## Sample Final Examination

This exam was given in the Fall of 1996. The actual final exam for this year (Fall, 1997) will be similar, although it will be weighted according to the emphasis of the lectures. We've covered most of the material (as of today Nov 26, 1997). I expect that we will cover the material needed for all the questions except 6, 18, and 33.

Actual Exam Was Given Monday, December 9, 1996, at 9:00 AM

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:

If you place a window air conditioning unit on a table in the middle of your sealed room, plug it in, and turn it on, you will find that the average temperature of your room will

(A) remain the same.

(B) fall.

(C) rise slightly for about one minute, then fall dramatically as the unit begins to function.

(D) rise.

Problem 2:

A typical home thermostat, responsible for keeping a home at a constant temperature, contains a metallic spiral that coils or uncoils as the temperature changes. As it moves, it operates a switch that controls the heating or cooling system. The reason it coils or uncoils as the temperature changes is that

(A) it is actually made of two thin metal sheets, sandwiched together. The sheets expand or contract at different rates as the temperature changes and the coil bends as a result.

(B) metals naturally straighten out as the temperature increases, much as hair becomes straight when you use a blow-dryer on it.

(C) heat flowing through the coil has angular momentum. As the temperature increases, there is more angular momentum and the coil unwinds to conserve it.

(D) the pressure of the air inside the coil rises as its temperature rises. The unbalanced pressure inside the coil exerts an outward force on it and makes it unwind.

Problem 3:

A city bus and a small car both roll down a 2 meter hill and coast across a parking lot. Which vehicle is moving faster as they coast horizontally? (Neglect friction and air resistance)

(A) the car moves faster.

(B) the bus moves faster.

(C) they both coast at essentially the same speed.

(D) The answer depends on how steep the hill is.

Problem 4:

A heat engine extracts usable work by permitting

(A) heat to undergo a complete transformation into work.

(B) work to undergo a complete transformation into heat.

(C) heat to flow from a hotter object to a colder object.

(D) heat to flow from a colder object to a hotter object.

Problem 5:

Heavy weights are often attached to the moveable cab of a crane on the side opposite the crane's boom. These weights

(A) help maintain stability of the crane by moving the center of gravity farther out toward the boom.

(B) reduce the crane's mass.

(C) reduce the crane's moment of inertia, making it easier to turn around the pivot.

(D) help maintain stability of the crane when it is lifting a heavy object by exerting a torque about the center of mass of the crane in the opposite direction to the torque exerted on the boom by the object.

Problem 6:

If you could look at the microscopic structure of table salt (sodium chloride) that is dissolved in water, you would see

(A) tiny salt crystals only a few tens of atoms on a side, floating around in shells of water molecules.

(B) individual salt molecules, NaCl, hydrogen bonded to water molecules.

(C) individual salt molecules, NaCl (a pair formed of a sodium atom and a chlorine atom), floating around in shells of water molecules.

(D) individual ions, Na+ (a sodium positive ion) and Cl- (a chlorine negative ion) floating around in shells of water molecules.

Problem 7:

Water hammer occurs when you suddenly stop the flow of water in a pipe. It happens because

(A) flowing water has angular momentum and can only be stopped by a torque.

(B) flowing water has momentum and can only be stopped by a force.

(C) flowing water has no friction.

(D) flowing water has acceleration and can only be stopped by a velocity.

Problem 8:

A hot air balloon floats even though its envelope (the bag of hot air) is open at the bottom. This floating is possible because

(A) the hot air in the balloon has a higher pressure than the surrounding cold air but their densities are the same.

(B) the hot air in the balloon is less dense than the surrounding cold air but their pressures are the same.

(C) the hot air in the balloon has a lower pressure than the surrounding cold air but their densities are the same.

(D) the hot air in the balloon is more dense than the surrounding cold air but their pressures are the same.

Problem 9:

If you were tightening a large bolt, you might use a very long wrench rather than a short wrench because the long wrench

(A) would allow you to apply more force to the handle of the wrench.

(B) would allow you to apply a larger torque to the bolt.

(C) would experience less friction.

(D) has a larger center of mass.

Problem 10:

A two kilogram hanging plant is being held up by a spring. The spring is stretched 10 centimeters from its equilibrium length. If you now add one kilogram of water to the plant's pot, how far will the spring be stretched from its equilibrium length?

(A) 25 centimeters

(B) 20 centimeters

(C) 15 centimeters

(D) 10 centimeters

Problem 11:

Once water is heated to 100 &deg;C (212 &deg;F) at sea level,

(A) water molecules first begin to leave the water's surface as a gas.

(B) it begins to boil, but it requires additional energy to convert from a liquid to a gas without changing temperature.

(C) it begins to boil, but its requires additional energy to convert from a liquid to a gas because it must change temperature to undergo the change of phase.

(D) it immediately turns to steam without the further introduction of energy.

Problem 12:

The tides are caused by

(A) the Coriolis effect due to the rotation of the Earth.

(B) the angular momentum of the Earth orbiting the Sun and the Moon orbiting the Earth.

(C) centrifugal "force" due to the rotation of the Earth.

(D) the gravitational forces of the Sun and the Moon on the Earth's oceans.

Problem 13:

An ice skater pulls her arms in as she spins and begins to rotate more rapidly. By pulling her arms in, she has

(A) reduced her moment of inertia so that she must rotate more rapidly in order to conserve her angular momentum.

(B) done work on the ice so that it pushes on her making her spin faster.

(C) decreased her air resistance so that she begins to rotate more rapidly.

(D) accelerated the air and received a torque that makes her rotate more rapidly.

Problem 14:

A man and a small boy are sitting together at the center of a perfectly slippery ice skating rink without skates. They are not moving and the man realizes that the only way to get off the rink is for the pair to push one another off the ice. Before the man can act, the boy pushes hard on the man and the man begins to slide across the ice towards the exit. The man had no time to push on the boy with his hands. As a result,

(A) the boy will remain at the center of the rink.

(B) the boy will slide with the man but only if the boy grabs onto the man before the man has drifted out of reach.

(C) the boy will slide with the man.

(D) the boy will slide across the rink in the direction opposite the man's motion.

Problem 15:

The recoil of a rifle as the bullet is pushed out of the barrel is a consequence of Newton's Third Law of Motion (action-reaction). Which one of the following would not reduce the recoil velocity of the rifle?

(A) increase the mass of the rifle.

(B) decrease the velocity of the bullet

(C) decrease the mass of the rifle.

(D) decrease the mass of the bullet

Problem 16:

An airplane obtains the lift it needs to keep itself from falling by

(A) using Bernoulli's principle to create a lower pressure above its wings than beneath them.

(B) accelerating the air upward using Bernoulli's principle.

(C) using Bernoulli's principle to create a higher pressure above its wings than beneath them.

(D) using an airfoil to initiate a stall.

Problem 17:

The gears of a bicycle help the rider obtain mechanical advantage. To pedal easily up a steep hill, the rider would normally choose a

(A) small crank sprocket and a small freewheel sprocket.

(B) small crank sprocket and a large freewheel sprocket.

(C) large crank sprocket and a large freewheel sprocket.

(D) large crank sprocket and a small freewheel sprocket.

Problem 18:

[No longer appropriate to the material in this course] In the Northern Hemisphere, the winds in a hurricane circulate counter-clockwise because

(A) hurricanes are high pressure regions. As air rushes away from the eye of the hurricane in all directions, it deflects to the right and ends up flowing around the eye counter-clockwise.

(B) warm air always flows counter-clockwise in the Northern Hemisphere while cold air always flows clockwise.

(C) the Moon orbits the Earth in a counter-clockwise direction and its gravitational forces induce a counter-clockwise circulation on the winds of a hurricane.

(D) hurricanes are low pressure regions. As air rushes toward the eye of the hurricane from all directions, it deflects to the right and ends up flowing around the eye counter-clockwise.

Problem 19:

A space-walking astronaut in orbit around the earth has a weight of 750 newtons. This means that the earth exerts a downward force of 750 newtons on the astronaut. How much upward force does he exert on the earth?

(A) 750 newtons.

(B) 0 newtons because he is in free fall and is thus weightless.

(C) somewhat less than 750 newtons because he is accelerating downward.

(D) somewhat more than 750 newtons because he is accelerating downward.

Problem 20:

You wish to lift a very heavy object with a hydraulic ram by pushing down on a second hydraulic ram. The two cylinders of the two rams are connected by a pipe. You only need to lift that heavy object a small distance and must push down on the second ram by hand. The piston lifting the heavy object should be

(A) much longer than the piston you push down on.

(B) much shorter than the piston you push down on.

(C) much smaller in diameter than the piston you push down on.

(D) much larger in diameter than the piston you push down on.

Problem 21:

The internal combustion engine turns heat into useful work when

(A) the piston travels toward the spark plug as it compresses the fuel and air mixture.

(B) the piston travels toward the spark plug as it ejects the exhaust gas from the cylinder.

(C) the piston travels away from the spark plug during the expansion of the hot gas.

(D) the piston travels away from the spark plug as it draws the fuel and air mixture into the cylinder.

Problem 22:

Electromagnetic radiation includes infrared, visible, and ultraviolet light. Although light travels as a wave, it is absorbed as individual particles called photons, which carry an amount of energy that depends on the frequency of the light. Of the three types of light mentioned above, the type of light that carries the most energy per photon is

(A) infrared light.

(B) ultraviolet light.

(C) dependent on the velocity with which the light moves.

(D) visible light.

Problem 23:

The reason that a watch with a balance ring and a spring keeps good time is that

(A) it contains a quartz crystal.

(B) the ring oscillates back and forth with a constant frequency determined principally by the ring's moment of inertia and the spring's stiffness.

(C) the ring oscillates back and forth with constant frequency determined principally by the force of gravity and the length of the pendulum rod.

(D) the ring oscillates back and forth with a constant frequency determined principally by the ring's weight and the spring's mass.

Problem 24:

If you wanted to raise the pitch of a guitar string, so that it vibrated at a higher frequency than before, you could

(A) shorten the string, increase the string's tension, or decrease the string's mass.

(B) lengthen the string, increase the string's tension, or decrease the string's mass.

(C) shorten the string, decrease the string's tension, or increase the string's mass.

(D) lengthen the string, decrease the string's tension, or increase the string's mass.

Problem 25:

When you drop a baseball and a bowling ball simultaneously, they will accelerate downward toward the Earth at exactly the same rate because the gravitational force each ball experiences is (ignore air resistance)

(A) exactly the same.

(B) exactly proportional to the moment of inertia of that ball.

(C) exactly proportional to the speed of that ball.

(D) exactly proportional to the mass of that ball.

Problem 26:

When faced with a pitcher who throws tricky curve balls and sliders, you need to be able to swing your bat quickly in order to respond to the movements of the baseball as it approaches home plate. The main reason for "choking up" on a baseball bat (moving your hands away from the end of the handle and closer to the middle of the bat) is so that the bat's

(A) mass is reduced and less torque is required to swing the bat.

(B) mass is increased and less torque is required to swing the bat.

(C) moment-of-inertia is reduced and less torque is required to swing the bat.

(D) moment-or-inertia is increased and less torque is required to swing the bat.

Problem 27:

If you try to cook vegetables with 100&deg; C air, it takes a very long time. But if you cook those same vegetables with 100&deg; C steam, they cook very quickly. This is because the steam

(A) condenses on the colder vegetables and absorbs a large amount of heat from the vegetables.

(B) condenses on the colder vegetables and releases a large amount of heat to the vegetables.

(C) causes moisture inside the vegetables to boil and transfer heat to the vegetables.

(D) causes moisture inside the vegetables to boil and absorb heat from the vegetables.

Problem 28:

A pitcher throws his best curve ball by

(A) throwing the ball moderately hard with a high rotation.

(B) throwing the ball moderately hard with no rotation.

(C) throwing the ball extremely hard with no rotation.

(D) throwing the ball extremely hard with a high rotation.

Problem 29:

You are working in the U.S. Patents Office and are approached by a man with a small black box. The box is featureless except for a single electrical socket on its front. The owner of the box claims that the box can convert heat from its surroundings into electricity, so that you can plug a small appliance into the socket and draw out electrical power from the box forever. You should suspect that the man is a fraud because

(A) the box would eventually become colder than absolute zero if it were to operate for a long time.

(B) random energy (heat) cannot be converted directly into ordered energy (electricity).

(C) he has shifty eyes.

(D) the box cannot be part of a complete electrical circuit.

Problem 30:

A diesel engine is more energy efficient than a gasoline engine, in large part because the diesel engine burns the fuel at a higher temperature. Burning the fuel at a higher temperature allows the diesel engine to

(A) reduce the amount of oxygen needed to burn each gram of fuel.

(B) slow the flow of heat from the hot burned gases to the metal walls of the cylinder.

(C) convert a larger fraction of heat into work as that heat flows from the hot burned gas toward the cold outside air.

(D) convert a smaller fraction of heat into work as that heat flows from the hot burned gas toward the cold outside air.

Problem 31:

Ice floats because

(A) the solid form of a material always floats on its liquid form.

(B) it is less dense than water and experiences an upward buoyant force that is greater than the downward force of gravity.

(C) water always contains salt making it much heavier than ice.

(D) the pressure on its bottom surface melts the ice and it refreezes on top.

Problem 32:

Most hot water heating systems use passive radiators: they simply hold hot water and need no fans. The principal mechanism whereby heated air is moved about the room is

(B) absorption

(C) convection

(D) conduction

Problem 33:

You mix together equal masses of salt, water, sugar, and grain alcohol and then distill the mixture. You condense the vapor that rises above the mixed liquid when it first begins to boil and collect it in a bottle. It contains mostly

(A) salt.

(B) grain alcohol.

(C) sugar.

(D) water.

Problem 34:

A large truck breaks down out on the road and receives a push back into town by a small compact car. While the car pushing the truck is speeding up to get up to cruising speed

(A) the amount of force of the car pushing against the truck is less than that of the truck pushing back against the car.

(B) the amount of force of the car pushing against the truck is greater than that of the truck pushing against the car.

(C) neither the car nor the truck exert any force on the other, the truck is pushed forward simply because it is in the way of the car.

(D) the amount of force of the car pushing against the truck is equal to that of the truck pushing back against the car.

Problem 35:

When a scuba diver, swimming 30 feet below the surface of the water, takes a full breath from her air tank, the number of air molecules in her lungs is

(A) about twice the number her lungs would hold at the surface of the water.

(B) about half the number her lungs would hold at the surface of the water.

(C) about a quarter of the number her lungs would hold at the surface of the water.

(D) almost exactly the same as the number her lungs would hold at the surface of the water.

Problem 36:

If you increase the length of the pendulum in your aunt's grandfather clock, which previously kept excellent time, she will discover that the clock is

(A) still keeping excellent time because the period of oscillation of a pendulum depends only on the mass of the pendulum bob and the force of gravity.

(B) still keeping excellent time because the period of oscillation of a pendulum depends only on the weight of the pendulum bob and the force of gravity.

(C) running fast (the clock's minute hand takes less than 60 minutes to complete a full turn).

(D) running slow (the clock's minute hand takes more than 60 minutes to complete a full turn).

Problem 37:

As you make a left turn on a bicycle, you tip the bicycle into the turn. You do this so that the two forces on the bicycle tires (upward contact force and leftward friction) exert a combined force directed at your overall center of mass. Because it is directed at your center of mass, this combined force

(A) is exactly zero.

(B) points in exactly the opposite direction as your weight.

(C) does not make you and the bicycle accelerate.

(D) exerts no torque on you and the bicycle about your center of mass.

Problem 38:

You are driving down the road on a cold winter day and encounter an icy spot as you travel around a sharp leftward curve in the road. Your car suddenly experiences no friction with the road. In all likelihood, your car will

(A) quickly come to a stop because it will no longer have a force propelling it forward.

(B) continue around the turn because of conservation of angular momentum.

(C) travel in a straight line and end up on the right-hand shoulder of the road.

(D) accelerate forward because friction will no longer be slowing it down.

Problem 39:

To make a very accurate clock, you need an oscillator with a very steady period. A quartz crystal is almost ideal because

(A) it is a harmonic oscillator and is able to transfer much of its vibrational energy to its surroundings during each cycle of its vibration.

(B) it is an anharmonic oscillator and loses very little of its vibrational energy each cycle.

(C) it is an anharmonic oscillator and is able to transfer much of its vibrational energy to its surroundings during each cycle of its vibration.

(D) it is a harmonic oscillator and loses very little of its vibrational energy each cycle.

Problem 40:

When you make a left turn on a bicycle, the force that causes you to accelerate to the left is applied by

(A) Your left hand on the handle bar.

(B) Either or both hands on the handle bar.

(C) friction between the ground and the wheels.

(D) Your right hand on the handle bar.

Problem 41:

The principal characteristic which our ears use to identify the particular musical instrument that produced a sound are that sound's

(A) speed of travel and its pitch.

(B) harmonic content.

(C) oscillations and vibrations.

(D) wavelength and its fundamental frequency.

Problem 42:

If you blow across the top of a soft drink bottle, you can get it to emit a tone similar to that of a flute or pipe organ. As the tone is sounding, air is oscillating back and forth through the mouth of the bottle. Inside the bottle,

(A) the air's pressure is also varying up and down.

(B) the air's velocity remains constant.

(C) the air's acceleration remains constant.

(D) the air's pressure remains constant.

Problem 43:

A ballistic missile after its launch engine has shut down, a communications satellite in Earth orbit, and the Moon

(A) have no net force acting on them.

(B) are all in free fall with respect to the Earth.

(C) all have the same angular velocity.

(D) all have constant kinetic energy.

Problem 44:

Momentum is transferred to an object by pushing on it with a force for a certain amount of time. One way to see why momentum is conserved is to notice that, as one object pushes on a second object and gives it momentum,

(A) there will always be a third object that will compensate for the extra momentum.

(B) the second object does work on the first object, forcing it to stop.

(C) gravity will always balance the forces so that the objects remain stationary.

(D) the second object pushes back in the opposite direction and extracts momentum from the first object. The first object loses exactly as much momentum as the second object gains.

Problem 45:

The reason that dust remains in still air for such a long time is that, as a dust particle slowly descends, it experiences

(A) only a small downward acceleration due to gravity. Since gravity exerts less downward force on small objects, they accelerate downward slowly.

(B) upward buoyant forces that are equal in amount to its weight.

(C) a repulsive force from the earth's magnetic field that is equal in amount to its weight.

(D) upward drag forces that are equal in amount to its weight

Problem 46:

A very-long-life incandescent light bulb insures that its filament will not sublime quickly by running the filament at a lower temperature than a normal bulb. Because of the low filament temperature,

(A) the bulb will save energy by drawing less power from the power line while still producing the same amount of useful light as a normal bulb.

(B) the bulb will emit a redder-than-normal light and will waste more energy producing infrared radiation.

(C) the bulb will help save energy by drawing the same amount of power from the power line while producing more useful light than a normal bulb.

(D) the bulb will emits bluer-than-normal light and will waste more energy producing ultraviolet radiation.

Problem 47:

A water molecule has a very small mass compared to most other molecules. Nonetheless, water tends to be a liquid at room temperature because adjacent water molecules are held together by

(A) covalent bonds.

(B) ionic bonds.

(C) rubber bonds and James bonds.

(D) hydrogen bonds.

Problem 48:

Two people are paddling a canoe across a lake. They reach forward with their paddles raised above the water, lower the paddles into the water, and then pull the paddles back toward them. The canoe accelerates forward as the people pull back on their paddles, because as they pull back,

(A) the weight of the canoe is reduced.

(B) the water exerts forward forces on their paddles.

(C) the water level behind the canoe rises and the canoe accelerates down the inclined plane that is produced.

(D) the people exert forward forces on their paddles.

Problem 49:

[No longer appropriate to the material in this course] In July and August the residents of Charlottesville experience very warm weather because

(A) that is when the Earth has the least average cloud cover.

(B) that is when the winds come from the south, rather than from the north as they do during winter.

(C) that is when the Earth's northern hemisphere is tilted toward the Sun.

(D) that is when the Earth is closest to the Sun.

Problem 50:

A string, vibrating in its second harmonic mode (the two halves of the string move in opposite directions) will emit a tone with a pitch that is

(A) one octave below that of the fundamental mode (half the frequency of the fundamental mode).

(B) the same as that of the fundamental mode.

(C) one octave above that of the fundamental mode (twice the frequency of the fundamental mode).

(D) not directly related to that of the fundamental mode.

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

Problem 1:

Revolving doors are popular in northern hotels and office buildings as a way to prevent cold outside air from blowing directly into the lobby. Most revolving doors have four panels arranged in a cross, as viewed from above. You step in between two panels of the door and push on the panel in front of you. The revolving door begins to rotate and once you reach the inside of the building, you step out into the lobby.

(A) It is much easier to make the revolving door rotate by pushing on the panel far from the central pivot than it is by pushing near the pivot. Why?

(B) As you push on the door, it begins to turn more and more quickly. What is your pushing doing to the door?

(C) One of the dangers of revolving doors is being hit by the panel behind you as you step out of the door. The door tends to keep on turning after you stop pushing on it and it can bump you if you are not careful. Why does it keep on turning after you stop pushing?

(D) What eventually stops the revolving door when no one uses it for a minute or two?

Problem 2:

Puffed grain cereals such as puffed wheat are made by heating the moist grains in a tightly sealed container.

(A) What happens to the pressure inside the container as the temperature of its contents increases to well above 100 &deg;C ?

(B) Why doesn't the water in the grains boil when the temperature reaches 100 &deg;C?

(C) What happens to the water in the hot grains when the container is suddenly opened to the outside atmosphere?

(D) Why do the grains suddenly puff up when the container is opened to the outside?

Problem 3:

An escalator is essentially a moving staircase. The individual steps are supported by metal tracks that run on either side of the escalator. These steps follow one another in a complete loop, driven by an electric motor. When you step onto an escalator at the ground floor, it soon begins to carry you upward and forward at a constant velocity toward the second floor.

(A) While you are moving toward the second floor at a constant velocity, what is the net force exerted on you by all outside forces (specify the amount and the direction of the net force)?

(B) You know that gravity gives you a weight in the downward direction. What force does the escalator exert on you as you move toward the second floor at a constant velocity (specify the amount and the direction of force)?

(C) Is the escalator doing work on you as you move toward the second floor?

(D) As you step onto the escalator, you begin to accelerate toward the second floor. Is the net force exerted on you by all outside forces the same as in part (A)?

Problem 4:

A spring bathroom scale is designed to report the amount of upward force it is applying to the objects touching its surface.

(A) When you first step on the scale, you usually have some downward velocity because you "land" on the scale. As it slows your downward motion during the process of bringing you to rest, does the scale report your correct weight, more than your weight, or less than your weight?

(B) If you stand still on one foot, rather than two feet, what fraction of your weight does the scale report?

(C) You decide to jump upward. What does the scale report as you are pushing yourself upward?

(D) You stand motionless on two identical bathroom scales, one foot on the left scale and one foot on the right scale. What can you say about the weights that the two scales report even if you are not perfectly centered between the two scales?

Problem 5:

If you extend a ruler off the edge of the table and pluck it with one hand while holding it against the table with the other, the ruler will vibrate up and down.

(A) Why does the ruler's frequency of oscillation decrease when you extend more of it off the table?

(B) Why doesn't the ruler's frequency of oscillation depend on how hard you pluck it?

(C) What forms does its energy take as the ruler vibrates up and down?

(D) What eventually happens to the ruler's energy?

Problem 6:

A boat floats on the surface of a still lake, supported by the buoyant force. The average density of the boat, including the air it contains, is less than that of the lake water.

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

(B) If the boat moves up or down a few centimeters, what would happen to the net force on the boat?

(C) The floating boat is in stable equilibrium with respect to up and down motion. Explain why this is so.

(D) Does the air exert a buoyant force on the boat? If so, why doesn't the boat float in the air?