Physics 109 : How Things Work : Spring 2006 Mike Noel - mnoel@brynmawri.edu Bob Ekey - rekey@brynmawr.edu

Practice Midterm Examination

PART I: MULTIPLE CHOICE QUESTIONS

Problem 1:

Even when you are driving at a constant 60 miles-per-hour along a straight, level road, your car's engine must be running. As the engine turns the car's wheels, friction between the ground and the tires exerts a forward force on the car. The car needs this forward force from the ground because

(A) air drag (air resistance) exerts a backward force on the car.

(B) an object that is moving requires a net force to keep it moving. In the absence of any net force, objects are motionless.

(C) an object's velocity points in the direction of the net force on that object.

(D) the car has a velocity and is thus accelerating. In order to accelerate, the car must be experiencing a net force.

Answer: (A) air drag (air resistance) exerts a backward force on the car.

Why: When your car is traveling at constant velocity, the net force on it must be zero. Since it needs a forward force from the ground, something must be exerting a backward force on it. On a level road, that something can only be air resistance.

Problem 2:

Your pet hamster has an exercise wheel in his cage. He can climb into this wire wheel and then run in it as though he were on a treadmill. When he is running in the wheel, he remains stationary at the bottom of the wheel while it spins around him. In this case his angular velocity is

(A) equal in magnitude to the wheel’s angular velocity, but in the opposite direction.

(B) zero.

(C) increasing as he does work on the wheel.

(D) equal in both size and direction to the angular velocity of the wheel.

Answer: (B) zero.

Why: Since the hamster isn’t moving at all, his orientation relative to the wheel’s pivot isn’t changing. With a constant angular position, the hamster has no angular velocity.

Problem 3:

Burning fuel in an engine turns the ordered chemical potential energy in gasoline into disordered thermal energy in the hot burned gases. The engine's ability to extract some work from this thermal energy reflects the fact that

(A) there is remaining order in an unequal distribution of temperatures: a hot region and a cold region.

(B) about 25% of thermal energy is actually ordered and can be extracted as work.

(C) about 10% of thermal energy is actually ordered and can be extracted as work.

(D) the second law of thermodynamics is only a statistical law and doesn't always hold true.

Answer: (A) there is remaining order in an unequal distribution of temperatures: a hot region and a cold region.

Why: Even though the car engine is working with only thermal energy, the fact that this thermal energy is unequally distributed allows it to extract some disordered energy as ordered energy while destroying the remaining order in the situation.

Problem 4:

The temperature of a glass of ice water (a mixture of ice and water)

(A) is proportional to the ratio of water to ice.

(B) depends on the total volume of ice and water in the glass.

(C) is 0 °C.

(D) is proportional to the ratio of ice to water.

Answer: (C) is 0 °C.

Why: Ice and water can only coexist at one temperature: the freezing/melting temperature of 0 °C.

Problem 5:

You're taking a nap on the couch. When you lower your head slowly into the elastic couch pillow and let it reach equilibrium, your head dents the pillow downward 2 inches. You lift your head to

see who just walked in, and then let it fall hard against the pillow. It dents the pillow downward 4 inches before bouncing back upward. The point at which your head reaches maximum speed is when it is

(A) denting the pillow downward 4 inches.

(B) just touching the pillow on its way downward.

(C) denting the pillow downward 2 inches.

(D) just touching the pillow on its way upward.

Answer: (C) denting the pillow downward 2 inches.

Why: Above the equilibrium point, the net force on your head is downward; below the equilibrium point, the net force on your head is upward. As your head falls from above the pillow, it continues to accelerate downward--picking up speed and kinetic energy--until the net force on it stops being downward. That change occurs at the equilibrium point. After the equilibrium point, your head decelerates, losing speed and kinetic energy.

Problem 6:

As you ride on a merry-go-round, you feel a strong outward pull that feels just like the force of gravity. This fictitious force occurs because

(A) your velocity is toward the center of the merry-go-round and you experience a fictitious force in the direction opposite your velocity.

(B) you are accelerating away from the center of the merry-go-round and experience a fictitious force in the direction of your acceleration.

(C) you are accelerating toward the center of the merry-go-round and experience a fictitious force in the direction opposite your acceleration.

(D) your velocity is away from the center of the merry-go-round and you experience a fictitious force in the direction of your velocity.

Answer: (C) you are accelerating toward the center of the merry-go-round and experience a fictitious force in the direction opposite your acceleration.

Why: Left to yourself, you would go in a straight line at a steady pace. But the merry-go-round pulls inward on you to bend your path into a circle. As it does this, you accelerate inward and feel your body’s inertia trying to make you continue straight. You feel an outward pull, a fictitious force in the direction opposite your inward acceleration.

Problem 7:

You have an indoor swimming pool in one room of your 87-room mansion. The ventilation is turned off in that room and the air and water are at the same temperature. You observe that the amount of water in the pool remains precisely constant—water is neither evaporating nor condensing. If you were to examine the water's surface microscopically to see if any water molecules were landing on the water's surface or leaving that surface, you would find that

(A) both landing and leaving are occurring, but that landing takes place more often than leaving.

(B) both landing and leaving are occurring, but at exactly equal rates.

(C) both landing and leaving are occurring, but that leaving takes place more often than landing.

(D) both landing and leaving are absent—no molecules are landing or leaving the water.

Answer: (B) both landing and leaving are occurring, but at exactly equal rates.

Why: Although there is no net movement of water molecules between the liquid and the gas, that doesn't mean that the surface of the water is totally static. Instead, water molecules are landing and leaving all the time, but at equal rates.

Problem 8:

You wander into the kitchen on a dark, moonless night and open the refrigerator door. Sadly, the light bulb in the refrigerator has burned out and the kitchen remains pitch black. Just as you are about to reach for the carton of chocolate milk, your pet squirrel leaps onto your back and you twirl around several times before the squirrel heads off for some other part of the house. You have no idea which way you are facing. Fortunately, the refrigerator door is still open and you can feel the cold on your face as you turn in its direction. The physics explanation for this feeling of cold that you get when you face the refrigerator is that

(A) heat is flowing from the rest of the kitchen into the refrigerator and the pressure of this heat flow causes coldness to accumulate on the side of your body that's facing the refrigerator.

(B) the cold contents of the refrigerator do a much better job of absorbing your thermal radiation than do the warmer contents of the rest of the kitchen.

(C) you are radiating far more heat toward the cold contents of the refrigerator than they are radiating toward you.

(D) the cold contents of the refrigerator radiate coldness toward your skin and lower your skin's temperature.

Answer: (C) you are radiating far more heat toward the cold contents of the refrigerator than they are radiating toward you.

Why: Radiation only transfers heat (not cold) and the cooling effect described here is the result of an unbalanced exchange of radiation. You radiate nicely at the refrigerator, but it doesn't return the favor very well. With so little radiant heat coming toward you, you are experience a net loss of heat through radiation and feel cold.

Problem 9:

When an acrobat tries to balance on top of a unicycle, she pedals the single wheel so as to

(A) minimize her overall gravitational potential energy.

(B) accelerate at a constant rate and minimize her velocity.

(C) place its contact point with the ground directly below her overall center of gravity.

(D) minimize the torque she exerts on it.

Answer: (C) place its contact point with the ground directly below her overall center of gravity.

Why: The unicycle has no static stability but can be made dynamically stable with constant effort. The cyclist tries to return the unicycle to its unstable equilibrium point by placing the support point directly under the center of gravity/mass.

Problem 10:

You’ve always wondered how much one of your friends weighs and devise a scheme to measure his weight secretly. You have him sit in a tubular steel chair. This popular style of chair (see Figure F) consists of a single steel tube that’s bent into a frame and that supports a seat bottom and a back. The empty chair weighs 10 pounds and is 30 inches tall. The frame acts as a spring and bends downward slightly when the chair is occupied. When you sit properly in the chair yourself, it bends downward 1 inch. When your friend sits properly in the chair, it bends downward 2 inches. From that observation, you know that your friend weighs about

(A) 300 pounds.

(B) twice as much as you do.

(C) four times as much as you do.

(D) 150 pounds.

Answer: (B) twice as much as you do.

Why: The chair is obeying Hooke’s law, the concept that a distorted spring experiences a restoring force that is proportional to the extent of its distortion. If your friend bends the chair twice as far as you do, the chair exerts twice as much restoring force on your friend as on you. That means that your friend weighs twice as much as you do.

Problem 11:

When playing hockey, you flick the puck across the ice rink with your stick. The puck then moves across the frictionless surface of the ice at constant velocity. As the puck moves across the ice, its kinetic energy is

(A) constant because kinetic energy is a conserved quantity.

(B) zero because it isn't accelerating.

(C) increasing as the ice does work on it to support it against the force of gravity.

(D) constant because its speed is constant.

Answer: (D) constant because its speed is constant.

Why: Since nothing pushes on the puck, it doesn’t accelerate and coasts forward at constant speed. While it thus maintains a constant kinetic energy as well, kinetic energy isn’t itself a conserved quantity. Only total energy is conserved. After all, if the puck were to coast uphill on sloping ice, its kinetic energy would decrease even though its total energy (kinetic plus gravitational) would remain constant.

Problem 12:

When you are out fishing on a lake one day, you get your line snagged on a floating tree branch. Luckily the branch is not attached to anything, so you can reel it in to unhook your line. As you reel in the branch, it moves toward you at a constant speed. The amount of work you are doing on the branch is

(A) exactly zero.

(B) constant, but negative—the branch does work on you.

(C) constant and positive—you do work on the branch.

(D) exactly equal to the kinetic energy of the branch.

Answer: (C) constant and positive—you do work on the branch.

Why: You are pulling the branch toward you and it is moving toward you. Although the branch is not accelerating and is thus experiencing a net force of zero, you are pulling it toward you while it is being pulled away from you by drag forces in the water.

Problem 13:

You are jumping up and down on a trampoline, under the watchful supervision of your gymnastics coach. (We’ve included the coach because trampolines are dangerous and we don’t want to be sued for any virtual injuries that might occur during this exam.) Each time you bounce off the trampoline, you stretch its surface and springs. Just before the surface and springs reach their maximum stretch, your velocity is

(A) downward but your acceleration is upward.

(B) downward and your acceleration is downward.

(C) upward but your acceleration is downward.

(D) upward and your acceleration is upward.

Answer: (A) downward but your acceleration is upward.

Why: The maximum stretch occurs just before you reach the bottom of the trampoline’s travel. (Whenever you are above the trampoline, its surface and springs are barely stretched at all. The only time at which the stretch is significant is when you are pushing the trampoline’s surface down hard and are those relatively near the ground.) Just before you reach this lowest point in your travels, you are heading downward (toward that lowest point) but you are losing your downward speed. You are accelerating upward.

Problem 14:

As you stand at the end of a diving board, the board bends downward. While you slowly bend your knees and prepare to jump, the board doesn’t move. Finally, when you begin to jump upward, the board

(A) moves upward since the board's restoring force is in the direction of its unbent equilibrium position.

(B) moves downward since you must apply a downward force on the board larger than your weight in order to jump upward.

(C) moves upward since your weight is no longer there to hold the board down.

(D) stays in the same position since the restoring force provided by the spring board balances your weight.

Answer: (B) moves downward since you must apply a downward force on the board larger than your weight in order to jump upward.

Why: To accelerate upward during the jump, something must exert an upward force on you that is larger than your downward weight. The board exerts this large upward force and as it does, it accelerates downward. When it is just supporting your weight, it bends only far enough so that its restoring force equals your weight. During the jump, the forces between you and the board become larger than your weight. The board accelerates downward as you accelerate upward.

Problem 15:

Natural convection is used to heat food in a conventional electric oven. That convection is most efficient at conveying heat to the food when the oven's heating element is located

(A) above the food. (B) below the food. (C) beside the food. (D) behind the food.

Answer: (B) below the food.

Why: Natural convection lifts heat upward in buoyant hot air. The heating element warms the air it touches and that hotter air is lifted upward by buoyant forces from the surrounding colder air. Food directly above the element heats rapidly as this hot air arrives and touches it.

Problem 16:

Your roommate’s car has a pair of “fuzzy dice” hanging by a string from its rearview mirror. Yes, they’re tacky but you don’t have the heart to say anything. Anyway, these dice do a nifty job of indicating how the car is moving. For example, if the dice swing forward toward the car’s windshield while the car is on a level road, you know that the car is

(A) accelerating backward.

(B) accelerating forward.

(C) traveling backward at a steady pace.

(D) traveling forward at a steady pace.

Answer: (A) accelerating backward.

Why: When the car accelerates backward, the dice continue at their original velocity for a while and drift forward relative to the car. The car effectively “drives out from under” the dice and they try to leave the car through the front windshield.

Problem 17:

You are in a store that sells bathroom scales and decide to stand on two spring scales at once. Both scales are resting on the ground and you stand stationary with one foot on each scale. You can determine your correct weight by

(A) taking the reading from either scale and doubling it.

(B) taking the reading from either scale and dividing it in half.

(C) taking the reading of either scale.

(D) adding together the readings of the two scales.

Answer: (D) adding together the readings of the two scales.

Why: The two scales are supporting your weight together and each is reporting how much force it is exerting. Their combined upward force is equal to your weight (you're not accelerating, after all) so if you add the values they report, you'll determine your total weight.

Problem 18:

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 good thermal conductor.

Problem 19:

You are practicing shooting free throws at the basketball court. When you throw the ball, it travels in an arc toward the hoop. Ignoring any forces that air exerts on the ball, the net force on the ball just after it leaves you hand is

(A) down and away from you.

(B) straight down.

(C) zero.

(D) up and away from you.

Answer: (B) straight down.

Why: Only gravity acts on the ball and gravity pulls the ball straight down. Even with air resistance included, the forces on the ball are never forward and thus never point away from you.

Problem 20:

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 21:

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 22:

When a modern car crashes into a tree and comes to an abrupt stop, the driver's face and chest collide with an air bag rather than with the steering wheel. The driver's chances of serious injury are reduced by hitting the air bag rather than the steering wheel because the driver transfers

(A) more momentum to the air bag than he would to the steering wheel if there were no air bag.

(B) the same amount of momentum to the air bag as he would to the steering wheel if there were no air bag, but he does so with a larger force because of the air bag.

(C) the same amount of momentum to the air bag as he would to the steering wheel if there were no air bag, but he does so with a smaller force because of the air bag.

(D) less momentum to the air bag than he would to the steering wheel if there were no air bag.

Answer: (C) the same amount of momentum to the air bag as he would to the steering wheel if there were no air bag, but he does so with a smaller force because of the air bag.

Why: The driver is eventually going to stop completely, so the momentum transfer is always the same: the driver gives up all the driver’s momentum to the tree. But it’s much more “pleasant” to transfer this momentum slowly via small forces than it is to transfer this momentum rapidly via large forces. The air bag slows the transfer and lessens the forces involved.

Problem 23:

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 24:

You are choosing the filament for a light bulb and want it to emit visible light as efficiently as possible when it becomes very hot. You should make that filament

(A) black (B) white (C) shiny like a mirror (D) gray

Answer: (A) black

Why: Black objects are best at emitting thermal radiation, so a black filament would be brighter than any other color.

Problem 25:

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.

PART II: SHORT ANSWER QUESTIONS

Please give a brief answer in the space provided.

Problem 1:

You are riding your bicycle over a large hill. You have just reached the top and as you start down the other side, you stop pedaling and begin to coast. It’s a long, steep hill with a constant downward slope. You are riding a superbly engineered bicycle, which wastes no energy in sliding friction.

(A) As you coast down the hill, your velocity increases. What is the direction of your acceleration?

Answer: Downhill.

Why: Your downward weight and the mostly upward support force from the ground combine to create a downhill residual force that causes you to accelerate directly downhill.

(B) At this point, how does the magnitude of your apparent weight compare to that of your actual weight?

Answer: Your apparent weight has a smaller magnitude than that of your actual weight.

Why: Your downhill acceleration is much less than it would be if you simply fell straight downward. The upward apparent weight you would experience if you fell straight downward would be equal in magnitude to your actual weight (which is why you would feel weightless). But the uphill apparent weight you feel as you accelerate slowly downhill is much less than your actual weight. You are simply not accelerating fast enough for that apparent weight to equal your actual weight.

(C) If you continue to coast down the hill, you will eventually stop accelerating and settle in at a constant downhill speed. Even though you are not accelerating, there are still three forces acting on you that perfectly balance each other. What are these three forces?

Answer: Your weight (or gravity), the support force of the road, and air resistance (or drag).

Why: In the absence of friction, the only three things that push on you are the earth (via gravity), the road (via a support force), and the air (via air resistance or drag).

(D) In what direction do each of these three forces act?

Answer: Your weight (or gravity) acts straight downward, the support force of the road acts at right angles to the road’s surface, and air resistance acts directly uphill.

Why: Gravity always acts straight down, support forces always act at right angles to the surfaces exerting them, and air drag acts in the direction opposite the relative motion of an object through the air. Since you are rolling directly downhill on your bicycle through stationary air, the air pushes you directly uphill.

Problem 2:

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

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

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

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

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

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

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

(D) What a day! You are about to head home to tell your friends about the crazy crew you've been talking with when someone comes in with a glass vase that's supposed to automatically reassemble itself if you accidentally break it. You just have to put the broken vase in a box and wait. In a minute or two, the vase will be as good as new. You agree with the inventor that this reconstruction

trick doesn't violate any of the laws of motion. However, you can still be sure that it won't work because

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

Problem 3:

You are part of a team designing an energy-efficient escalator system for a new department store. The store has two floors and patrons will ride between the floors on the escalator. Your team plans to use a single belt of stairs that will travel from the ground floor up to the second floor and then return to the ground floor in a perfectly symmetrical arrangement (see Figure G). The belt will then travel underneath the first floor and reemerge at its starting point. A single motor will turn the belt and convey all of the people up and down between floors.

(A) The belt moves at a very steady pace so that a person riding it upward toward the second floor travels at constant velocity. What is the amount and direction of the net force on that person?

Answer: Zero net force (no direction).

Why: The person is moving at constant velocity and is not accelerating, so the net force on the person is zero.

(B) As that person rides upward toward the second floor, is there any (positive) work being done and, if so, is it being done by the person or by the belt of stairs?

Answer: The belt of stairs is doing positive work on the person.

Why: The stairs are pushing the person upward and the person is moving at least partially upward. Since the force and the direction of motion are somewhat in the same direction (not at right angles and not in opposite directions), the belt of stairs is doing work on the person.

(C) The total weight of patrons on the escalators is 10,000 newtons (about 2,200 pounds). Half the people (weight 5,000 newtons) are riding the upward escalator and half (weight 5,000 newtons) are riding the downward escalator. The belt advances 1 meter each second. Neglecting friction and air resistance, how much power must the motor provide to the belt?

Answer: Zero.

Why: The belt is raising the same mass of people on one side as it's lowering on the other. The people going down do work on the belt and this work is just enough to raise the other people. The motor doesn't have to do any work (except to overcome friction and air resistance, which we're neglecting).

(D) If the only person on the escalators is riding down from the second floor toward the first floor, energy is being transferred from what to what?

Answer: From the person to the belt of stairs.

Why: The person riding down is pushing downward on the stairs and they are moving at least partially downward. Thus the person is doing work on the stairs, transferring energy to those stairs.