Download Midterm solutions - Bryn Mawr College

NAME:
Physics 109 : How Things Work : Spring 2006
Mike Noel - [email protected]
Bob Ekey - [email protected]
Midterm Examination
This examination consists of two parts. Answer all questions in both parts of the exam. Each part
will be weighted equally in determining the overall exam grade.
This is a closed book 50-minute exam.
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PART I: MULTIPLE CHOICE QUESTIONS
There is one right answer to each question. Clearly mark your answer choice by placing a dark
mark over the appropriate letter as indicated below.
(A)
(B)
(C)
(D)
Problem 1:
You have a very nice frictionless merry-go-round. To start it moving you run along side it pushing
perpendicular to its radius with a constant force. What is true about its motion?
(A) The angular speed of the merry-go-round is constant.
(B) The angular momentum of the merry-go-round is constant.
(C) The merry-go-round is undergoing an angular acceleration.
(D) There is no net-torque on the merry-go-round.
Answer: (C) The merry-go-round is undergoing an angular acceleration.
Why: You are applying a torque to the merry-go-round (force at a distance), which according to
Newton’s II law for rotation means that the merry-go-round is undergoing an angular acceleration.
Problem 2:
You have an elephant that weighs at least 10,000 N, and have a bunch of scales that can measure
weights between 0 and 5,000 N. How can you measure the elephant’s correct weight with these
scales?
(A) Have the elephant stand on one scale.
(B) Have the elephant stand on two scales at the same time with different parts of his body (say one
under each foot) and subtract the readings from each other.
(C) Have the elephant stand on four scales at the same time with different parts of his body (say one
under each foot) and add the each scales readings together.
(D) Have the elephant stand four scales at the same time with different parts of his body (say one
under each foot) and find the average reading of each scale.
Answer: (C) Have the elephant stand on four scales at the same time with different parts of his body
(say one under each foot) and add the each scales readings together.
Why: The four scales are supporting the elephant’s weight together and each is reporting how much
force it is exerting. Their combined upward force is equal to the elephants weight (he’s not
accelerating, after all) so if you add the values they report, you'll determine the elephant’s total
weight. (A) can’t work, since the scale only reads from 0-5,000N and the elephant weighs over
10,000N
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Problem 3:
You are dropping food supplies from your airplane to your friends who are camping on the plains
below. You fly at a constant horizontal velocity. Assuming that the supplies survive the fall and
neglecting air resistance and other sources of friction, when should you drop the supplies to ensure
they land on the target right next to their campsite?
(A) When the plane is directly above the target.
(B) Before the plane is directly above the target.
(C) After the plane is directly above the target.
(D) It doesn’t matter.
Answer: (B) Before the plane is directly above the target.
Why: Once you release the supplies, they are still traveling at the same horizontal constant velocity
as the plane (neglecting air resistance), so if you drop the supplies when you are directly above or
after you pass the target the supplies will overshoot the target (but luckily not land on your friends
campsite).
Problem 4:
You decide to use an old oven element to heat up your room. You place it near the top of the room
to keep it out of the way, and to prevent accidentally burning yourself. Evidently the room you
are in is quite free of drafts, so the air in the room is still. What’s the main way the element will
provide heat to the room?
(A) By convection only.
(B) By convection and radiation.
(C) By radiation only.
(D) By convection, radiation, and conduction.
Answer: (C) By radiation only.
Why: The infrared and red light from the hot element transfer heat to you and the rest of the room
via radiation. The heated air near the top element floats on the cooler air below it and doesn't
undergo convection.
Problem 5:
You need light bulbs and decide to look at some different brands. You’ve narrowed your options
down to two choices, one that runs at 2,000 °C the other runs at 1,500 °C. Both have the same type
of filament, intert gas and bulb color (frosted). Which bulb provides more visible light?
(A) The 2,000 °C bulb.
(B) The 1,500 °C bulb.
(C) Both provide the same amount of visible light
(D) Can’t tell from the information provided.
Answer: (A) The 2,000 °C bulb.
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Why: Both filaments act essentially like black-bodies, and the higher the temperature the greater
the contribution of the radiation in the visible spectrum. Hence the 2,000 °C bulb.will provide more
visible light than the 1,500 °C bulb.
Problem 6:
You walk to the end of a springy diving board and find that it bends downward by 2 inches. Next
you start bouncing up and down at the end of the diving board. During one bounce you deflect the
board downward by 4 inches before bouncing back upward. The point at which you reach your
maximum speed during this bounce is when the board is
(A) bent downward by 4 inches.
(B) not bent at all, but you are on your way down.
(C) bent downward by 2 inches.
(D) not bent at all, but your are on your way up.
Answer: (C) bent 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
decellerates, losing speed and kinetic energy.
Problem 7:
Two metal balls are the same size, but one weighs twice as much as the other. The balls roll off of a
horizontal table with the same speed. In this situation,
(A) both balls hit the floor at approximately the same horizontal distance from the base of the table.
(B) the heavier ball hits the floor at about half the horizontal distance from the base of the table than
does the lighter ball.
(C) the lighter ball hits the floor at about half the horizontal distance from the base of the table than
does the heavier ball.
(D) the heavier ball hits the floor considerably closer to the base of the table than the lighter ball,
but not necessarily at half the horizontal distance.
Answer: (A) both balls hit the floor at approximately the same horizontal distance from the base of
the table.
Problem 8:
A hockey puck slides across the ice with constant speed in a straight line from point P to point Q as
view from above the rink. As the puck passes a player at point Q, she gives it a sharp kick in a
direction perpendicular to its motion as shown by the heavy arrow in the figure below. Which path
(indicated by the dotted line) would the puck most closely follow after receiving the kick?
Physics 109, How Things Work, Spring 2006
Answer: (B)
Problem 9:
A woman exerts a constant horizontal force on a large box. As a result the box moves across the
floor at a constant speed. If the woman doubles the constant horizontal force that she exerts on the
box to push it across the same horizontal floor, the box then moves
(A) with a constant speed that is double the speed in the first situation.
(B) with a constant speed that is greater than the speed in the first situation, but not necessarily
twice as great.
(C) for a while with an increasing speed, then with a constant speed thereafter.
(D) with a continuously increasing speed.
Answer: (D) with a continuously increasing speed.
Problem 10:
An engineer has decided to design a new roller coaster. Her design has a large hill followed by a
loop (a perfect circle oriented vertically). She has carefully calculated the height of the hill so that
the passengers will feel weightless at the top of the loop. To add to the excitement she decides to
remove the top half of the loop as shown below. In her test run of the newly constructed ride she
finds that the cart follows which of the paths shown below by the dotted lines.
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Physics 109, How Things Work, Spring 2006
Answer: (C)
Why: Without the track to push the cart along the circular path it will move like a freely falling
object. It was moving straight up when it left the track so it will continue straight up.
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Problem 11:
When you stand in front of an open refrigerator, trying to decide which flavor of Ben and Jerry's to
eat, you feel cold, even though no chilled air actually touches your skin. The reason you feel cold is
that
(A) the cold refrigerator is radiating cold toward you and is lowering the temperature of your skin
directly.
(B) you are radiating heat toward the refrigerator but receiving relatively little radiated heat in
return.
(C) you can sense the presence of nearby cold air, even though it is not exchanging heat with your
skin.
(D) you can sense the presence of nearby cold air, even though it is not exchanging cold with your
skin.
Answer: (B) you are radiating heat toward the refrigerator but receiving relatively little radiated
heat in return.
Why: You and the refrigerator are exchanging heat via radiation. Since your temperature is higher
than its temperature, you send more heat toward it as thermal radiation than it sends toward you.
Overall, you lose heat and feel cold.
Problem 12:
A gymnast doing a double back flip leaps off the floor with her arms and legs extended and then
pulls herself into a very compact position. In her compact shape, she rotates very rapidly and
completes two full rotations before opening back up to land on the floor. During the time that she is
not touching the floor, the one aspect of her motion that is constant is her
(A) angular momentum.
(B) angular velocity.
(C) momentum.
(D) velocity.
Answer: (A) angular momentum.
Why: The gymnast is free of torques while she is in the air. She is not free of forces because gravity
exerts a force on her. Since her angular momentum can't change as long as she experiences no
torques, her angular momentum is constant. Everything else in the list does change during her flight
through the air.
Problem 13:
A car has been wrapped in thermal insulation so that it can't lose any heat to the surrounding air. As
a result of this insulation, the car's engine will
(A) lose its ability to turn thermal energy into work.
(B) become more fuel-efficient because it will retain more of the burned fuel's energy.
(C) be essentially unaffected, since its main function--producing disordered work--is not dependent
on ordered heat.
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(D) be essentially unaffected, since its main function--producing ordered work--is not dependent on
disordered heat.
Answer: (A) lose its ability to turn thermal energy into work.
Why: As a heat engine, the car engine can only produce work out of heat by letting heat flow from
hot to cold. If you spoil this heat transfer (from hot burned gases to cold outside air), you prevent it
from operating as a heat engine and it stops producing work.
Problem 14:
Suppose you are standing motionless on a frictionless skateboard and are trying to propel yourself
forward by throwing tennis balls at the wall behind you. You throw one of the balls and soon find
yourself heading forward. You first begin to head forward
(A) when the tennis ball comes to a complete stop during its bounce off the wall.
(B) when the tennis ball just begins to touch the wall at the start of its bounce off the wall.
(C) while the tennis ball is still in your hand as you push it backward.
(D) when the tennis ball just finishes bouncing off the wall.
Answer: (C) while the tennis ball is still in your hand as you push it backward.
Why: The wall has nothing to do with your acceleration forward (unless the rebounding ball
happens to hit you on its way back). It is the very act of throwing the ball—of pushing on the ball—
that causes it to push on you and propel you forward.
Problem 15:
You are enjoying the view from 50 meters in the air as you parasail in the Bahamas during Spring
Break. You are presently traveling at a constant velocity, supported by a parachute as a speedboat
pulls you forward at the end of a long cable. The net force you are experience
(A) points in the forward direction, the direction in which you are heading.
(B) points toward the boat, directly along the cable that is pulling you.
(C) points straight up, opposite the force of gravity.
(D) is zero.
Answer: (D) is zero.
Why: Since you are traveling at constant velocity, you are not accelerating and the net force on you
is zero.
Problem 16:
When you pull a tablecloth out from under a set of dishes, it's important to pull the cloth as fast as
possible because
(A) the force of sliding friction that the cloth exerts on the dishes is proportional to the time during
which the cloth is moving.
(B) the work done on the dishes by the cloth is proportional to the time during which the cloth pulls
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on them.
(C) the weight of the dishes on the cloth is proportional to the time during which the cloth is
moving.
(D) the momentum transferred to the dishes is proportional to the time during which the cloth pulls
on them.
Answer: (D) the momentum transferred to the dishes is proportional to the time during which the
cloth pulls on them.
Why: You are trying to keep the dishes from building up momentum and you do this by minimizing
the impulse they receive. You can't change the force that the tablecloth exerts on them, except
perhaps by making the tablecloth slicker or greasing the dishes, but you can reduce the time
involved in that impulse. You reduce this time by pulling as quickly as possible.
Problem 17:
A steam engine manages to do real work using only hot steam and cold air. It needs both the steam
and the air because
(A) there is order present in their difference in temperature.
(B) total entropy decreases when heat flows spontaneously from hot steam to cold air.
(C) work is released when heat flows from cold air to hot steam.
(D) there is order present in the hot steam and energy present in the cold air.
Answer: (A) there is order present in their difference in temperature.
Why: Even though thermal energy is itself disordered energy, there is still order present in the
uneven distribution of that thermal energy.
Problem 18:
You roll a marble down the side of a round bowl—a bowl with a spherical bottom. The marble rolls
back and forth between the front and back of the bowl, passing right through the bottom of the bowl
on each trip. At this exact moment, the marble has just rolled down your side of the bowl and is
exactly at the bottom of the bowl. It is about to begin rolling up the far side of the bowl. It is
accelerating
(A) away from you.
(B) upward.
(C) downward.
(D) toward you.
Answer: (B) upward.
Why: At the exact bottom of the bowl, the marble is essentially moving in a circle about the center
of the bowl's curvature. It is experience a pure centripetal acceleration upward.
Problem 19:
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Airports often provide you with moving sidewalks to help you get from one place to another
quickly and easily. Suppose you are riding one of these sidewalks up a gentle hill to your departure
gate. You are traveling at a constant velocity, forward and slightly upward. Neglect any air
resistance. During this time, the sidewalk is pushing you
(A) in the direction you are moving (up the hill) and you are doing work on the sidewalk.
(B) upward and forward, but it is not doing any work on you.
(C) in the direction you are moving (up the hill) and it is doing work on you.
(D) straight up and it is doing work on you.
Answer: (D) straight up and it is doing work on you.
Why: You are being carried up a ramp at constant velocity, so the net force on you is zero. The
ramp must be balancing your weight by pushing you straight up with a force equal to your weight.
Since you are moving upward (as well as sideways), the sidewalk is doing work on you.
Problem 20:
Steam at 100 °C is much more effective for cooking broccoli than air at 100 °C because steam
(A) undergoes convection much better than does air.
(B) at 100 °C water is much hotter than air at 100 °C.
(C) is an electric conductor and thus a much better conductor of heat than is air.
(D) condenses to water on the broccoli and releases chemical potential energy.
Answer: (D) condenses to water on the broccoli and releases chemical potential energy.
Why: The 100 °C steam has too high a density of molecules to remain purely gaseous when it comes
in contact with the colder broccoli. Some of the water molecules in the steam land on and stick to
the broccoli and there is a net transfer of water molecules from the gas to the liquid. This transfer,
which is called condensation, releases lots of chemical potential energy. The water molecules bind
reasonably strongly to one another and release chemical potential energy as thermal energy in the
process.
Problem 21:
The second law of thermodynamics allows you to transfer heat from a colder object to a hotter
object, but only if you accompany that transfer by a destruction of
(A) momentum from some other source.
(B) angular momentum from some other source.
(C) energy from some other source.
(D) order from some other source.
Answer: (D) order from some other source.
Why: Ordering the world by moving heat against its natural direction of flow requires that you
disorder the world somewhere else. Though this usually involves turning ordered energy into
disordered energy, but it can actually be done by turning any sort of ordered system into a less
ordered one.
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Problem 22:
Inspired by the Olympic games, my kids decided to try out bobsledding. First they carried a
cardboard box to the top of the stairs. Next, my son convinced his little sister that she should go
first. She climbed into the box and he gave her a push down the stairs. Seeing that his sister
survived the run it was now his turn. He weighs about twice as much as his sister. If we neglect
friction, then the time it takes him to reach the bottom will be
(A) about the same as the time it took his sister to reach the bottom.
(B) longer than the time it took his sister to reach the bottom.
(C) shorter that the time it took his sister to reach the bottom.
(D) determined by what he had for breakfast.
Answer: (A) about the same as the time it took his sister to reach the bottom.
Why: Part of the gravitational force (weight) is downhill. This is what accelerates the kids
downhill. While Jacob’s weight is double that of Emma’s weight, Jacob’s inertia is also double that
of Emma’s so the two kids will experience the same acceleration.
Problem 23:
You've missed a turn on a go-cart track and you're headed for disaster. You can crash into either a
brick wall or a haystack. After a rapid review of all the physics you know, you decided to aim for
the haystack. Good choice. Although either obstacle would have brought you to a complete stop, the
haystack extracted
(A) the same amount of momentum from you that the brick wall would have, but while exerting less
force on you.
(B) more momentum from you than the brick wall would have.
(C) less momentum from you than the brick wall would have.
(D) almost no momentum from you and thereby exerted less force on you than the brick wall would
have.
Answer: (A) the same amount of momentum from you that the brick wall would have, but while
exerting less force on you.
Why: In coming to a stop, you will lose all your momentum. Therefore, the amount of momentum
you transfer to the object you hit is always the same. What changes when you hit something soft is
the time over which that momentum transfer occurs. The haystack takes away your momentum
gradually with a gentle force.
Problem 24:
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 pushed back on Mike, but with more force than Mike exerted on him.
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(C) Johnny did push back on Mike, with exactly the same amount of force as Mike exerted on him.
(D) Johnny didn't push back on Mike.
Answer: (C) Johnny did push back on Mike, with exactly the same amount of force as Mike exerted
on him.
Why: The force that Johnny exerts on Mike and the force that Mike exerts on Johnny are a Newton's
third law pair and must be equal and opposite.
Problem 25:
People fighting forest fires carry emergency tents that have shiny aluminum outer surfaces. If there
is trouble, a fire fighter can lie under the tent to block the heat from burning trees overhead. The tent
helps because
(A) only conduction carries heat downward toward the fire fighter and the aluminum tent conducts
that heat harmlessly into the ground.
(B) only radiation carries heat downward toward the fire fighter and the aluminum tent reflects most
of that radiation.
(C) only convection carries heat downward toward the fire fighter and the aluminum tent blocks
most of the heat carried by convection.
(D) both conduction and radiation carry heat downward toward the fire fighter and the aluminum
tent blocks most of that heat.
Answer: (B) only radiation carries heat downward toward the fire fighter and the aluminum tent
reflects most of that radiation.
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PART II: SHORT ANSWER PROBLEMS
Please give a brief answer to all of the questions asked in this section. Please use only the space
provided for each question.
Problem 1:
It’s lantern night and your are excited to try out your new lantern. You assemble with the rest of the
Mawrters and light the candle in the lantern.
(A) To light the candle you strike a match by rubbing it across the side of the matchbox. How does
this action cause the match to ignite?
Answer: Sliding friction provides thermal energy that acts as the activation energy to initiate the
chemical reactions of combustion.
Why: Although molecules in the match head can recombine in new ways to release chemical
potential energy, they need some initial energy to get this process started. That activation energy is
provided by work done against sliding friction and the resulting thermal energy.
(B) The candle wax begins to burn. Which molecules have stronger chemical bonds: (1) the wax
and oxygen molecules before burning or (2) the water and carbon dioxide molecules that are formed
as a result of burning?
Answer: The water and carbon dioxide have stronger chemical bonds.
Why: Energy is released when chemical bonds form. The stronger those bonds are, the more energy
is released. By rearranging from weakly bound molecules to more strongly bound molecules, wax
and oxygen release chemical potential energy and burn.
(C) The candles emit a pleasant reddish-orange glow. The temperature in the candle flame is less
than that of a normal light bulb's filament. How can you tell?
Answer: The candle flame is redder (and dimmer) than a bulb's filament.
Why: The candle and the filament are both emitting black body spectra. The cooler candle flame
emits a black body spectrum that is farther toward the infrared and thus appears redder in color.
The hotter filament emits more green and blue light and appears more yellow-white.
(D) You find that the top of the lantern is much warmer than the bottom. Briefly explain why.
Answer: Hot air rises allowing convection to carry more heat to the top of the lantern.
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Problem 2:
Pine derby cars are small wooden cars that roll down a gently curving track that starts with a fairly
steep slope and ends up traveling horizontally for several meters. The cars are released from rest
and the first one that crosses the finish line at the bottom of the hill wins.
(A) Assuming no air resistance or friction, during which part of its trip does the car have its
greatest speed?
Answer: Along the horizontal portion at the bottom of the hill.
Why: The car's total energy remains constant during the descent, but it converts gravitational
potential energy into kinetic energy. Along the straightaway at the bottom of the hill, the car's
kinetic energy is maximal and constant. Since kinetic energy is directly related to speed, the point of
maximum kinetic energy is also the point of maximum speed.
(B) Assuming no air resistance or friction, during which part of its trip does the car have its greatest
acceleration?
Answer: At the top of the hill (at the start of the race).
Why: The car's acceleration is highest when the net force on it is strongest. That occurs at the
steepest part of the hill, which in this case is the starting line.
(C) In reality, friction does affect these little cars. The plastic car wheels spin on fine, stationary
wire axles. There is friction between each wheel and the ground, and there is friction between each
wheel and the axle that supports it. Why is more energy wasted by friction between the wheel and
axle than by friction between the wheel and ground?
Answer: The wheel and axle experience sliding friction (converting ordered energy into thermal
energy), while the wheel and ground experience only static friction (which wastes no ordered
energy).
Why: Even though the wheel and axle aren't moving very far across one another, they are sliding as
they do and that sliding wastes energy as thermal energy. The wheel and ground simply touch and
release; they don't slide. As a result, they don't waste energy making thermal energy.
(D) You must put a 20-gram weight on your car to reach the required racing weight. If you want
your car to travel as fast as possible, roughly where on the car should you put that weight? Briefly
explain your answer in terms of energy conservation.
Answer: At the back end of the car.
Why: The farther the weight descends, the more gravitational potential energy it will release and
the faster the car will go. By putting the weight in the rear of the car, you are making it so that the
weight is high up at the start (while the car is tilted with its rear end highest) and low at the end of
the race (while the car is horizontal and its rear end isn't particularly high any more).
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Problem 3:
In a “barrel of fun” ride at a carnival people stand against the walls of a
cylindrical room as shown below. Once all of the passengers are in
place the room begins to spin about a vertical axis.
(A) As the ride starts spinning each passenger’s speed increases at a
constant rate. In what direction does a particular passenger accelerate
(be specific – draw a picture if that helps)? In other words, indicate the
direction of the linear acceleration of a person at one particular instant of time.
Answer: Part of their acceleration is toward the center of the barrel and part of their acceleration
is in the direction they are moving.
(B) Once the ride has reached the proper speed it rotates at a constant rate and the floor drops from
beneath the passenger’s feet. Describe all forces that act on one of the passengers.
Answer: The wall provides a support force that pushes them toward the center of the barrel. The
weight of the rider pulls them straight downward. A frictional force from the wall pushes upward to
balance their weight.
(C) People describe this ride by saying that they were being “pressed against the wall.” Is there
really an outward force pressing them against the wall? If so, what is its source? If not, what is the
proper description of their situation (besides nausea)?
Answer: Without the wall the person would move in a straight line. The wall pushes them inward to
turn them in a circle. The resulting inward acceleration gives the person a feeling of weight in the
outward direction, but there is no outward directed force.
(D) After waiting in line for an hour, one rider is told that she cannot ride because she is improperly
dressed. She is wearing a smooth silk shirt. Why is this a problem?
Answer: The frictional force from the wall might not be large enough to balance her weight.