Physics 105

Physics 105 - How Things Work - Fall, 1999

Final Examination

Given Wednesday, December 15, 1999, 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:

You are riding a skateboard down a gradual incline. In order to waste as little energy as possible while still maintaining control over your direction of motion, the contact between the sidewalk and the wheels should experience

(A) only static friction.

(B) no friction.

(D) only sliding friction.

Problem 2:

In Charlottesville, an egg left in boiling water for 10 minutes becomes a firm, "hard boiled" egg. On the top of Mount Everest, with a height of 29,029 feet, an egg left in boiling water remains soft indefinitely. The egg fails to cook on Mount Everest because

(A) water boils at low temperature when the air pressure is very low.

(B) water boils at low temperature when gravity is weak.

(D) an egg cannot get very hot when gravity is weak.

Problem 3:

Your car has a flat tire on a deserted road and you can't find the jack. Fortunately, you have a box of enormous plastic bags and a portable leaf blower. You put one of the bags under the car and use the blower to inflate it. The bag easily lifts the corner of the car so that the damaged tire is off the ground. You change the tire and continue on your trip. While the pressure inside the bag never reached more than twice atmospheric pressure, the bag was able to exert a tremendous upward force on the car because

(A) the increased pressure was exerted on a large surface area underneath the car.

(B) inflating the bag made it spherical and spherical objects are stronger than any other shape.

(D) air from the leaf blower was traveling fast and fast-moving air exerts drag forces on anything it encounters.

Problem 4:

You have just landed a new job with a corner office near the top of a high-rise building. You soon find out why this office was available; it is on the sunny side of the building and becomes uncomfortably hot on sunny days even when it is quite cool outside. Although your college physics course is a distant memory you have an idea of how to solve the problem. You cover the inside of the windows with aluminum foil. This results in

(A) a reduction of radiative heat transfer since the shiny aluminum foil has a low emissivity.

(B) a reduction of convective heat transfer.

(D) a reduction of conductive heat transfer from the cool outside air to the warm room inside.

Problem 5:

When a log is floating on water, much of the log is above the water and is actually surrounded by air. If that surrounding air were to suddenly disappear, the log would

(A) move downward slightly and float somewhat lower (deeper) in the water.

(B) float at the same height as before the air left.

(D) move upward slightly and float somewhat higher (less deep) in the water.

Problem 6:

You are juggling grapefruits in your hands and are about to toss one far above your head. After it leaves your hand, the grapefruit will experience

(A) the upward force of its weight as it rises. Once the grapefruit reaches its maximum height, it will begin to experience the downward force of its weight.

(B) an upward force as it rises. This upward force will gradually diminish to zero at the grapefruit's maximum height, after which the grapefruit will experience only the downward force of its weight.

(C) both an upward force and the downward force of its weight as it rises. The upward force will gradually diminish to zero at the grapefruit's maximum height, after which the grapefruit will experience only the downward force of its weight.

(D) only the downward force of its weight, both before and after it reaches its maximum height.

Problem 7:

You are taking a shower in your dormitory when someone flushes a toilet nearby. The pressure in the cold water line drops and you find yourself showering in what feels like molten lava. This loss of cold-water pressure occurs when the flushing toilet lets more cold water flow through the pipes delivering it to the bathroom and the water's speed in those pipes increases. The cold water's faster motion in the delivery pipes reduces its pressure in the showerhead because faster moving water

(A) has less kinetic energy than slower moving water.

(B) losses more energy to viscous drag as it flows through the delivery pipes.

(D) has less gravitational potential energy than slower moving water.

Problem 8:

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 your hand is

(A) down and away from you.

(B) up and away from you.

(D) zero.

Problem 9:

You are swimming at the beach. You swim out past the breaking surf so that you can float among the waves. Each time a wave crest passes, you travel

(A) vertically—directly up and then directly down.

(B) horizontally toward shore for a distance that's proportional to the slope of the wave crest.

(D) horizontally toward shore for a distance equal to one wavelength of the passing wave.

Problem 10:

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) the lighter ball impacts the floor at about half the horizontal distance from the base of the table than does the heavier.

(B) 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.

Problem 11:

A flashlight equipped with new batteries produces bright, yellow-white light. As the batteries in the flashlight wear out, the bulb will

(A) suddenly go out even if the filament doesn't break.

(B) glow dimly and produce reddish light.

(D) glow dimly, but continue to produce yellow-white light.

Problem 12:

A pedestrian bridge crosses Emmet Street near Ruffner Hall (the Education School). This bridge is entirely supported by columns from below. A gap at each end of the bridge separates the bridge's surface from the sidewalks leading to the bridge. The width of each gap changes with time. This width is smallest

(A) on hot days.

(B) at noon.

(D) on cold day.

Problem 13:

One warm spring day you and some friends go to the beach at a nearby lake. You are tossing a soft, almost fully inflated beach ball around when someone accidentally knocks it into the lake. Although it is a warm day, the water is still very cold so nobody wants to retrieve the ball. You notice that the ball seems to have deflated somewhat after sitting in the water for a while. The contact with the cool water has caused the temperature of the air inside the ball to drop, resulting in

(A) a decrease in the pressure inside the ball.

(B) an increase in the density of the air inside the ball.

(D) an increase in the pressure inside the ball.

Problem 14:

The strings of a guitar vibrate at different frequencies. They have different thicknesses because

(A) a thinner string has more tension than a thicker string and vibrates more quickly.

(B) a thicker string has more tension than a thinner string and vibrates more quickly.

(D) a thinner, less massive string vibrates more slowly than a thicker string of the same length and tension.

Problem 15:

A child is playing on a swing. As long as he doesn't swing too high the time it takes him to complete one full oscillation will be independent of

(A) the weight of the child, but not the amplitude of the motion.

(B) both the amplitude of the motion and the weight of the child.

(D) the amplitude of the motion, but not the weight of the child.

Problem 16:

You're operating a propane gas grill from a fuel tank that's located below the grill. This tank is half filled with liquid propane. As the grill consumes gaseous propane, the tank's temperature drops below room temperature. This refrigerating effect occurs because

(A) heat naturally flows from a cooler object to a hotter object.

(B) heat is needed to initiate and sustain combustion in the grill.

(D) heat naturally rises from the tank to the grill above it.

Problem 17:

Two boys are swinging a long jump rope while a girl jumps in the middle. Despite its overall rotating motion, the jump rope is actually vibrating up and down in its fundamental mode while the boys circle their hands gently to keep the rope vibrating. To speed up the jump rope's vibration so that the girl has to jump more often, the boys must circle their hands more quickly and

(A) reduce the tension in the rope.

(B) increase the tension in the rope.

(D) increase the height (amplitude) of the arc formed by the swinging rope.

Problem 18:

A popular holiday house ornament consists of a little metal fan with horizontal blades, that pivots above a couple of burning candles. As the candles burn, their heat makes the fan spin and little hammers that move with the fan ring several tiny bells. While the decoration runs on heat alone, it won't work when you remove the candles and put it inside a hot, dark oven. It's inability to use the oven's heat is explained by the fact that

(A) the candles produced burned gases while the oven contains only hot air.

(B) the candle's heat is ordered, while the heat in the oven is completely disordered.

(D) both a hot region and a cold region are needed in order to convert heat into work.

Problem 19:

When you blow gently across the top of a particular soda bottle, it emits a tone. The column of air in the bottle is vibrating up and down in its fundamental mode. If you replace the air in the bottle with helium and then blow gently across the top of the bottle, it will emit

(A) a higher pitched tone.

(B) a tone at the same pitch as before.

(D) a lower pitched tone.

Problem 20:

Two of your friends are bungee jumping from Beta Bridge. After the initial fall and rebound, each jumper bounces up and down as a harmonic oscillator—a mass on the end of spring. The period of the oscillator is the time between successive bounces. One friend weighs twice as much as the other. Since they use the same bungee cord for their jumps,

(A) the two friends will have the same period, regardless of how high they bounce.

(B) the heavier friend will have a longer period than the lighter friend.

(D) the heavier friend will have a shorter period than the lighter friend.

Problem 21:

Suppose that a shoelace passes without friction through 5 holes on each side of your shoe. If the tension in that shoelace is 10 N, how much total force is the shoelace exerting on the right side of your shoe?

(A) 100 N

(B) 10 N

(D) 25 N

Problem 22:

You are surfing on a large wave. You are half way up the front edge of the wave and maintaining a steady height. You and the wave are moving steadily toward shore at a constant speed. The net force on you is

(A) downhill—toward the trough in front of you.

(B) zero.

(D) horizontal—toward the shore.

Problem 23:

You are mountain biking through the woods and come to a deep gully. The bottom of the gully is a smooth bowl shape without any obstacles. Neglecting friction and air resistance, you are able to coast down one side and back up the other without pedaling. When you are at the bottom of the gully, you feel

(A) heavier than normal since you are accelerating upward.

(B) lighter than normal since you are accelerating upward.

(D) heavier than normal since you are accelerating downward.

Problem 24:

You are at the park throwing a stick for your dog to fetch. When you throw a smooth straight stick by one end, it tends to tumble end over end as it flies through the air. However, when you throw a stick that still has some leaves attached to one end, it flies through the air without tumbling and travels in a smooth arc with the stick leading and the leaves trailing. This automatic alignment occurs because

(A) the center of mass of the stick is no longer near its geometric center.

(B) the center of pressure is at the same point as the center of mass in the stick, stabilizing its flight.

(C) the viscosity of the air near the leaves is highest, producing torques which oppose any rotation the stick had after leaving your hand.

(D) the drag forces acting on the leafy stick are not uniform around the stick's center of mass.

Problem 25:

On a windy day you notice that a tall light pole is bent away from its equilibrium position. If the wind speed were to increase the pole would

(A) remain bent by the same amount since aerodynamic drag forces, like sliding friction, are independent of the relative speed of the objects.

(B) straighten out because the airflow would become laminar and reduce the drag force.

(D) bend further from its equilibrium position because the aerodynamic drag forces that are bending the pole will increase with the speed of the air moving around the pole.

Problem 26:

You construct a water-powered go-cart by attaching a large tank of water to a cart. The water can be forced out a nozzle by connecting a tank of high-pressure air to the water tank. In preparation for your first ride, you position this contraption facing away from a brick wall. You climb on and start spraying the water against the wall. To your delight you accelerate away from the wall and begin to move. When you have moved far enough away from the wall that the stream of water can no longer hit it, you

(A) continue to accelerate as the water sprays out the back of the cart.

(B) continue to move, but stop accelerating since the water can no longer push against the wall.

(D) continue to accelerate, but less since it takes more force to accelerate a moving object than a stationary one.

Problem 27:

You are enjoying an elegant candlelit dinner for two but the waiter has been a little careless with the ice. Your glass of ice water contains 25% water and 75% ice, while your friend's glass contains 75% water and 25% ice. The temperature of your glass of ice water

(A) is higher than that of your friend.

(B) is the same as that of your friend.

(D) depends on when it was filled. The glass that was filled first will now be warmer than the glass that was filled second.

Problem 28:

You can put your hand in a 400° F oven briefly without getting burned. However, even a second or two of contact with 212° F steam can be quite painful. The steam delivers heat much faster to your hand because steam

(A) undergoes much more rapid convection than air.

(B) condenses into water and deposits its heat of vaporization into your hand.

(D) is actually a liquid with a high thermal conductivity. It is composed of countless tiny droplets suspended in the air.

Problem 29:

When you get new tires installed on your car the wheels are carefully balanced by placing small weights around the outside of the rim. If one of these weights falls off, your car may vibrate violently when you drive at certain speeds. This vibration occurs for speeds at which

(A) the vibration frequency of the off-balance wheel matches the frequency at which the car likes to vibrate allowing a resonant energy transfer between the two.

(B) the rotational kinetic energy of the wheel exactly matches the translational kinetic energy of the car, allowing a resonant energy transfer between the two.

(D) the amplitude of the vibrating wheel becomes large enough to overcome the inertia of the massive car.

Problem 30:

Two-part epoxy is a versatile adhesive that can be used to glue things together. Unlike most glues, it consists of two liquids that must be mixed together. When the liquids are combined, the mixture becomes warm indicating that a chemical reaction is taking place in which

(A) the bonds holding together the molecules in the reacted mixture are stronger that the bonds holding together the molecules of the unmixed liquids.

(B) the bonds holding together the molecules in the reacted mixture are weaker that the bonds holding together the molecules of the unmixed liquids.

(D) chemical potential energy is increasing.

Problem 31:

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 pushed back on Mike, but with less force than Mike exerted on him.

(B) Johnny did push back on Mike, with exactly the same amount of force.

(D) Johnny pushed back on Mike, but with more force than Mike exerted on him.

Problem 32:

The brake system in most cars makes use of a hydraulic system. This system consists of a fluid filled tube connected at each end to a piston. Assume that the piston attached to the brake pedal has a cross sectional area of one half a square inch and the piston attached to the brake pad has a cross section area of two square inches. When you apply a force of 10 pounds to the piston attached to the brake pedal, the force at the brake pad will be,

(A) 5 pounds.

(B) 10 pounds.

(D) 40 pounds.

Problem 33:

You are filling a large lightweight dry cleaning bag with helium. At first, the plastic bag doesn't float. But as you keep adding helium to the bag, it eventually begins floating because

(A) at the same pressure and temperature, the upward buoyant force on a helium-filled bag is larger than the buoyant force on an air-filled bag with the same volume.

(B) the helium-filled bag's weight decreases as you put more lightweight helium particles inside it.

(C) the average density of the helium-filled bag decreases even though the buoyant force on the bag remains constant as it fills.

(D) as the volume of displaced air increases, the buoyant force increases until it is greater than the weight of the helium-filled bag.

Problem 34:

Moments before it's ignited by the sparkplug, the mixture of fuel and air inside an automobile cylinder is compressed to very high density. During the compression process, the mixture's

(A) temperature stays the same but its pressure rises.

(B) temperature rises dramatically and so does its pressure.

(D) temperature rises dramatically but its pressure drops.

Problem 35:

A thermoelectric cooler is a type of heat pump that uses electric power to move heat against its natural direction of flow. In such a heat pump electrical power must be converted to thermal energy because,

(A) the entropy of the system must be conserved.

(B) Newton's laws of motion prevent heat from moving from a cool region to a warm region.

(D) the flow of heat from a cool region to a warm region alone would violate the conservation of energy.

Problem 36:

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 5 feet below the surface of the water.

(D) at least 40 feet below the surface of the water.

Problem 37:

The glass envelope of an ordinary incandescent light bulb is filled with a low-pressure mixture of nitrogen and argon gases. If there were no gas at all inside a bulb's envelope, this special bulb would be

(A) more energy efficient but would have a shorter operating life than an ordinary bulb.

(B) less energy efficient and would have a shorter operating life than an ordinary bulb.

(D) more energy efficient and would have a longer operating life than an ordinary bulb.

Problem 38:

You are frosting some holiday cookies using a tube of frosting with a long narrow tip attached. You must squeeze the tube very hard to get the frosting to come out of the narrow opening because,

(A) viscous drag between the walls of the tip and the frosting waste considerable energy as heat.

(B) viscous drag between the walls of the tip and the frosting causes the frosting to swirl around chaotically.

(C) Newton's third law requires most of the energy in the frosting to be used to push back on you rather than moving it through the tip.

(D) the high density of the frosting impedes its flow through the small opening.

Problem 39:

To improve a xylophone's appearance, the orchestra director decides to have it painted. Each xylophone bar is actually a harmonic oscillator that vibrates when struck by a wooden mallet. When bending in its fundamental mode, the bar's middle and ends move in opposite directions. Painting the bar adds mass to the bar without affecting its stiffness, so the paint will

(A) not affect the pitch or sound volume of the bar.

(B) raise the bar's pitch.

(D) not affect the pitch of the bar, but will reduce its sound volume.

Problem 40:

A new bowling alley has just opened in which the lanes are not horizontal, but slope upward slightly from where you release the ball to where the pins are standing. The lanes in this new bowling alley are highly polished, so there is no friction between the ball and the floor. Moreover, the ball never moves fast enough for air resistance to effect its motion. Once you release the ball and allow it to roll on its own up one of these lanes, the ball

(A) moves uphill because of the uphill acceleration on the ball.

(B) moves with a constant velocity because of Newton's first law; an object in motion tends to remain in motion.

(D) decelerates because of the uphill velocity of the ball.

Problem 41:

A fan can be used to circulate air around a room. The pressure at the inlet side of the fan is

(A) less than the pressure at the outlet side and less than atmospheric pressure..

(B) less than the pressure at the outlet side but more than atmospheric pressure.

(D) more than the pressure at the outlet side.

Problem 42:

You place three nonflammable objects in a fire. They are identical in shape and size, but one object is black, the second is white, and the third is shiny silver. After a few minutes, all three objects are at the same temperature: 1800° C. They remain solid and are now glowing with thermal radiation. Which one is glowing most brightly?

(A) The first object (black).

(B) They are all glowing with equal brightness.

(D) The second object (white).

Problem 43:

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) 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.

(C) 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.

(D) your velocity is less as you land on the mattress than it would have been if you'd landed on the sand heap.

Problem 44:

You're the first person to visit Mars and you've just met a group of Martian school children. They are playing street hockey with parts from the Mars Polar Lander. After years of watching Star Trek reruns, they are fluent in English. One of them asks you how your weight and mass have changed since you left earth. You take a moment to measure both and reply correctly that

(A) your mass is still essentially unchanged but your weight is less than on earth.

(B) your weight is still essentially unchanged but your mass is less than on earth.

(D) your weight and mass have both changed significantly.

Problem 45:

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 glass bowl to both the plastic bowl and the metal bowl.

(B) heat will flow from the plastic bowl to the glass bowl, and from the glass bowl to the metal bowl.

(D) heat will flow from the metal bowl to the glass bowl, and from the glass bowl to the plastic bowl.

Problem 46:

On a visit to the pet store you notice that some fish are able to hover motionless near the center of the tank, even without moving their fins or tail. This indicates that

(A) the fish is dead.

(B) the density of the fish is less than the density of the water.

(D) the density of the fish is equal to the density of the water.

Problem 47:

You and a friend are wondering how your weights compare. You don't have a scale, but you do have a piece of rope. To compare your weights you throw the rope over the branch of a tree and each hang from one end of the rope. To your surprise, when you both pick your feet up the rope remains motionless indicating that your weights are exactly the same (neglecting any friction between the rope and the branch). From this observation you know that the tension in the rope is

(A) equal to four times your weight.

(B) equal to half your weight.

(D) equal to your weight.

Problem 48:

You place a bottle of water over a burner and bring it to a rapid boil. You then cover the bottle with a stopper and remove it from the heat. As soon as the water stops boiling you push the stopper snugly into the opening to seal the bottle, which now contains no air, only liquid water and steam. If you let the sealed bottle cool to room temperature,

(A) the pressure will remain the same as when you sealed it since the rate at which water evaporates balances the rate at which it condenses.

(B) a partial vacuum will form since the vapor pressure of water at room temperature is much less than atmospheric pressure.

(D) the water will begin to boil again since a vacuum will form and water in a vacuum boils.

Problem 49:

If you blow across the top of a half full bottle of soda you can produce a clear tone. If you take a drink of soda to reduce the amount of liquid in the bottle and try this again the pitch (frequency) of the sound produced will

(A) increase.

(B) stay the same.

(D) decrease.

Problem 50:

It's a warm summer day and you're having lunch outdoors on a patio. A window air conditioning unit hums quietly nearby as it cools an office inside the building. Your friend notices that the unit's outdoor part is emitting a considerable amount of heat and comments on how strange that is. You explain correctly that the air conditioner's outside part is emitting the heat

(A) it produces from the electricity it consumes.

(B) that is left over when it converts thermal energy from the inside air into electricity.

(D) it produces during its defrost cycle; when it warms up its evaporator to remove ice that forms because of the humidity.

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:

You are sitting by the pool on a hot summer day, sipping a glass of ice water.

(A) Why is the ice floating near the surface of the water?

(B) You notice that droplets of water are forming on the outside surface of the glass. What does this tell you about the relative humidity (the measure of the condensation rate as a percentage of the evaporation rate) at the surface of the glass?

(C) When you put the glass down on the hot surface of a black table the ice-water mixture remains at a uniform temperature of 0° C even thought heat is flowing from the hot table to the cold ice water. What is happening to the thermal energy that is being added to the ice water?

Problem 2:

Some distant relatives have left you something in their will: a company that manufactures bathroom scales. Sadly, the company has fallen on hard times because their scales aren't popular anymore. You begin to examine the current model and soon realize that whoever designed it had never taken a course in basic physics. You make a few changes and soon have business booming again. Let's take a look at why the scale was flawed prior to your changes.

(A) The scale uses a spring to measure weight. However, to save money, the scale uses a cheap spring that gradually loses its stiffness. As the years pass, its restoring force gets weaker and weaker. Will this flaw affect the scale's reading and, if so, will the scale read heavier or lighter as the years pass?

(B) Its soft rubber base gives the scale a pleasant "bouncy" feeling when you step on it. But the bouncing base also makes the scale's needle swing back and forth so that it's hard to read your weight. Why does the up and down motion of the scale cause the needle to swing?

(C) The top surface of each scale is made of shiny copper metal. The copper looks great but feels unpleasantly cold when you step on it in bare feet. You redesign the scale to use a copper-colored plastic top and the scale becomes much more comfortable to step on. Why does the plastic top feel warmer than the metal top, even when they are at the same temperature?

Problem 3:

It's your first day on the staff of the U.S. Patents Office and you're excited about having some new ideas come across your desk.

(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. You can be sure that this claim is nonsense because

(B) Another inventor comes in with a small motor-like device that is powered by a burning candle. The inventor claims that this device takes the heat from the candle and turns it entirely into work. The device thus doesn't warm the room at all. Your knowledge of the laws of thermodynamics assures you that this claim, too, is nonsense because

(C) As though the entire population of loser inventors was released on you in one day, another clown comes in claiming to have a heat pump that can transfer heat out of a box of corn flakes for as long as you like. The cereal just gets colder and colder. Once again, you know that this is impossible because

Problem 4:

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.)

(B) If the cue ball had half the mass of the other ball, would the cue ball remain stopped after the collision?

(C) If the cue ball had half the mass of the other ball, which ball would experience a greater force during the collision?

Problem 5:

You have recently arrived on the galactic megacruiser "Hollywood." This enormous spaceship was designed in part by unemployed screenwriters, so it has a few quirks that naturally occur when you ignore the laws of physics and build things according to what makes movie stars look their best.

(A) The ship has a huge flight deck from which small sightseeing spacecraft can depart. You watch from the flight office as tourists walk across the flight deck and board one of the little ships. The flight attendant shuts the passengers in and the flight controller immediately opens a huge door between the flight deck and empty space beyond. Suddenly there is a horrendous roar as air rushes out of the flight deck. Why does the air begin flowing toward the flight deck doors?

(B) Think of the air in the flight deck as being in two halves: one nearest to the doors and one farthest from the doors. Use the definition of work to show that the half farthest from the doors does work on the half nearest to the doors.

(C) Even though it's turned off, the small ship is unceremoniously tossed into space moments after the doors open. What type of force causes the ship's spaceward acceleration?

Problem 6:

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. 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?

(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?

(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?

Problem 7:

You are pushing a child on a playground swing. She swings back and forth, completing one full cycle of motion every 5 seconds.

(A) What form(s) of energy is/are involved in the child's swinging motion?

(B) You want to reduce the amplitude of her swing. When during each cycle should you push her gently forward in order to reduce the size of her swing?

(C) How would you have to change the playground swing or the child in order to increase her period from 5 seconds to more than 5 seconds?

Problem 8:

You are competing in a bicycle race, but have some trouble along the way.

(A) One of your tires develops a slow leak. As the air slowly leaks out of the tire, why does the wheel become harder to keep moving at the same speed?

(B) Finally you notice what is happening and stop to fix the leak. What happens to the temperature of the air inside the tire as you quickly pump it up?

(C) When you get back on your bike you realize that you have left it in a gear where the chain is on a small crank sprocket (the gear attached to the pedals) and a large freewheel sprocket (the gear attached to the rear wheel). Does this make it easy or difficult to start pedaling?