horizontally past the spectators. While her plane and its wings are upside-down and she is flying horizontally, the average air pressure is highest on the
(A) sky side of each wing and the average air speed is highest on the ground side of each wing.
(B) sky side of each wing and the average air speed is highest on the sky side of each wing.
(C) ground side of each wing and the average air speed is highest on the ground side of each wing.
(D) ground side of each wing and the average air speed is highest on the sky side of each wing.
Answer: (D) ground side of each wing and the average air speed is highest on the sky side of each wing.
Why: Since the plane is traveling horizontally, it must be obtaining lift from the air. Therefore, the pressure on the ground side of its wings must be higher than the pressure on the sky side. For that to happen, the average speed of the air on the sky side of the wings must be faster than on the ground side of those wings.
Problem 12:
You're taking a nap on the couch. A pillow is supporting your head so that your head is in equilibrium. The pillow is dented downward 2 inches from its equilibrium shape. Someone walks into your room so you lift your head off the pillow. You then let your head fall freely against the pillow. Your head bounces off the pillow, denting the pillow downward 4 inches before rebounding back upward. The point at which your head reaches maximum speed during this fall and bounce is when it is
(A) just touching the pillow as it rebounds back upward.
(B) denting the pillow downward 2 inches as it travels downward.
(C) denting the pillow downward 4 inches during the bounce.
(D) just touching the pillow as it travels downward.
Answer: (B) denting the pillow downward 2 inches as it travels downward.
Why: At the 2-inch dent point, your head is in equilibrium and is no longer accelerating downward. Up to that moment, your head was picking up speed in the downward direction. It thus reaches its maximum speed just as it stops accelerating downward.
Problem 13:
You open the refrigerator in your room and put in a case of room-temperature root beer. After an hour, the root beer is ice cold. If your room air didn't exchange any heat with the outdoor air during that time, the room air will be
(A) colder because the refrigerator reverses natural heating, so that things get colder rather than hotter.
(B) colder because as the refrigerator struggles to cool the root beer, some of the cold it produces inevitably leaks out into the room as the result of imperfect insulation.
(C) warmer because the refrigerator will have pumped heat out of the root beer and into the room air.
(D) warmer because some of the heat from the root beer inevitably leaks out into the room as the result of imperfect insulation.
Answer: (C) warmer because the refrigerator will have pumped heat out of the root beer and into the room air.
Why: The refrigerator can get rid of the heat in the root beer, so it pumps that heat into the room air. In the process, it even creates a little additional heat out of electric energy. Overall the room air's thermal energy increases and so does its temperature.
Problem 14:
A harmonic oscillator has energy as it vibrates. While complicated harmonic oscillators can involve many different forms of energy, the fewest energy forms that a vibrating harmonic oscillator can have is
(A) one.
(B) three.
(C) two.
(D) zero.
Answer: (C) two.
Why: A harmonic oscillator always involves kinetic energy and at least one form of potential energy in its motion. The prototypical harmonic oscillator is a mass on a spring, arranged horizontally so that gravity doesn't get involved at all. Then the only two forms of energy that are active are kinetic energy (when the mass is moving) and elastic potential energy (when the spring isn't at its equilibrium length).
Problem 15:
Soil heats up much faster than water when the two are exposed to sunlight. Use that fact and your understanding of heat transfer to predict which way the wind will blow near the surface of the earth as the sun rises near the seashore.
(A) The surface wind will blow from the land toward the water.
(B) The surface wind will blow alternately back and forth along the shore, parallel to the boundary between land and water. It will reverse directions every few minutes.
(C) The surface wind will blow steadily in one direction along the shore, parallel to the boundary between land and water.
(D) The surface wind will blow from the water toward the land.
Answer: (D) The surface wind will blow from the water toward the land.
Why: When sunlight strikes the land, it heats quickly and warms the nearby air. This air is lifted upward by buoyant forces and is replaced by cooler air from elsewhere. Since the water doesn't heat quickly, the air above water remains relatively cool and it is this air that flows toward land to replace the rising air over that land.
Problem 16:
Flowing honey is less likely to become turbulent than flowing water because
(A) honey's large density favors laminar flow.
(B) water's large viscosity favors turbulent flow.
(C) water's large pressure favors turbulent flow.
(D) honey's large viscosity favors laminar flow.
Answer: (D) honey's large viscosity favors laminar flow.
Why: Honey is so thick (viscous) that its internal frictional forces keep it flowing smoothly except in extraordinary circumstances. Viscosity always favors laminar flow while density, speed, and larger obstacle size favor turbulent flow.
Problem 17:
When the space shuttle is in orbit outside the atmosphere, its orientation becomes completely flexible. In which orientation do the astronauts experience the greatest sensation of weightlessness?
(A) When the tail of the shuttle is pointing in the direction of its velocity.
(B) When the shuttle is turned at right angles to the direction of its velocity.
(C) Any orientation.
(D) When the nose of the shuttle is pointing in the direction of its velocity.
Answer: (C) Any orientation.
Why: The astronauts are in free fall regardless of the shuttle's orientation, so they simply fall along with it. They always feel weightless, except when the shuttle's engines are firing and it is accelerating at a rate other than free fall.
Problem 18:
A sealed bottle contains only liquid water and gaseous water. The container's temperature can be
(A) below 100 °C only.
(B) above 100 °C only.
(C) equal to 100 °C only.
(D) below 100 °C, equal to 100 °C, or above 100 °C.
Answer: (D) below 100 °C, equal to 100 °C, or above 100 °C.
Why: Liquid and gaseous water can be in equilibrium over a very wide range of temperatures. The only thing special about 100 °C is that the equilibrium pressure of gaseous water at that temperature (water's vapor pressure) is atmospheric pressure.
Problem 19:
If you place one end of a copper bar in the fire and hold on to the other end, you're likely to have hot fingers very soon. The main carrier of thermal energy as heat flows through that metal bar is/are
(A) vibrating atoms pushing against one another.
(B) molecules moving through the bar.
(C) thermal radiation flowing through the bar.
(D) electrons moving through the bar.
Answer: (D) electrons moving through the bar.
Why: Metals are better conductors than insulators because the same electrons that carry electricity through metals also carry heat. Since they travel long distances in a single, quick flight, they also carry heat quickly through metal.
Problem 20:
You are trying to clean your car and have just poured a bucket of water across the hood. The dirt on the surface barely moved at all as the water flowed past it. That's because
(A) the moving water has zero kinetic energy, due to Bernoulli's equation.
(B) the moving water has zero pressure, due to Bernoulli's equation.
(C) water very near the hood's surface is almost motionless and barely pushes on the dirt.
(D) water exerts no significant drag forces on very small particles.
Answer: (C) water very near the hood's surface is almost motionless and barely pushes on the dirt.
Why: Water in the boundary layer is moving more slowly than the free flowing stream farther from the surface. Right at the surface, the water is motionless altogether. Since the boundary layer water is relatively slowly moving, it doesn't push well on dirt that's attached to the surface and thus doesn't clean all that well without help from a brush or sponge.
Problem 21:
Which of the following quantities is not conserved?
(A) energy
(B) angular momentum
(C) entropy
(D) momentum
Answer: (C) entropy
Why: Entropy is a quantity that's interesting because it never diminishes in a thermal isolated system. It's certainly not conserved.
Problem 22:
When you pull a tablecloth out from under a set of dishes, it's important to pull the cloth as fast as possible because
(A) the work done on the dishes by the cloth is proportional to the time during which the cloth pulls on them.
(B) the weight of the dishes on the cloth is proportional to the time during which the cloth is moving.
(C) the force of sliding friction that the cloth exerts on the dishes is proportional to the time during which the cloth is moving.
(D) the momentum transferred to the dishes is proportional to the time during which the cloth pulls on them.
Answer: (D) the momentum transferred to the dishes is proportional to the time during which the cloth pulls on them.
Why: The momentum transferred to the dishes involves an impulse, which is equal to the force times the time over which that force acts. By keeping that time as short as possible, you minimize the impulse and therefore the total momentum given to the dishes. They then tend to remain nearly at rest.
Problem 23:
To make it less likely that a car engine will "knock" (have its fuel/air mixture ignite too early), the engine is designed so that
(A) the fuel/air mixture is not compressed too tightly.
(B) the fuel/air mixture is compressed as tightly as possible.
(C) the fuel/air mixture remains cold until the sparkplug fires.
(D) the fuel/air mixture stays at atmospheric pressure until the sparkplug fires.
Answer: (A) the fuel/air mixture is not compressed too tightly.
Why: Knocking occurs when the work done during compression causes the fuel/air mixture to heat all the way to the ignition temperature. By limiting the compression, the engine limits the ultimate temperature reached during compression and avoids knocking.
Problem 24:
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) Their temperatures rise until they are able to radiate heat away into space as fast as it arrives from the sun.
(B) They have solar panels that convert the sun's thermal radiation completely into electricity and avoid any need to eliminate heat.
(C) They use air conditioners to eliminate the excess thermal energy as rapidly as it arrives.
(D) 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.
Answer: (A) Their temperatures rise until they are able to radiate heat away into space as fast as it arrives from the sun.
Why: A satellite reaches thermal equilibrium, at which point the heat flowing into it exactly balances the heat flowing out of it. The hotter the satellite becomes, the more it radiation thermal energy. Therefore, the satellite's temperature rises until it radiates heat away as fast as it comes in from the sun.
Problem 25:
One of the strength training machines in the exercise facility has an interesting behavior: as you lift its handles upward, you must push up with a force of 450 newtons (100 pounds). But as you lower its handles back downward, you must push up with a force of 600 newtons (133 pounds). During your exercise routine, you move these handles slowly up and down a dozen times, and leave them exactly where you found them. As the result of this routine, your total energy (the total energy of you personally, and not including that of the machine)
(A) decreases.
(B) stays the same but you convert thermal energy into food energy.
(C) increases.
(D) stays the same but you convert food energy into thermal energy.
Answer: (C) increases.
Why: On the way up, you do work on the machine. On the way down, the machine does work on you. Since the forces between you and the machine are larger on the way down, the machine does more work on you during the lowering process than you do on the machine during the raising process. Overall, the machine transfers energy to you and your total energy increases.
Problem 26:
The space shuttle is orbiting the earth at an altitude of several hundred kilometers and completes each circular orbit in about 90 minutes. If the pilot fires the rocket engines for a few minutes, increasing the shuttle's speed in the forward direction, it will
(A) shift into a new circular orbit with a larger diameter but will still complete each orbit in about 90 minutes.
(B) shift into a new elliptical orbit that is larger than its previous circular orbit and will complete each orbit slower--in more than 90 minutes.
(C) shift into a new circular orbit with a larger diameter and will complete each orbit faster--in less than 90 minutes.
(D) remain in the same circular orbit but will complete each orbit faster--in less than 90 minutes.
Answer: (B) shift into a new elliptical orbit that is larger than its previous circular orbit and will complete each orbit slower--in more than 90 minutes.
Why: Speeding the shuttle up will increase the amount of centripetal acceleration it needs in order to follow a circular path. Instead, it will arc outward into a new orbit that isn't circular, but rather elliptical.
Problem 27:
Which of these stars has the hottest surface temperature?
(A) A yellowish star.
(B) A reddish star.
(C) The sun.
(D) A bluish star.
Answer: (D) A bluish star.
Why: The star is bluish because of its extreme temperature; its black-body spectrum includes a great deal of short wavelength light, bluish light.
Problem 28:
A car has been wrapped in thermal insulation so that it can't lose any heat to the surrounding air. As a result of this insulation, the car's engine will
(A) lose its ability to turn thermal energy into work.
(B) become more fuel-efficient because it will retain more of the burned fuel's energy.
(C) be essentially unaffected, since its main function--producing disordered work--is not dependent on ordered heat.
(D) be essentially unaffected, since its main function--producing ordered work--is not dependent on disordered heat.
Answer: (A) lose its ability to turn thermal energy into work.
Why: As a heat engine, the car engine can only produce work out of heat by letting heat flow from hot to cold. If you spoil this heat transfer (from hot burned gases to cold outside air), you prevent it from operating as a heat engine and it stops producing work.
Problem 29:
After clearing the bar in the high jump, you land softly on a giant mattress. Landing on the mattress is much more comfortable than landing on a sand heap of equal size because
(A) you transfer less momentum to the mattress in coming to a stop than you would have transferred to the sand heap in coming to a stop.
(B) you transfer more momentum to the mattress in coming to a stop than you would have transferred to the sand heap in coming to a stop.
(C) the force that the mattress exerts on you to stop your descent is much less than the force that the sand heap would have exerted on you.
(D) your velocity is less as you land on the mattress than it would have been if you'd landed on the sand heap.
Answer: (C) the force that the mattress exerts on you to stop your descent is much less than the force that the sand heap would have exerted on you.
Why: When you land and stop after the jump, you're going to lose all your downward momentum one way or the other. The impulse involved doesn't depend on how fast you stop. But the impulse is force times time, so you'd like to maximize time in order to minimize force. The mattress lengthens you stop and thus reduces the force involved.
Problem 30:
The tides are strongest near the equator because that's where the
(A) centripetal force of the earth is strongest.
(B) earth's gravity is weakest.
(C) centrifugal force due to the earth's rotation is strongest.
(D) tidal bulges caused by the moon are tallest.
Answer: (D) tidal bulges caused by the moon are tallest.
Why: The moon causes the earth's waters to bulge outward at the point nearest the moon and at the point farthest from the moon. These two bulges are near the equator and thus make the tides largest near the equator.
Problem 31:
A stream of smoothly flowing water arcs through the air and hits the side window of a house. It then spreads out smoothly in all directions along the window. At the surface of the window, right where the stream of water hits it, the water's pressure is
(A) lower than atmospheric and the water's speed is faster than in the stream.
(B) higher than atmospheric and the water's speed is faster than in the stream.
(C) higher than atmospheric and the water's speed is slower than in the stream.
(D) lower than atmospheric and the water's speed is slower than in the stream.
Answer: (C) higher than atmospheric and the water's speed is slower than in the stream.
Why: When the water hits the window, it undergoes an outward bend--a bend away from the surface. That type of bend requires that the pressure nearest the window be higher than the pressure far away from it. The water's pressure rises as it approaches the window and to obtain the higher pressure, the water loses speed.
Problem 32:
Mike and Johnny are in trouble for scuffling in the school cafeteria. While Mike admits that he pushed Johnny, who immediately fell over backward, Mike claims that Johnny pushed back and is thus just as guilty. From the perspective of physics,
(A) Johnny didn't push back on Mike.
(B) Johnny did push back on Mike, with exactly the same amount of force.
(C) Johnny pushed back on Mike, but with less force than Mike exerted on him.
(D) Johnny pushed back on Mike, but with more force than Mike exerted on him.
Answer: (B) Johnny did push back on Mike, with exactly the same amount of force.
Why: In accordance with Newton's third law, any time Mike pushes on Johnny, Johnny must push back on Mike with an equal but oppositely directed force.
Problem 33:
Two steel balls, one of which weighs twice as much as the other, roll off of a horizontal table with the same speeds. In this situation,
(A) both balls impact the floor at approximately the same horizontal distance from the base of the table.
(B) the lighter ball impacts the floor at about half the horizontal distance from the base of the table than does the heavier.
(C) the heavier ball impacts the floor at about half the horizontal distance from the base of the table than does the lighter.
(D) the heavier ball hits considerably closer to the base of the table than the lighter, but not necessarily half the horizontal distance.
Answer: (A) both balls impact the floor at approximately the same horizontal distance from the base of the table.
Why: Both balls travel horizontally at the same speed and take the same amount of time to fall. They thus hit the ground together. The fact that one has more mass than the other has no effect on their trajectories. All objects fall at the same rate, in the absence of air resistance.
Problem 34:
You're sitting on a park bench while your dog walks at the end of a spring-loaded leash. This leash emerges from a plastic container with a handle and can extend up to 5 meters (17 feet) if the dog pulls on it hard enough. As the leash extends outward, a spring in the container stretches. When the dog stops pulling, that spring then retracts the leash back into the container. As the dog pulls the leash outward, stretching the spring, she does work on the leash. During which meter of extension does the dog do the most work on the leash?
(A) The work the dog does is the same during each of the five meters of extension.
(B) During the first meter--when the leash first begins to extend.
(C) During the fifth meter--just before the leash is fully extended.
(D) During the third meter--when the leash is at the middle of its extension.
Answer: (C) During the fifth meter--just before the leash is fully extended.
Why: The spring that controls the leash pulls more and more strongly on the leash as it stretches. The force it exerts on the leash is proportional to how far it has been stretched. As the dog pulls the leash out of its container, the force on the leash increases and the leash pulls harder on the dog. The dog thus pulls harder on the leash to pull it out and does the most work during the last meter of extension.
Problem 35:
If you hold the bottom of a water-filled test tube and heat the top of that tube with a flame, the water inside will boil while your fingers remain cool. If you reverse this arrangement--holding the top of the tube and heating the bottom of the tube--you'll burn your fingers. The reason for this difference is that
(A) heat flows naturally from a hot object to a cold object, not the reverse.
(B) conduction doesn't function when the hot object is above the cold object.
(C) convection doesn't function when the hot object is above the cold object.
(D) radiation doesn't function when the hot object is above the cold object.
Answer: (C) convection doesn't function when the hot object is above the cold object.
Why: Natural convection isn't magic. It requires that the buoyant force lift heated fluid away from a hot object and carry that fluid upward to a cold object. If the hot object is above the cold object, natural convection doesn't work.
Problem 36:
Ice floats in your glass of water because
(A) the 2nd law of thermodynamics prevents a solid from sinking in its own liquid form.
(B) having ice sink in liquid water would decrease the overall entropy of the system.
(C) having a solid sink in its own liquid form would violate the conservation of energy.
(D) the density of ice is less than the density of water.
Answer: (D) the density of ice is less than the density of water.
Why: Floating is a density problem. Ice is simply less dense than water. However, this situation is highly unusual; most solids sink in their own liquid because their solid form is more dense than their liquid form.
Problem 37:
You are in a dark 20 °C room, looking at a perfectly shiny metal ball that has a temperature of 1000 °C. The ball doesn't emit any visible light because the shiny ball
(A) isn't hot enough to emit visible light.
(B) neither emits nor absorbs any thermal radiation.
(C) would need some white in it in order to produce visible light.
(D) has none of the flat surfaces needed to emit light.
Answer: (B) neither emits nor absorbs any thermal radiation.
Why: A perfectly shiny object has an emissivity of 0, meaning that it is completely unable to emit or absorb electromagnetic radiation. It simply reflects back any radiation that hits it.
Problem 38:
When a basketball bounces against the ground and dents, the air inside that ball is temporarily compressed. The compression ends when the ball undents during the rebound. The temperature of air inside the ball
(A) remains constant throughout the bounce, because thermal energy is conserved.
(B) decreases during the denting process and increases during the undenting processes.
(C) increases during the denting process and decreases during the undenting processes.
(D) increases during both the denting and undenting processes.
Answer: (C) increases during the denting process and decreases during the undenting processes.
Why: As the air compresses during a bounce, the ball's skin does work on it and its temperature rises. During the rebound, the air does work on the ball's skin and its temperature drops. This all happens so fast that it's difficult to detect except with sophisticated instruments.
Problem 39:
You fill two identical mugs with coffee, but the coffee in one mug is hotter than that in the other mug. You place the two mugs simultaneously in a microwave oven and turn it on briefly. As a result, you add 1 joule of thermal energy to each mug. Which mug experiences the larger increase in entropy (if any)?
(A) The two mugs experience equal increases in entropy.
(B) The mug containing the colder coffee experiences the larger increase in entropy.
(C) Neither mug experiences any increase in entropy.
(D) The mug containing the hotter coffee experiences the larger increase in entropy.
Answer: (B) The mug containing the colder coffee experiences the larger increase in entropy.
Why: A joule of heat is more disordering to a cold object than it is to a hot object. Therefore the cold coffee experiences the larger rise in entropy.
Problem 40:
It's a windy day and there are waves on the surface of the open ocean. The wave crests are 40 feet apart and 5 feet above the troughs as they pass a school of fish. The waves push on fish and making them accelerate. The fish don't like this jostling, so to avoid it almost completely the fish should swim
(A) as fast as possible.
(B) at least 20 feet below the surface of the water.
(C) at least 5 feet below the surface of the water.
(D) as close to the surface of the water as possible.
Answer: (B) at least 20 feet below the surface of the water.
Why: The local water moves in a circular motion as a wave passes. This motion is strongest at the surface and diminishes with depth. By the time the fish are about ½ a wavelength below the surface, the motion is rather small and not so annoying to the fish. That's a depth of about 20 feet.
Problem 41:
Many old homes were heated by steam. The steam was produced in a basement boiler and it floated upward through pipes to radiators in various rooms. The steam became water inside those radiators and sank downward through the pipes to the boiler to begin its journey again. In the process, the radiators heated the room air. The rising steam and the descending water both had exactly the same temperature, so where did the thermal energy that heated the room air come from?
(A) From the work done when steam contracted to become liquid water.
(B) From the gravitational potential energy released when the dense water descended.
(C) From the chemical potential energy released when the molecules in steam bound together to become liquid water.
(D) From the kinetic energy of the fast-flowing steam as it turned into slow-flowing liquid water.
Answer: (C) From the chemical potential energy released when the molecules in steam bound together to become liquid water.
Why: As the steam condenses to liquid water, it releases an enormous amount of thermal energy--the latent heat of vaporization. This thermal energy comes from chemical potential energy in the steam that is released as the molecules bind together to form water.
Problem 42:
You are bouncing up and down on a springboard, preparing to dive into the pool. While you're in the air above the board, your acceleration is
(A) zero because you are not touching anything.
(B) upward and constant until you reach the peak, then it becomes downward and constant.
(C) initially upward but it gradually diminishes to zero as you reach the peak and then it gradually becomes more and more downward.
(D) downward and constant.
Answer: (D) downward and constant.
Why: When you're in the air, you are falling. Whether you are heading upward or downward, your acceleration is always the acceleration due to gravity, which is in the downward direction. The fact that you continue upward for a while is the result of your inertia.
Problem 43:
If you strike a stiff, spring-like surface with a mallet and listen to the sound it emits, you'll notice that this sound is more complicated than that emitted by a string or a thin bar. That's because surfaces
(A) cannot experience nonuniform accelerations (accelerations that vary from place to place).
(B) have overtones that aren't integer multiples of their fundamental frequencies.
(C) are not harmonic oscillators.
(D) are harmonic oscillators.
Answer: (B) have overtones that aren't integer multiples of their fundamental frequencies.
Why: While one-dimensional objects such as strings can vibrate in integer fractional pieces (1/2, 1/3, 1/4, etc.) and thus have simple harmonics, two-dimensional surfaces vibrate in complicated patterns and have complicated overtones.
Problem 44:
Which of the following produces the most disorder (entropy) when done in the most efficient possible manner?
(A) Stretching a 10-kilogram spring 10 meters, using energy from water flowing in a river.
(B) Lifting 1000 kilograms of water upward a distance of 6 meters, using energy from a windmill (a huge wind-driven fan).
(C) Burning a 1-kilogram candle.
(D) Raising a 7-kilogram bowling ball 1000 meters into the sky, using energy from a car battery.
Answer: (C) Burning a 1-kilogram candle.
Why: Converting one form of ordered energy into another doesn't create any entropy. However, turning ordered energy (such as the chemical potential energy in wax) into disordered energy (thermal energy) creates disorder and entropy. Only burning the candle converts ordered energy into disordered energy.
Problem 45:
You are holding a drinking straw in your hand so that both its ends are open to the air. When you blow air across one of those ends, the air in that straw vibrates and the straw emits a tone--its fundamental pitch. If you replace the air in the straw with carbon dioxide, which is more dense than air, the sound that the straw emits will
(A) have the same pitch but will decrease in volume.
(B) decrease in pitch (shift to a lower frequency).
(C) increase in pitch (shift to a high frequency).
(D) have the same pitch but will increase in volume.
Answer: (B) decrease in pitch (shift to a lower frequency).
Why: Carbon dioxide gas is more dense than air and gives more mass to the column of gas in the straw. The forces involved in the gas's vibration won't change but the mass will, so the motions will be slowed and the pitch will be lower.
Problem 46:
The air in this room consists of countless tiny, independent molecules. You can be sure that these air molecules won't all shift spontaneously to the other side of the room (leaving you in a vacuum) because that would
(A) violate Newton's laws of motion.
(B) be extremely unlikely and therefore violate the 2nd law of thermodynamics.
(C) violate Bernoulli's equation.
(D) not conserve energy and therefore violate the 1st law of thermodynamics.
Answer: (B) be extremely unlikely and therefore violate the 2nd law of thermodynamics.
Why: The laws of motion don't rule out a shift of all the air molecules to one side of the room. But that shift would be incredibly unlikely. The second law of thermodynamics observes that the universe tends toward more and more likely arrangements, not toward unlikely arrangements.
Problem 47:
At what place in or near the jet engine is gas moving the fastest relative to the flying airplane?
(A) In the air flowing into the engine's inlet duct.
(B) In the plume of exhaust gas flowing out of the engine's outlet duct.
(C) In the engine's turbine section.
(D) In the engine's compressor section.
Answer: (B) In the plume of exhaust gas flowing out of the engine's outlet duct.
Why: The jet engine's great achievement is that it works with the air at low speed and high pressure. The air slows as it enters the jet's inlet duct, travels relatively slowly through the compressor, combustion chamber, and turbines, and then speeds up dramatically as it expands out of the outlet duct. It is in that outlet duct that it reaches its greatest speed and carries away the most momentum. The plane receives momentum in the opposite direction and is thus propelled forward.
Problem 48:
The maximum speed a rocket can achieve is
(A) the speed of light.
(B) equal to the speed of its exhaust plume.
(C) less than the speed of its exhaust plume.
(D) greater than the speed of its exhaust plume but less than the speed of light.
Answer: (D) greater than the speed of its exhaust plume but less than the speed of light.
Why: The exhaust speed doesn't limit the rocket's ultimate speed. Only the speed of light is beyond a rocket's grasp because no massive object can ever travel at the speed of light.
Problem 49:
A fine crystal wineglass (actually made from lead-based glass) emits a long, pure tone when you flick it with your finger, while a cheap ordinary wineglass emits a "thunk" sound instead. Although you can break either wineglass with sound by choosing the right tone and making it sufficiently loud, it's easier to break the crystal wineglass because the crystal wineglass
(A) is made from a weaker material and fractures more easily.
(B) vibrates in response to a broader range of pitches.
(C) wastes less energy as it vibrates and thus stores energy better.
(D) can't bend at all without breaking.
Answer: (C) wastes less energy as it vibrates and thus stores energy better.
Why: Even though lead crystal is stronger than ordinary glass, its resonant behavior makes it vulnerable to sympathetic vibration and damage. Hitting a crystal wineglass's resonance with a tone is difficult, but if that tone is loud enough it will gradually pour enough energy into the glass to break it. An ordinary wineglass retains energy so poorly that it's hard to break it with a tone. You need too much volume.
Problem 50:
An incandescent light bulb places its tungsten filament inside a glass enclosure because the enclosure
(A) allows the pressure around the filament to be reduced so that the tungsten doesn't melt.
(B) keeps the tungsten atoms from subliming.
(C) protects the filament from air and keeps it from burning.
(D) keeps the filament from losing heat to its surroundings.
Answer: (C) protects the filament from air and keeps it from burning.
Why: Tungsten burns in air and keeping the air away from it is one of the crucial steps in making a practical light bulb.
PART II: SHORT ANSWER QUESTIONS
Please give a brief answer in the space provided. Words written outside of the allotted space will not be read during grading. Part II is worth 33% of the grade on this examination.
Problem 1:
Pine derby cars are small wooden cars that roll down a gently curving track that starts with a fairly steep slope and gradually becomes less steep. The track ends up traveling horizontally for several meters before the finish line. The cars are released from rest and the first one that crosses the finish line at the end of the track wins.
(A) Assuming no air resistance or friction, during which part of its trip does the car have its greatest speed?
Answer: Along the horizontal portion at the bottom of the hill.
Why: The car's total energy remains constant during the descent, but it converts gravitational potential energy into kinetic energy. Along the straightaway at the bottom of the hill, the car's kinetic energy is maximal and constant. Since kinetic energy is directly related to speed, the point of maximum kinetic energy is also the point of maximum speed.
(B) Assuming no air resistance or friction, during which part of its trip does the car have its greatest acceleration?
Answer: At the top of the hill (at the start of the race).
Why: The car's acceleration is highest when the net force on it is strongest. That occurs at the steepest part of the hill, which in this case is the starting line.
(C) In reality, friction does affect these little cars. The plastic car wheels spin on fine, stationary wire axles. There is friction between each wheel and the ground, and there is friction between each wheel and the axle that supports it. Why is more energy wasted by friction between the wheel and axle than by friction between the wheel and ground?
Answer: The wheel and axle experience sliding friction (converting ordered energy into thermal energy), while the wheel and ground experience only static friction (which wastes no ordered energy).
Why: Even though the wheel and axle aren't moving very far across one another, they are sliding as they do and that sliding wastes energy as thermal energy. The wheel and ground simply touch and release; they don't slide. As a result, they don't waste energy making thermal energy.
(D) You must put a 20-gram weight on your car to reach the required racing weight. If you want your car to travel as fast as possible, roughly where on the car should you put that weight? (This is a challenging question that I have been asked dozens of times by the parents of children with pine derby cars. If you think in terms of energy, you should be able to answer this question.)
Answer: At the back end of the car.
Why: The farther the weight descends, the more gravitational potential energy it will release and the faster the car will go. By putting the weight in the rear of the car, you are making it so that the weight is high up at the start (while the car is tilted with its rear end highest) and low at the end of the race (while the car is horizontal and its rear end isn't particularly high any more).
Problem 2:
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 above atmospheric pressure (about 5 times atmospheric pressure plus ordinary 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?
Answer: The water pressure at ground level can't support a column of water taller than 50 meters.
Why: It takes pressure to support the weight of a column of water and one atmosphere of pressure can support a column of water about 10 meters tall. With only 5 atmospheres of pressure to support it, the column of water in the fire hose can't exceed about 50 meters in height.
(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.
Answer: The water's total energy isn't large enough to lift it more than 50 meters above the ground, regardless of how you try to make it flow higher.
Why: In the flowing water, energy is conserved. The water obeys Bernoulli's equation. It simply doesn't have enough total energy to rise that high, even if it turned all its energy into gravitational potential energy.
(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
Answer: Using a narrow nozzle allows the water to move slowly through the hose and speed up only as it sprays out of the nozzle. The slower moving water wastes less energy to friction in the hose.
Why: The water wastes energy if it moves quickly through the entire hose. By constricting the hose only at its end with a nozzle, the firefighters reduce the water's speed through the hose and also the amount of energy wasted to viscous drag as the water flows through the hose.
(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?
Answer: It takes considerable thermal energy to convert water at 100 °C into steam at 100 °C.
Why: If the materials are only just above water's boiling temperature, they'll cool quickly and only be able to boil a very small amount of water. They have to be extremely hot to heat the water to its boiling temperature and still have enough thermal energy left to convert water at 100 °C into steam at 100 °C.
Problem 3:
You and a friend are playing pool (billiards) at a bar one evening. In this game, one ball (the cue ball) is used to knock the other balls into pockets around the edges of a table. For this problem assume that there is no friction between the balls and the table.
(A) It is your shot and you hit the cue ball toward one of the other balls. If the two balls have the same mass and the cue ball hits the other ball squarely, the cue ball will stop and the other ball will begin to move. What will the velocity (magnitude and direction) of the other ball be after the collision? (Answer by comparing to the original velocity of the cue ball.)
Answer: The second ball's final velocity will be exactly equal to the cue ball's initial velocity, both in magnitude and direction.
Why: Since momentum is conserved, the cue ball must give all of its initial momentum to the second ball. Since the two balls have identical mass and the momentum is equal to mass times velocity, the second ball's final velocity must equal the cue ball's initial velocity in order to conserve momentum properly.
(B) If the cue ball had twice the mass of the other ball, would the cue ball remain stopped after the collision?
Answer: No.
Why: The cue ball would continue forward with the other ball because the other ball hasn't enough mass to stop the first ball's momentum and still conserve energy.
(C) If the cue ball had half the mass of the other ball, which ball would experience a greater force during the collision?
Answer: They would experience equal forces (but in opposite directions).
Why: The two balls would repel one another with equal but opposite forces, in accordance with Newton's third law.
(D) If the cue ball strikes one of the table's side bumper at right angles, it will rebound directly backward; the ball's velocity will reverse perfectly. Will the ball's (1) energy and (2) momentum change as the result of this bounce, and if so, by how much?
Answer: (1) energy will not change but (2) momentum will reverse perfectly in direction
Why: The ball's energy doesn't depend on its direction of motion. Since its speed doesn't change, neither does its kinetic energy. But the ball's momentum has the direction of its velocity, so it reverses directions.
Problem 4:
Because of the greenhouse effect, it's important to reduce our consumption of fossil fuels. With that in mind, scientists and engineers at Ideal Motors Corporation are designing a car that will use as little gasoline as possible.
(A) Their first prototype moves without any sliding friction at all, inside or out, so when it travels along a horizontal roadway, the only horizontal force it experiences is air resistance (pressure drag). The force that air resistance exerts on the car increases as the car's speed through the air increases, but a faster-moving car gets to its destination faster. If you are trying to minimize the fuel needed to travel 100 km along a horizontal road at constant velocity, how fast should you drive this car or does it not matter?
Answer: Drive as slowly as possible.
Why: The work the engine must do is equal to the force it exerts on the car (with the help of friction from the ground) times the distance the car travels. The distance traveled is fixed, but you can reduce the force to a minimum by going as slowly as possible.
(B) Their second prototype is so well built and aerodynamically perfect that it moves without either air resistance or sliding friction. It can coast at constant velocity along a horizontal roadway for hours on end, even with the engine turned off. What force, if any, pushes the car forward while it is coasting like this?
Answer: No force.
Why: The car is traveling at constant velocity, so the net force on it is zero. It is coasting forward. If nothing pushes it backward, then it doesn't need anything pushing it forward either.
(C) To get the second prototype moving, the engine must twist the car's wheels so that the ground pushes the car forward. The more passengers the car contains, the harder and/or longer the ground must push forward on the car to get it up to highway speed. Why do the occupants of the car affect the starting process in this manner?
Answer: Their masses (inertia) make them hard to accelerate forward so the ground must push the car forward harder to bring the car and passengers up to speed.
Why: During the starting process, the occupant's mass adds to that of the car and the ground must push forward harder on the car to accelerate it. Ultimately, the car and engines must do more work to get the occupied car up to speed because the occupied car has more kinetic energy than it would have if it were empty.
(D) The second prototype has reached highway speed and is traveling at constant velocity along the horizontal road. How does the number of passengers in the car affect the amount of energy the engine must supply during the 100 km trip at constant velocity?
Answer: It has no effect.
Why: At constant velocity, the experiences no net force. As in part (B), there is no slowing force, so there need be no forward force. The engine doesn't do any work on the car, regardless of how many occupants it contains.
Problem 5:
Prairie dogs are cute little burrowing animals that live in the Midwest and are wonderful or a nuisance, depending on whether you own the land they dig up. What makes them interesting to physicists is that they use aerodynamics to ventilate their underground homes.
(A) A prairie dog digs a long, nearly horizontal tube underground and opens each end of the tube to the surface. If both openings were identical--simply level holes cut in the flat, horizontal ground above tube--air wouldn't naturally flow through the tube, even when the wind was blowing overhead. Why not?
Answer: The pressure would be equal at each end of the tube and the air would experience no net force. (Drag forces would quickly slow it to a stop if it were moving at all.)
Why: To start or keep air flowing through the tube, it needs a pressure imbalance. With two identical openings to the surface, there is no pressure imbalance to push air through the tube. While the air would coast in a perfect world, air resistance would slow any movement of air so that it wouldn't keep flowing after a short while.
(B) However, the prairie dog builds a raised mound or "dome" around one of the tube ends. The tube opening is placed at the highest point of the dome, far above the dome's base and the level ground around the dome. As wind blows across the level ground, it encounters the dome and deflects. The first deflection occurs when the air bends upward as it collides with the base of the dome. This air deflects outward--away from the dome's surface. Compare the speed and pressure of the air near base of the dome to their values in the open air stream. (Just indicate more, less, or equal for each quantity.)
Answer: The pressure at the base is more than in the open air stream and the speed of the air at the base is less that in the open air stream.
Why: For air to deflect away from a surface, it needs a pressure imbalance to push it away from that surface. The pressure at the base of the dome rises in order to push the air away. The air there loses kinetic energy so it gains pressure potential energy. The air speed decreases near the base.
(C) The second deflection occurs when the air bends downward as it arcs around the top of the dome. This air deflects inward--toward the dome's surface. Compare the speed and pressure of the air near the top of the dome to their values in the open air stream. (Just indicate more, less, or equal for each quantity.)
Answer: The pressure at the top of the dome is lower than in the open air stream and the speed of air at the top of the dome is more than in the open air stream.
Why: For air to deflect toward a surface, it needs a pressure imbalance to push it toward that surface. The pressure at the top of the dome falls in order to all air to be pushed toward the top of the dome. The air there losses pressure potential energy and its kinetic energy rises. The air speed rises at the top of the dome.
(D) Since one end of the prairie dog's tube opens at the top of the dome and the other opens onto level ground, air flows through the tube from one end of the tube to the other whenever the wind blows. Toward which end of the tube does the air flow (dome end or flat end), and what pushes the air in that direction?
Answer: Toward the dome end and it is pushed by a pressure imbalance.
Why: The pressure at the top of the dome is lower than atmospheric while the pressure at the flat end of tube is simply atmospheric pressure. There is thus a pressure imbalance and air accelerates and flows toward the low pressure at the top of the dome.
Problem 6:
You're in a festive mood, so you decide to light candles for your dinner party.
(A) You strike a match by rubbing it across the side of the matchbox. Why does this action cause the match to ignite?
Answer: Sliding friction turns work into thermal energy and this thermal energy provides the activation energy needed to start the match's chemical reactions of burning.
Why: Although the match can release chemical potential energy by undergoing various chemical reactions, it needs some activation energy to initiate those chemical reactions. This activation energy is provided by sliding friction.
(B) Liquid wax doesn't burn but gaseous wax does. In terms of individual wax molecules, how does raising the temperature of the liquid wax increase the density of gaseous wax nearby?
Answer: At higher temperatures, more wax molecules leave the liquid surface than return to it, so the wax evaporates into gas (and raises the local density of gaseous wax molecules).
Why: At any temperature, liquid and gaseous wax quickly reach an equilibrium at which there is no net movement of molecules between the two phases. But as you heat the two phases, the equilibrium balance shifts toward less liquid wax and more gaseous wax. More specifically, the density of wax molecules in the gas phase increases.
(C) Which molecules are "more tightly bound" (require more energy to separate): (1) the wax and oxygen molecules before burning or (2) the water and carbon dioxide molecules they become after burning?
Answer: The water and carbon dioxide molecules, i.e. (2), are more tightly bound.
Why: It takes more energy to disassemble the water and carbon dioxide molecules than to disassemble the wax and oxygen molecules from which they were made. This difference in binding energy reflects the fact that chemical potential energy is released when wax and oxygen react or burn to form carbon dioxide and water.
(D) When you blow out the candle, a white mist rises from the wick for a few seconds. What is that white mist?
Answer: Tiny particles of solid (or liquid) wax.
Why: As gaseous wax cools, it condenses to form liquid or solid wax. In the air, this condensation takes to form of tiny wax droplets or particles.