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How Things Work
(Bloomfield)
Chapter 1 Test
Problems for 5th ed.
Section
1.1 – Skating
1.
Suppose you have two cars, and the larger one is twice as massive as the
smaller one. If you and a friend push on them so that their accelerations are
equal, how must the forces applied to the cars compare?
A) The force on the larger car is equal to that on the
smaller car
B) The force on the larger car is ½ that on the smaller car.
C) The force on the larger car is twice that on the smaller
car.
D) The force on the larger car is more than three times that
on the smaller car.
ANS:
C DIFF: E
2.
Which of the following devices on a car can be used to cause the car to
accelerate?
A) The gas pedal
B) The brake pedal
C) The steering wheel
D) All the above
ANS: D DIFF: E
3.
The acceleration of an object is equal to
A) the rate of change of its position
B) the rate of change of its velocity
C) the rate of change of its speed only
D) the time an object has been in motion
ANS:
B DIFF: E
4.
Suppose you are at a stop light and realize that an important antique physics
textbook sale ends in five minutes. Naturally, you start off very rapidly. To
you, some papers on the dashboard fly straight backwards. To an observer on the
ground they
A) remained where they were.
B) moved forward rapidly.
C) moved backwards rapidly.
D) fell straight down.
ANS:
A DIFF: E
5.
The SI units of acceleration are
A) m/s
B) kgm/s2
C) m/s2
D) kg m2/s2
ANS:
C DIFF: E
6.
Suppose you have a car traveling down the road at constant speed and not
changing direction. It is experiencing gravity, wind resistance and frictional
forces from the road. What can be said about the car’s acceleration?
A) It is accelerating because there are forces acting on it.
B) It accelerating because the motor is running, propelling
the car forward.
C) It is not accelerating because gravity holds it down.
D) It is not accelerating because it has constant velocity.
ANS:
D DIFF: M
7.
Suppose you are driving north and suddenly hit your brakes to avoid a dog in the
road. As you come to a stop your acceleration is directed
A) North
B) South
C) Nowhere because acceleration is a scalar
D) Downwards
ANS:
B DIFF: M
8.
If you are backing up but slowing down, your acceleration is directed
A) backwards
B) nowhere
C) forwards
D) to the left
ANS:
C DIFF: M
9.
Under what conditions are the values of average speed and the magnitude of the
average velocity equal?
A) When moving in a straight line
B) When moving in a straight line and not turning around
C) When moving in a circular path
D) When walking around the perimeter of a rectangle
ANS:
B DIFF: M
10.
You are making a round trip from City A to City B and back to City A again at
constant speed. At what point in the trip is your average speed equal to three
times the magnitude of your average velocity?
ANS: Since velocity = change in position divided by time
interval and average speed = total distance divided by time interval we need to
find a point in the trip where the distance traveled is equal to three times
the object’s change in position. Here it is useful to break the trip into four
equal parts. We can see that halfway between the two cities on the way back to
city A, three parts distance have been covered but the difference in position
is only one part. Hence it is at the midway point on the return where the
average speed is three times the average velocity.
DIFF:
H
11.
A frequent flyer is suing an airline. She claims that during landing, the
plane’s rapid acceleration caused a suitcase on a luggage rack in front of her
to fly backwards and hit her. Using any of Newton’s laws of motion, please
support or refute the passenger’s claim.
ANS: Here I would use Newton’s first law of
motion. The plane is accelerating backwards when landing. The book indeed has
inertia, so Newton’s first law suggests that the book would tend to remain in a
constant state of motion, so it would tend to slip forward (relative to the
plane), not backward. Hence the passenger’s claim is refuted. DIFF: M
12. A friend states Newton’s
First Law of Motion as “An object will move in a straight line unless acted
upon by a force” Please evaluate the scientific merit of his statement.
ANS: the friend is almost right but
has left out some very important loopholes. First off, it is a non-zero net
force that causes acceleration, not necessarily any lone force. Also, a
non-zero net force will make an object accelerate, meaning it will speed up,
slow down or curve – not just curve as the friend suggests. The object could
accelerate in a straight line.
DIFF: H
13.
You walk in a given direction for 20 m during the first 5 seconds of a trip and
then 15 m during the next 2 seconds.
Your average speed is equal to
A) 8 m/s
B) 2 m/s
C) 5 m/s
D) –5 m/s
ANS:
C DIFF: M
14.
To cause a 25 kg object to experience an acceleration of 2 m/s2 the
net force that needs to be applied to the object is
A) 10 N
B) 5 N
C) 50 N
D) 100 N
ANS:
C DIFF: E
15.
A net force of 8 N is applied to a 2 kg object. The object’s acceleration is
A) 4 m/s2
B) 8 m/s2
C) 16 m/s2
D) 2 m/s2
ANS:
A DIFF: E
16.
An object experiences a net force of 20 N and has an acceleration of 4 m/s2.
The object’s mass must be
A) 20 kg
B) 5 kg
C) 80 kg
D) 2 kg
ANS:
B DIFF: E
17.
At a speed of 12 m/sec how far can you travel in one minute?
A)12 m
B) 72 m
C) 60 m
D) 720 m
ANS:
D DIFF: E
18. Consider a 6 kg box of holiday candy on a horizontal
surface such as a table. There is a 10N applied force to the right and a 7 N
frictional force to the left. Suppose the block moves 3 m to the right across
the table, to its impending doom of hungry guests.
A) Please calculate the work done
by the 10 N force.
ANS: W = Fd
= (10)(3) = 30J
B) What is the work done by the 7
N frictional force?
ANS: W = Fd
= (-7)(3) = -21J
DIFF: H
19. Is it possible for the magnitude of an object’s average
velocity to be greater than its average speed? How about average speed being
greater than the magnitude of the average velocity? Please explain.
ANS: The magnitude of the average velocity for an
object may be less than its average speed but not the other way around. One can
look at the definition of the two quantities involved for an explanation.
Average speed is distance divided by time and average velocity is displacement
(finishing position minus initial position) divided by time. Since the time
intervals are the same for both quantities the question boils down to comparing
net displacement to distance traveled. If an object changes direction the
difference in its position will be less than the distance traveled but under no
circumstances can the finishing point minus starting point ever be greater than
the distance traveled.
DIFF: M
20.
Suppose an ice skater is moving on the surface of a frozen lake at constant
velocity. What is true about the external (outside) forces acting on the
skater?
A) There are none.
B) There could be some but they all
cancel out.
C) Gravity can be ignored.
D) The all are perfectly horizontal.
ANS:
B DIFF: E
21. The
value of the average velocity for any round trip is equal to
A) Total distance traveled divided
by total trip time.
B) The final acceleration multiplied
by trip time
C) Zero.
D) The person’s speed halfway
through the path.
ANS:
C DIFF: E
22. Suppose
that the night before your big physics exam you stayed up late watching stand –
up physics comedians. Sides sore from having laughed too hard you come to class
and are in the middle of the test when you get stuck. You are doing a
calculation problem and know the answer must have units of velocity and are
searching for a possible formula. Which of the following formulae would work
for the problem?
A) acceleration x time
B) acceleration / time
C) velocity squared x distance
D) mass / volume
ANS:
A DIFF: M
23.
The neighborhood joker comes up to you and is really on a roll this morning.
After several “good ones” they then say “OK so you’re taking physics, right?
Here’s one – if the acceleration of gravity is 9.8 m/s2 then why
isn’t everything accelerating? HAHAHA”. Being a dedicated student you give this
question some real thought and come up with a reasonable response. You might
say
A) All things really do accelerate
but we accelerate with them so we can’t tell.
B) Gravity acts only on things that
are not touching a surface.
C) Gravity is just part of the story and it is the total net
external force that determines acceleration.
D) Most objects have too much inertia for us to see them
accelerate under the influence of gravity.
ANS:
C DIFF: M
24.
You are in your car at a stop light and start off really quickly. As you
accelerate several items fall off the dashboard and on to the floor. Please
explain why your car is a non – inertial reference frame.
ANS:
An inertial reference frame is one where Newton’s Laws work perfectly.
Imagining the car to be a reference frame and riding along with it, when it
accelerates there seems to be something that pulled the objects off the dash.
Such behavior invalidates Newton’s first law of motion locally unless we add
this “force” in the discussion. Answers will vary here.
DIFF:
H
25. A
friend is casually talking with you about physics concepts and brings up the
following claim. They say that average speed for a trip is total distance
divided by total time, which is true.
Then they say that if the trip consists of a person traveling at two
different speeds for two different times then you can get the average speed by
just finding the average speeds for the two parts of the trip and then take
their average. Is their claim true? Please explain.
ANS:
Their claim is not true because unless the times for the two parts of the trip
are equal, the part taking the longer time will count more for the average.
DIFF:
H
Section 1.2 – Falling Balls
26. Your class is rather unhappy with the instructor, and
they pitch in and decide to fund a sabbatical for him to go to Mars.
Unbeknownst to the students the following semester, the instructor has made
long distance course arrangements so the “show can go on”. The instructor
begins talking about mass, weight and related things. He correctly makes which
following statement:
A) his mass is still essentially
unchanged but his weight is less than on earth.
B) his weight is still essentially
unchanged but his mass is less than on earth.
C) neither his weight nor his mass
have changed much.
D) his weight and mass have both
changed significantly.
ANS: A DIFF:
E
27.
Suppose you are a football player and you kick a ball for a field goal.
Ignoring air resistance, the ball’s horizontal velocity
A) changes throughout the path due to gravitational
acceleration
B) is zero at the top of the path
C) is maximum at the top of the path
D) remains constant throughout the path
ANS:
D DIFF: E
28.
A child throws a ball perfectly horizontally at the same time a dirt clod falls
off it at the same height above the ground. The clod falls vertically downward.
Ignoring air resistance, the time when the clod hits the ground will
A) be equal to the time the ball hits the ground
B) be earlier than when the ball hits
C) be later than when the ball hits
D) not depend upon how high it started falling from
ANS:
A DIFF: E
29.
Your weight and mass are different in that
A) your weight is measured in kg but not your mass
B) your mass depends upon local gravity but your weight does
not.
C) your weight depends upon local gravity but your mass does
not.
D) being weightless means that you have to lose mass.
ANS:
C DIFF: E
30.
Suppose a tree branch falls down to the ground with constant acceleration and
takes 2 seconds to hit the ground. Which of the following statements regarding
the path of the branch is true?
A) It covers the same distance during the first second as it
does during the last second.
B) It covers more distance during the last second.
C) It covers less distance during the last second.
D) Its acceleration is increasing during the time it falls
ANS:
B DIFF: M
31.
Suppose you go from the earth to a planet where the acceleration of gravity is
2.5 m/s2. On the new planet your weight will be about
A) be ¼ its value on Earth
B) quadruple
C) double
D) the sane as
ANS:
A DIFF: M
32.
Suppose you go from the earth to a planet where the acceleration of gravity is
3 m/s2. On the new planet your mass will
A) be 1/3 its value on Earth
B) be 9 times its value on Earth
C) be 3/10 its value on Earth
D) not change
ANS:
D DIFF: M
33.
A projectile is thrown directly upward and caught again. At the top of its path
A) it stops accelerating
B) its vertical velocity is zero
C) its horizontal velocity changes
D) its acceleration changes
ANS:
B DIFF: M
34.
Suppose you throw a ball downwards with a certain initial speed from a certain
height h above the ground, and someone else throws a ball directly
upward at the same speed, so the two balls collide. Will the two balls collide
in the middle of the path (h/2), above the middle or below? Please
explain.
ANS: The ball on top is speeding up while the bottom ball is
slowing down. Hence, the ball on top will have covered a greater distance and
so they will meet below the midpoint h/2.
DIFF:
H
35.
Suppose you are on another planet and you want to measure its acceleration of
gravity so you drop an object from rest. It hits the ground, traveling a
distance of 0.8 m in 0.5 second and then bounces back up and stops exactly
where it started from.
a. Please calculate the acceleration of gravity on this
planet.
ANS: d = ½ g t2 so
0.8 = ½ g (0.5)2 and 1.6 =
0.25 g, giving g = 6.4 m/sec2
b. Taking downward to be positive, how does the ball’s
average speed compare to the magnitude of its average velocity on the way down?
ANS: On the way down the average
speed and average velocity are numerically equal because the distance traveled
from the starting point is the same as the change in position.
c. Taking the beginning of the motion as the time the ball
was dropped, how does its average speed compare to the magnitude of its average
velocity on the way up?
ANS: On the way up, the average
speed and average velocity are not equal because the ball has stopped and
turned around. In fact the average speed will be some positive number while the
average velocity is approaching zero when it returns to the point it started
from, because the ball’s change in position will be zero.
d. With what speed
did the ball hit the ground?
ANS: v = gt = 6.4 m/sec2
x 0.5 sec = 3.2 m/sec
e. When distance is divided by time the result is 1.6
m/sec. Please explain why this result does not agree with the answer in (D).
ANS: This is because d/t gives us the average speed
(over the entire downward part of the trip) but the equation used in (D) gives
us the final speed (at the end of the downward part of the trip).
Another way you could look at it is that over the entire trip the ball was
accelerating so it covered the first half of its trip in a longer time interval
than it did the second. Hence it had to be moving faster at the end.
DIFF: H
36.
When someone throws a football, what should the launch angle be (ignoring air
resistance) so that it travels a maximum distance?
ANS: Without air resistance, the launch angle that gives
maximum range is 45 degrees.
DIFF:
E
37.
Suppose your instructor staggers into class after an all – night physics
textbook sampling party and states Newton’s second law as “If an object
experiences a force then it will accelerate. If there are no forces acting on
it then it will stand still.” Please give three examples (from class, real life
or made up) which expose mistakes on his part and briefly explain how they show
his inaccuracies.
ANS (Answers will vary):
1) An object has to experience a non-zero net external
force to accelerate. For example look at a book sitting on a desk. There is a
force acting on it (gravity) but it is not accelerating because there is
another force (the normal force) canceling it out.
2) Consider a car traveling down the road at constant
velocity. Although it is moving and definitely not standing still, there is a
zero net force on it because it is not accelerating.
3) The entire issue of mass has been left out of the
picture, and Newton’s second law clearly says that F = m a. Consider a 10 kg crate on a level frictionless surface
with a force of 10 N on it. The way the second law was presented the simple
example can’t even be solved!!
DIFF: M
38. You throw
brick straight up. Ignoring air resistance, after it leaves your hand it will
experience
A) only the downward force of its weight, both
before and after it reaches its maximum height.
B) both an upward force, and the downward force of its weight after it rises. The upward force will gradually diminish to zero at the ball's maximum height, after which the ball will experience only the
downward force of its weight.
C) an upward force as it rises. This upward force will gradually diminish to zero at the ball's maximum height, after which the ball will experience only the downward force of its weight.
D) the upward force of its weight as it rises. Once the ball reaches its maximum height, it will begin to experience the downward force of its weight.
B) both an upward force, and the downward force of its weight after it rises. The upward force will gradually diminish to zero at the ball's maximum height, after which the ball will experience only the
downward force of its weight.
C) an upward force as it rises. This upward force will gradually diminish to zero at the ball's maximum height, after which the ball will experience only the downward force of its weight.
D) the upward force of its weight as it rises. Once the ball reaches its maximum height, it will begin to experience the downward force of its weight.
ANS: A DIFF:
M
39.
If you have a mass of 80 kg and are in a planet where the acceleration of
gravity is 5 m/s2, your weight on the planet is
A) 400 N
B) 4000 N
C) 16 N
D) 80 N
ANS:
C DIFF: E
40.
A gymnast jumps upward with an initial speed of 10 m/s. She is in the air for a
total time of
A) 1 second
B) 5 seconds
C) 2 seconds
D) 10 seconds
ANS:
C DIFF: M
41. The
maximum height above the ground for a the gymnast jumping straight upward with
an initial speed of 10 m/s is
A) 5 m
B) 10 m
C) 2 m
D) 15 m
ANS:
A DIFF: M
42.
A car starts from rest and accelerates at 4 m/s2. How much time will
it take the car to reach a speed of 20 m/s?
A) 5 s
B) 10 s
C) 4 s
D) 8 s
ANS: A DIFF:
M
43.
Suppose you are a football player and you kick a ball for a field goal.
Including air resistance, the ball’s horizontal velocity
A) changes throughout the path due to gravitational acceleration
B) is zero at the top of the path
C) decreases throughout the path
D) increases throughout the path
ANS:
C DIFF: E
44.
Suppose an object is traveling at terminal velocity, so it is falling through
air but not accelerating. How does the force of air resistance compare to its
weight?
A) The
two forces are equal and opposite.
B) The
two forces are equal.
C) Air resistance is greater than the ball’s
weight.
D) Air
resistance is less than the ball’s weight.
ANS: A DIFF:
E
45. Suppose you drop an object out of the window of a
building and wait for it to hit the ground. How does the halfway point in
distance compare to the halfway point in time? Please explain.
ANS: The object is accelerating downwards, and is therefore
speeding up. As a result, it will take less time to cover the second half of
the distance than it did the first. So when the object has traveled half the
distance, it has taken more than half the travel time.
DIFF: M
46. Suppose a 2 kg object is falling through the air and
accelerating downwards at 8 m/s2. Taking g = 10 m/s2 What is the magnitude and direction of the
force of air resistance on it?
A) 2N
downward
B) 2N
upward
C) 1N
downward
D) 1N
upward
ANS: B DIFF:
M
47.
Suppose you throw a ball upwards with a certain initial speed from a certain
height h above the ground, and you wait for it to go up, stop and come
back down to the same (initial) position.
Including air resistance, how will its speed hitting the ground on the
way back down compare to its launch speed? Please explain.
ANS: Its speed hitting the ground on the way back down will
be less than its launch speed. This can be explained many ways, but one way to
look at it is that, because of air resistance the ball will not go as high as
it would have otherwise. Then, on the way down air resistances acts again. Both
effects act together to reduce the speed of the ball on impact.
DIFF:
H
48. In our calculations of motion, we have ignored certain
aspects of the object and its environment. Please briefly discuss three such
aspects, and what kind of differences they make.
ANS: One aspect is air resistance, or drag. This causes the
speed of an object in free fall to be slightly smaller than we assume it to be.
A second aspect we ignore is the variation of gravitational acceleration with
height above the ground. This would cause the acceleration of gravity g to be a variable and not constant,
which would considerably complicate our calculations. A third aspect we ignore
is the rotation of the earth, which causes slight variations to the motion of
falling objects.
DIFF: H
Section 1.3 - Ramps
49.
Suppose you weigh 986 N. How much force does the Earth exert on you, if any?
A) it cannot be determined
B) 986 N
C) 98.6N
D) none
ANS:
B DIFF: E
50.
You are riding a bicycle into a strong head wind, but manage to keep moving in
a straight line at a constant speed. The net force on you is
A) 0
B) in the direction of your motion
C) in the direction tie wind is pushing you (backwards)
D) downward due to your weight
ANS
: A DIFF: E
51.
In order to do a positive amount of work you must
A) exert a force and move in the direction of the force
B) exert a force and just move
C) exert a force or move
D) change an object’s position
ANS:
A DIFF: E
52.
Driving down the road, you hit an insect. How does the force your car exerts on
the insect compare to the force the insect exerts on the car?
A) The force the car exerts on the insect is less.
B) The force the insect exerts on the car is less.
C) The two forces are equal in magnitude.
D) The insect exerts no force on the car
ANS:
C DIFF: E
53.
Suppose your car is on a 5% grade, meaning that for every 100 m you travel
along the road you raise or lower only 5 m in elevation. If your car weighs
1500 kg, what is the component of its weight parallel to the road?
A) 15000 N
B) 1500 N
C) 7500 N
D) 750 N
ANS:
D DIFF: M
54.
Suppose you are helping take groceries inside your house and you carry a heavy
bag from the car to the house, keeping the bag at a constant level and walking
at a constant speed. During your trip the work you do on the bag is
A) positive
B) 0
C) negative
D) equal to its potential energy
ANS:
B DIFF: M
55.
Suppose you push horizontally on the wall of a building. For you to do work on
the wall, which of the following need to happen?
A) the wall moves away from you
B) the wall lifts up
C) the wall moves sideways
D) b and c
ANS:
A DIFF: M
56.
Suppose Larissa throws a ball up in the air and it comes back down to the same
place she threw it from. Ignoring times when the ball is in contact with her
hand, and ignoring air resistance (friction with the air), identify the
point(s) of
a.
Maximum and minimum potential energy.
ANS: Here the points of maximum and
minimum height are the points of maximum and minimum potential energy,
respectively. This is because potential energy depends on height and increases
with increasing height.
b. Maximum and minimum kinetic energy.
ANS: The maximum kinetic energy
occurs at the point where the ball is moving fastest, namely right after it
leaves Larissa’s hand and right before she catches it. The minimum kinetic
energy will occur when the ball is moving slowest – right at the top of the
path where it instantaneously stops.
c. Maximum and minimum total mechanical energy.
ANS: Since friction or other
dissipative forces are acting, the total mechanical energy will be conserved
and hence constant everywhere.
d. Please briefly describe the energy transformation taking
place as the ball rises in the air, and also when it is falling back to earth.
ANS: As the ball rises, its kinetic
energy is being converted into potential energy such that their sum is
constant. On the way back down the opposite conversion is happening but still
the total mechanical energy is constant.
DIFF: H
57.
Suppose you do some work on an object. Think of two ways you can tell work has
been done on the object just by observing the object.
ANS: One way to tell is to look at the height of the object.
If it is at a new elevation then the work went into changing its potential
energy. Another way to tell is to look at the speed of the object. If it sped
up or slowed down then the work went into changing its kinetic energy.
DIFF:
M/H
58. You are riding on a flat train car and are climbing up
the side of a hay stack. You are half way up the stack and are maintaining a steady
height. You and the stack are moving steadily along the straight tracks at
constant speed. The net force on you is
A) downhill—toward the bottom of
the front of the stack.
B) zero.
C) uphill—behind you.
D) horizontal—parallel to the
tracks.
ANS: B DIFF:
M
59.
You push on a box with a horizontal force of 20 N and the box moves a distance
of 8 m. The amount of work you have done on the box is
A) 160 J
B) 320 J
C) 20J
D) 0
ANS:
A DIFF: E
60.
Suppose you do 1000 J of work on a 5 kg object, and all the work went into
lifting it above the ground. How high above the ground will the object be when
all the work has been done?
A) 100 m
B) 5 m
C) 20 m
D) 1 m
ANS:
C DIFF: M
61.
What is the potential energy of a 40 kg box that is 6m above the ground?
A) 240 J
B) 2400 J
C) 6 J
D) 60 J
ANS:
B DIFF: E
62.
Suppose you push a 50 kg box 10 m up a frictionless incline that has a 10%
grade. What is the change in potential energy for the box?
A) 500 J
B) 5000 J
C) 250 J
D) 2500 J
ANS:A DIFF: H
63.
In order to do a negative amount of work you must
A) exert a force and move in the direction of the force
B) exert a force and move opposite to the direction of the
force.
C) exert a force or move
D) change an object’s position
ANS:
B DIFF: E
64.
Please briefly discuss two situations where no work is done by a force.
One
is where there is no distance the force acts through and another is where the
force and motion are perpendicular.
DIFF:
E
65.
Suppose you use a ramp to lift a 200 kg object. You raise it 2 m above the ground
and did 5000 J of work. Assuming that gravity and friction could be the only
forces you had to work against, was there any friction, and if so ho much work
did you have to do against it?
Yes
there was friction because the work without friction is equal to mgh which is in this case 4000J. Since I
did 5000J of work there had to be 1000J which went against friction.
DIFF:
M
66. Your
friend and you are at the mall shopping. She stops, grabs your arm and exclaims
that she is worried about her physics test she took last Friday because she
ignored the work done by (or against) the normal force when an object slides
across a surface. What would you (correctly) reply to her?
ANS:
I would say (correctly) that the normal force is always normal (perpendicular)
the surface the object is in contact
with and for sliding there is not any motion perpendicular to the surface.
Therefore no work can be done by or against the normal force.
DIFF:
M
67. Your
friend and you are at the mall shopping. She stops, grabs your arm and exclaims
that she is worried about her physics test she took last Friday because she
ignored the work done by (or against) the normal force when a person is being
lifted in an elevator. What would you (correctly) reply to her?
ANS:
I would say (correctly) that the normal force is always normal (perpendicular)
the surface the object is in contact
with and in this case the normal force indeed did work on the person. I would
also tell her that I hoped she did well on her other questions.
DIFF:
H
68.
In physics we often make approximations. We say, for example that when you push
against a stationary wall, no work is done. Thinking about details of the
system is this true? Please explain.
ANS:
No this is not strictly true. The human hand is elastic and (although to a much
less extent) so is the wall. Therefore
there really is some work done in pushing against a wall because there is a
distance that the forces act through.
DIFF:
M/H
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