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Chapter 4: Forces in One Dimension

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Title: Chapter 4: Forces in One Dimension


1
PHYSICS Principles and Problems
Chapter 4 Forces in One Dimension
2
Forces in One Dimension
CHAPTER4
BIG IDEA
  • Net forces cause changes in motion.

3
Table Of Contents
CHAPTER4
Section 4.1 Force and Motion Section 4.2
Weight and Drag Force Section 4.3 Newtons
Third Law
Click a hyperlink to view the corresponding
slides.
Exit
4
Force and Motion
SECTION4.1
MAIN IDEA A force is a push or a pull.
Essential Questions
  • What is a force?
  • What is the relationship between force and
    acceleration?
  • How does motion change when the net force is
    zero?

5
Force and Motion
SECTION4.1
  • Review Vocabulary
  • Acceleration the rate at which the velocity of an
    object changes.
  • New Vocabulary
  • Force
  • System
  • Free-body diagram
  • Newtons second law
  • Newtons first law
  • Inertia
  • Equilibrium

6
Force and Motion
SECTION4.1
Force
  • Consider a textbook resting on a table. To cause
    it to move, you could either push or pull on it.
  • A force is defined as a push or pull exerted on
    an object.

7
Force and Motion
SECTION4.1
Force (cont.)
  • If you push harder on an object, you have a
    greater effect on its motion.
  • The direction in which force is exerted also
    matters. If you push the book to the right, the
    book moves to the right.
  • The symbol F is a vector and represents the size
    and direction of a force, while F represents only
    the magnitude.

8
Force and Motion
SECTION4.1
Force (cont.)
  • Forces can cause objects to speed up, slow down,
    or change direction as they move.
  • Based on the definitions of velocity and
    acceleration, a force exerted on an object causes
    that objects velocity to change that is, a
    force causes an acceleration.
  • All accelerations are the result of an unbalanced
    force acting on an object.

9
Force and Motion
SECTION4.1
Force (cont.)
  • When considering how a force affects motion, it
    is important to identify the object of interest.
    This object is called the system.
  • Everything around the object that exerts forces
    on it is called the external world.

10
Force and Motion
SECTION4.1
Force (cont.)
  • Think about the different ways in which you could
    move a textbook.
  • You could touch it directly and push or pull it,
    or you could tie a string around it and pull on
    the string. These are examples of contact forces.

11
Force and Motion
SECTION4.1
Force (cont.)
  • A contact force exists when an object from the
    external world touches a system and thereby
    exerts a force on it.

12
Force and Motion
SECTION4.1
Force (cont.)
  • There are other ways in which the motion of the
    textbook can change.
  • If you drop a book, the gravitational force of
    Earth causes the book to accelerate, whether or
    not Earth is actually touching it. This is an
    example of a field force.
  • Field forces are exerted without contact.

13
Force and Motion
SECTION4.1
Force (cont.)
  • Forces result from interactions thus, each force
    has a specific and identifiable cause called the
    agent.
  • Without both an agent and a system, a force does
    not exist.
  • A physical model which represents the forces
    acting on a system, is called a free-body diagram.

14
Force and Motion
SECTION4.1
Force (cont.)
Click image to view movie.
15
Force and Motion
SECTION4.1
Combining Forces
  • When the force vectors are in the same direction,
    they can be replaced by a vector with a length
    equal to their combined length.
  • If the forces are in opposite directions, the
    resulting vector is the length of the difference
    between the two vectors, in the direction of the
    greater force.
  • Vector sum of all the forces on an object is net
    force.

16
Force and Motion
SECTION4.1
Acceleration and Force
  • To explore how forces affect an objects motion,
    consider the situation explored in the figure, in
    which, a horizontal force is exerted on an
    object.

17
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • Notice, in order to reduce complications
    resulting from the object rubbing against the
    surface, the investigation was performed on a
    smooth, well-polished table and the cart has
    wheels.

18
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • To exert a constant force, a spring scale was
    used to pull the cart.
  • The velocity of the cart was measured for a
    period of time.
  • Using the data, a velocity-time graph was
    constructed.

19
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • The data indicates for a constant force there is
    a constant acceleration on an object.
  • Thus, indicating the relationship between force
    and acceleration is linear and allowing the
    application of the equation for a straight line
  • The y-intercept is 0, so the linear equation
    simplifies to ykx. The y-variable is
    acceleration and x-variable is force.

20
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • What is the physical meaning of the slope of the
    acceleration-force graph?
  • To determine this, increase the number of carts
    gradually.

21
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • A plot of the force versus acceleration for one,
    two, and three carts indicates that if the same
    force is applied in each situation, the
    acceleration of two carts is the acceleration
    of one cart and the acceleration of three carts
    is the acceleration of one cart.

22
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • This means that as the number of carts is
    increased, a greater force is needed to produce
    the same acceleration.
  • The slopes of the lines in the graph depend upon
    the number of carts that is, the slope depends
    on the total mass of the carts.

23
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
24
Force and Motion
SECTION4.1
Acceleration and Force (cont.)
  • The formula, F ma, tells you that if you double
    the force, you will double the objects
    acceleration.
  • If you apply the same force to several different
    objects, the one with the most mass will have the
    smallest acceleration and the one with the least
    mass will have the greatest acceleration.
  • One unit of force causes a 1-kg mass to
    accelerate at 1 m/s2, so one force unit has the
    dimensions 1 kgm/s2 or one newton and is
    represented by N.

25
Force and Motion
SECTION4.1
Newtons Second Law
  • The observation that acceleration of an object is
    proportional to the net force exerted on it and
    inversely proportional to its mass is Newtons
    second law, which can be represented in the
    following equation.
  • Newtons second law states that the acceleration
    of an object is equal to the sum of the forces
    (the net force) acting on the object, divided by
    the mass of the object.

26
Force and Motion
SECTION4.1
Newtons Second Law (cont.)
  • One of the most important steps in correctly
    applying Newtons second law is determining the
    net force acting on the object.
  • Draw a free-body diagram showing the direction
    and relative strength of each force acting on the
    system.
  • Then add the force vectors to find the net force.

27
Force and Motion
SECTION4.1
Newtons Second Law (cont.)
  • Next, use Newtons second law to calculate the
    acceleration.
  • Finally, if necessary, use what you know about
    accelerated motion to find the velocity or
    position of the object.

28
Force and Motion
SECTION4.1
Fighting Over a Toy
Anudja is holding a stuffed dog with a mass of
0.30 kg, when Sarah decides that she wants it and
tries to pull it away from Anudja. If Sarah pulls
horizontally on the dog with a force of 10.0 N
and Anudja pulls with a horizontal force of 11.0
N, what is the horizontal acceleration of the dog?
29
Force and Motion
SECTION4.1
Fighting Over a Toy
Step 1 Analyze and Sketch the Problem
  • Sketch the situation.
  • Identify the stuffed dog as the system and the
    direction in which Anudja pulls as positive.
  • Draw the free-body diagram. Label the force.

30
Force and Motion
SECTION4.1
Fighting Over a Toy
Step 2 Solve for the Unknown
31
Force and Motion
SECTION4.1
Fighting Over a Toy
Identify known and unknown variables.
Known m 0.30 kg FAnudja on dog 11.0 N
FSarah on dog 10.0 N
Unknown a ?
32
Force and Motion
SECTION4.1
Fighting Over a Toy
Use Newtons second law to solve for a.
Fnet FAnudja on dog (-FSarah on dog)
33
Force and Motion
SECTION4.1
Fighting Over a Toy
Substitute Fnet FAnudja on dog (FSarah on
dog)
34
Force and Motion
SECTION4.1
Fighting Over a Toy
Substitute FAnudja on dog 11.0 N, FSarah on dog
10.0 N, m 0.30 kg
35
Force and Motion
SECTION4.1
Fighting Over a Toy
Step 3 Evaluate the Answer
36
Force and Motion
SECTION4.1
Fighting Over a Toy
  • Are the units correct?
  • m/s2 is the correct unit for acceleration.
  • Does the sign make sense?
  • The acceleration is in the positive direction
    because Anudja is pulling in the positive
    direction with a greater force than Sarah is
    pulling in the negative direction.

37
Force and Motion
SECTION4.1
Fighting Over a Toy
  • Is the magnitude realistic?
  • It is a reasonable acceleration for a light,
    stuffed toy.

38
Force and Motion
SECTION4.1
Fighting Over a Toy
The steps covered were
  • Step 1 Analyze and Sketch the Problem
  • Sketch the situation.
  • Identify the stuffed dog as the system and the
    direction in which Anudja pulls as positive.
  • Draw the free-body diagram. Label the forces.

39
Force and Motion
SECTION4.1
Fighting Over a Toy
The steps covered were
  • Step 2 Solve for the Unknown
  • Step 3 Evaluate the Answer

40
Force and Motion
SECTION4.1
Newtons First Law
  • What is the motion of an object with no net force
    acting on it?
  • Newtons second law states says that if net force
    is zero, then acceleration equal zero.
  • If acceleration is zero, then velocity does not
    change.
  • A stationary object with no net force acting on
    it will stay at rest.

41
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • What about a moving object like a rolling ball?
    How long will it roll?
  • Depends on the surface thick carpet exerts more
    force than a smooth hard surface like a bowling
    alley.
  • So the ball will stop rolling sooner on the
    carpet than the bowling alley.

42
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • Galileo did many experiments, and he concluded
    that in the ideal case of zero resistance,
    horizontal motion would never stop.
  • Galileo was the first to recognize that the
    general principles of motion could be found by
    extrapolating experimental results to the ideal
    case, in which there is no resistance to slow
    down an objects motion.

43
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • In the absence of a net force, the motion (or
    lack of motion) of both the moving object and the
    stationary object continues as it was. Newton
    recognized this and generalized Galileos results
    in a single statement.
  • This statement, an object that is at rest will
    remain at rest, and an object that is moving will
    continue to move in a straight line with constant
    speed, if and only if the net force acting on
    that object is zero, is called Newtons first
    law.

44
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • Newtons first law is sometimes called the law of
    inertia.
  • Inertia is the tendency of an object to resist
    change.
  • If an object is at rest, it tends to remain at
    rest.
  • If it is moving at a constant velocity, it tends
    to continue moving at that velocity.
  • Forces are results of interactions between two
    objects they are not properties of single
    objects, so inertia cannot be a force.

45
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • If the net force on an object is zero, then the
    object is in equilibrium.
  • An object is in equilibrium if its velocity is
    not changing.
  • Newtons first law identifies a net force as
    something that disturbs the state of equilibrium.
  • Thus, if there is no net force acting on the
    object, then the object does not experience a
    change in speed or direction and is in
    equilibrium.

46
Force and Motion
SECTION4.1
Newtons First Law (cont.)
  • Some of the common types of forces are displayed
    on the right.
  • When analyzing forces and motion, it is important
    to keep in mind that the world is dominated by
    resistance. Newtons ideal, resistance-free world
    is not easy to visualize.

47
Section Check
SECTION4.1
  • Two horses are pulling a 100-kg cart in the same
    direction, applying a force of 50 N each. What is
    the acceleration of the cart?

A. 2 m/s2 B. 1 m/s2 C. 0.5 m/s2 D. 0 m/s2
48
Section Check
SECTION4.1
Answer
49
Section Check
SECTION4.1
  • Two friends Mary and Maria are trying to pull a
    10-kg chair in opposite directions. If Maria
    applied a force of 60 N and Mary applied a force
    of 40 N, in which direction will the chair move
    and with what acceleration?

50
Section Check
SECTION4.1
A. The chair will move towards Mary with an
acceleration of 2 m/s2. B. The chair will move
towards Mary with an acceleration of 10 m/s2. C.
The chair will move towards Maria with an
acceleration of 2 m/s2. D. The chair will move
towards Maria with an acceleration of 10 m/s2.
51
Section Check
SECTION4.1
Answer
52
Section Check
SECTION4.1
  • State Newtons first law.

Answer Newtons first law states that an object
that is at rest will remain at rest, and an
object that is moving will continue to move in a
straight line with constant speed, if and only if
the net force acting on that object is zero.
53
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54
Weight and Drag Force
SECTION4.2
MAIN IDEA Newtons second law can be used to
explain the motion of falling objects.
Essential Questions
  • How are the weight and the mass of an object
    related?
  • How do actual weight and apparent weight differ?
  • What effect does air have on falling objects?

55
Weight and Drag Force
SECTION4.2
  • Review Vocabulary
  • viscosity a fluids resistance to flowing.
  • New Vocabulary
  • Weight
  • Gravitational pull
  • Apparent weight
  • Weightlessness
  • Drag force
  • Terminal velocity

56
Weight and Drag Force
SECTION4.2
Weight
  • Weight is the gravitational force experienced by
    an object.
  • This gravitational force is a field force whose
    magnitude is directly proportional to the mass of
    the object experiencing the force
  • Fg mg, where m is the mass of the object
    and g is the gravitational field.
  • Because weight is a force, the proper unit used
    to measure weight is the newton.

57
Weight and Drag Force
SECTION4.2
Weight (cont.)
  • Gravitational field is a vector quantity that
    relates the mass of an object to the
    gravitational force it experiences at a given
    location.
  • Near Earths surface, g is 9.8N/kg toward Earths
    center.
  • When you step on a scale, the scale exerts an
    upward force on you equal in magnitude to the
    gravitational force pulling down on you.
  • The scale is calibrated to convert the stretch of
    the springs, the upward force necessary to give a
    net force of zero, to weight .

58
Weight and Drag Force
SECTION4.2
Weight (cont.)
  • Apparent weight and weightlessness.

Click image to view movie.
59
Weight and Drag Force
SECTION4.2
Drag Force
  • When an object moves through any fluid, such as
    air or water, the fluid exerts a drag force on
    the moving object in the direction opposite to
    its motion.
  • A drag force is the force exerted by a fluid on
    the object moving through the fluid.
  • This force is dependent on the motion of the
    object, the properties of the object, and the
    properties of the fluid (viscosity and
    temperature) that the object is moving through.

60
Weight and Drag Force
SECTION4.2
Drag Force (cont.)
  • As a dropped tennis balls velocity increases, so
    does the drag force. The constant velocity that
    is reached when the drag force equals the force
    of gravity is called the terminal velocity.

61
Weight and Drag Force
SECTION4.2
Drag Force (cont.)
Click image to view movie.
62
Weight and Drag Force
SECTION4.2
  • If the mass of a person on Earth is 20 kg, what
    will be his mass on the Moon? (Gravity on the
    Moon is six times less than the gravity on Earth.)

63
Weight and Drag Force
SECTION4.2
Answer
Reason The mass of an object does not change
with the change in gravity, only the weight
changes.
64
Weight and Drag Force
SECTION4.2
  • Your mass is 100 kg, and you are standing on a
    bathroom scale in an elevator. What is the scale
    reading when the elevator is falling freely?

65
Weight and Drag Force
SECTION4.2
Answer
Reason Since the elevator is falling freely with
acceleration g, the contact force between the
elevator and you is zero. As scale reading
displays the contact force, it would be zero.
66
Weight and Drag Force
SECTION4.2
  • In which of the following cases will your
    apparent weight be greater than your real weight?

A. The elevator is at rest. B. The elevator is
accelerating upward. C. The elevator is
accelerating downward. D. Apparent weight is
never greater than real weight.
67
Weight and Drag Force
SECTION4.2
Answer
Reason When the elevator is moving upward, your
apparent weight
Fapparent ma Fg (where m is your mass and
a is the acceleration of the elevator). So your
apparent weight becomes more than your real
weight.
68
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69
Newtons Third Law
SECTION4.3
MAIN IDEA All forces occur in interaction pairs.
Essential Questions
  • What is Newtons third law?
  • What is the normal force?

70
Newtons Third Law
SECTION4.3
  • Review Vocabulary
  • symmetry correspondence of parts on opposite
    sides of a dividing line.
  • New Vocabulary
  • Interaction pair
  • Newtons third law
  • Tension
  • Normal force

71
Newtons Third Law
SECTION4.3
Interaction Pairs
  • When you exert a force on your friend to push him
    forward, he exerts an equal and opposite force on
    you, which causes you to move backward.
  • The forces FA on B and FB on A are an interaction
    pair.
  • An interaction pair is two forces that are in
    opposite directions and have equal magnitude.

72
Newtons Third Law
SECTION4.3
Interaction Pairs (cont.)
  • An interaction pair is also called an
    action-reaction pair of forces.
  • This might suggest that one causes the other
    however, this is not true.
  • For example, the force of you pushing your friend
    doesnt cause your friend to exert a force on
    you.
  • The two forces either exist together or not at
    all.
  • They both result from the contact between the two
    of you.

73
Newtons Third Law
SECTION4.3
Interaction Pairs (cont.)
  • The force of you on your friend is equal in
    magnitude and opposite in direction to the force
    of your friend on you.
  • This is summarized in Newtons third law, which
    states that all forces come in pairs.

74
Newtons Third Law
SECTION4.3
Interaction Pairs (cont.)
  • Newtons Third Law states that the force of A on
    B is equal in magnitude and opposite in direction
    of the force of B on A.
  • The two forces in a pair act on different objects
    and are equal and opposite.
  • Numerically, FA on B FB on A

75
Newtons Third Law
SECTION4.3
Interaction Pairs (cont.)
  • When identifying an interaction pair, remember
    that they always occur in two different free-body
    diagrams and they always have the symmetry in
    subscripts noted on the previous slide.

76
Newtons Third Law
SECTION4.3
Earths Acceleration
A softball has a mass of 0.18 kg. What is the
gravitational force on Earth due to the ball, and
what is Earths resulting acceleration? Earths
mass is 6.01024 kg.
77
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Step 1 Analyze and Sketch the Problem
  • Draw free-body diagrams for the two systems the
    ball and Earth.
  • Connect the interaction pair by a dashed line.

78
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Identify known and unknown variables.
Known mball 0.18 kg mEarth 6.01024 kg g
-9.80 m/s2
Unknown FEarth on ball ? aEarth ?
79
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Step 2 Solve for the Unknown
80
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Use Newtons second law to find the weight of the
ball.
FEarth on ball mballg
81
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Substitute mball 0.18 kg, g -9.80 m/s2
FEarth on ball (0.18 kg)(-9.80 m/s2)
-1.8 N
82
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Use Newtons third law to solve for Fball on
Earth.
Fball on Earth FEarth on ball
83
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Substitute FEarth on ball 1.8 N
Fball on Earth ( 1.8 N) 1.8N
84
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Use Newtons second and third laws to find aEarth.
85
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Substitute Fnet 1.8 N, mEarth 6.01024 kg
86
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
Step 3 Evaluate the Answer
87
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
  • Are the units correct?
  • Dimensional analysis verifies force in N and
    acceleration in m/s2.
  • Does the sign make sense?
  • Force and acceleration should be positive.

88
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
  • Is the magnitude realistic?
  • Because of Earths large mass, the acceleration
    should be small.

89
Newtons Third Law
SECTION4.3
Earths Acceleration (cont.)
The steps covered were
  • Step 1 Analyze and Sketch the Problem
  • Draw free-body diagrams for the two systems the
    ball and Earth.
  • Connect the interaction pair by a dashed line.
  • Step 2 Solve for the Unknown
  • Step 3 Evaluate the Answer

90
Newtons Third Law
SECTION4.3
Tension
  • The force exerted by a string or rope is called
    tension.
  • At any point in a rope, the tension forces are
    pulling equally in both directions.

91
Newtons Third Law
SECTION4.3
Tension (cont.)
92
Newtons Third Law
SECTION4.3
The Normal Force
  • The normal force is the perpendicular contact
    force exerted by a surface on another object.
  • The normal force is important when calculating
    resistance.

93
Section Check
SECTION4.3
  • Explain Newtons third law.

94
Section Check
SECTION4.3
Answer
  • Answer Suppose you push your friend. The force
    of you on your friend is equal in magnitude and
    opposite in direction to the force of your friend
    on you. This is summarized in Newtons third law,
    which states that forces come in pairs. The two
    forces in a pair act on different objects and are
    equal in strength and opposite in direction.
  • Newtons third law FA on B FB on A
  • The force of A on B is equal in magnitude and
    opposite in direction of the force of B on A.

95
Section Check
SECTION4.3
  • If a stone is hung from a rope with no mass, at
    which place on the rope will there be the most
    tension?

A. The top of the rope, near the hook. B. The
bottom of the rope, near the stone. C. The
middle of the rope. D. The tension will be the
same throughout the rope.
96
Section Check
SECTION4.3
Answer
Reason Because the rope is assumed to be without
mass, the tension everywhere in the rope is equal
to the stones weight.
97
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98
Forces in One Dimension
CHAPTER4
Resources
Physics Online Study Guide Chapter Assessment
Questions Standardized Test Practice
99
Force and Motion
SECTION4.1
Study Guide
  • A force is a push or a pull. Forces have both
    direction and magnitude. A force might be either
    a contact force or a field force.
  • Newtons second law states that the acceleration
    of a system equals the net force acting on it
    divided by its mass.

100
Force and Motion
SECTION4.1
Study Guide
  • Newtons first law states that an object that is
    at rest will remains at rest and an object that
    is moving will continue to move in a straight
    line with constant speed, if and only if the net
    force acting on that object is zero. An object
    with zero net force acting on it is in
    equilibrium.

101
Weight and Drag Force
SECTION4.2
Study Guide
  • The objects weight (Fg) depends on the objects
    mass and the gravitational field at the objects
    location.
  • An objects apparent weight is the magnitude of
    the support force exerted on it. An object with
    no apparent weight experiences weightlessness.

102
Weight and Drag Force
SECTION4.2
Study Guide
  • A falling object reaches a constant velocity when
    the drag force is equal to the objects weight.
    The constant velocity is called the terminal
    velocity. The drag force on an object is
    determined by the objects weight, size and shape
    as well as the fluid through which it moves.

103
Newtons Third Law
SECTION4.3
Study Guide
  • Newtons third law states that the two forces
    that make up an interaction pair of forces are
    equal in magnitude, but opposite in direction and
    act on different objects. In an interaction
    pair, FA on B does not cause FB on A. The two
    forces either exist together or not at all.

104
Newtons Third Law
SECTION4.3
Study Guide
  • The normal force is a support force resulting
    from the contact between two objects. It is
    always perpendicular to the plane of contact
    between the two objects.

105
Forces in One Dimension
CHAPTER4
Chapter Assessment
Combining Forces
  • If you and your friend exert a force of 100 N
    each on a table, first in the same direction and
    then in opposite directions, what is the net
    force?

106
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Chapter Assessment
Combining Forces
  • In the first case, your friend is pushing with a
    negative force of 100 N. Adding them together
    gives a total force of 0 N.

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Chapter Assessment
Combining Forces
  • In the second case, your friends force is 100 N,
    so the total force is 200 N in the positive
    direction and the table accelerates in the
    positive direction.

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Chapter Assessment
Newtons Second Law
  • Newtons second law can be rearranged to the form
    F ma, which you
    learned about previously.
  • Assume that the table that you and your friend
    were pushing was 15.0 kg and the two of you each
    pushed with a force of 50.0 N in the same
    direction.
  • To find out what the acceleration of the table
    would be, calculate the net force, 50.0 N 50.0
    N 100.0 N, and apply Newtons second law by
    dividing the net force of 100.0 N by the mass of
    the table, 15.0 kg, to get an acceleration of
    6.67 m/s2.

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Chapter Assessment
Forces of Ropes and Strings
  • Tension forces are at work in a tug-of-war.
  • If team A, on the left, is exerting a force of
    500 N and the rope does not move, then team B,
    must also be pulling with 500 N.

Tim Fuller
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Chapter Assessment
Fighting Over a Toy
Anudja is holding a stuffed dog, with a mass of
0.30 kg, when Sarah decides that she wants it and
tries to pull it away from Anudja. If Sarah pulls
horizontally on the dog with a force of 10.0 N
and Anudja pulls with a horizontal force of 11.0
N, what is the horizontal acceleration of the dog?
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Chapter Assessment
Earths Acceleration
When a softball with a mass of 0.18 kg is
dropped, its acceleration toward Earth is equal
to g, the acceleration due to gravity. What is
the force on Earth due to the ball, and what is
Earths resulting acceleration? Earths mass is
6.01024 kg.
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Chapter Assessment
  • If a golf ball, baseball and bowling ball are
    thrown with the same force, which ball will move
    with a greater acceleration?

A. Golf ball B. Baseball C. Bowling ball D.
The three balls will have equal acceleration.
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Chapter Assessment
114
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Chapter Assessment
  • Jack is boating in a river applying a contact
    force of 30 N, in a direction opposite to the
    flow of water. At the same time, the water is
    exerting a force of 30 N on the boat. In which
    direction will the boat move?

A. The boat will move in the direction of the
flow of water. B. The boat will not move at
all. C. The boat will move back and forth within
a particular distance. D. The boat will move in
the direction opposite to the flow of water.
115
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Chapter Assessment
Reason Since two equal and opposite forces are
acting together, the net force is zero. Hence,
the boat will not move at all.
116
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Chapter Assessment
  • What is inertia?

A. Force. B. The tendency of a body to stay
only at rest C. The tendency of a body to move
with constant acceleration D. The tendency of a
body to move with constant velocity
117
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Chapter Assessment
  • Reason Inertia of a body is the tendency of a
    body to stay at rest and/or to move with a
    constant velocity. Remember being at rest is
    simply a special case of constant velocity, v 0
    m/s.

118
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Chapter Assessment
  • If the weight of a person on Earth is 120 N, what
    will his weight be on the Moon? (Gravity on the
    Moon is six times less than the gravity on Earth.)

119
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Chapter Assessment
Reason Gravity on the Moon is .
120
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Chapter Assessment
Reason
Weight of person on the Moon
Gravity on the Moon
mass of person
121
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Chapter Assessment
  • What happens when the drag force is equal to the
    force of gravity?

A. The object comes to rest. B. The object
moves with constant acceleration. C. The object
moves with constant velocity. D. The velocity of
the object increases.
122
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Chapter Assessment
Reason When drag force equals the force due to
gravity, the net force acting on the object is
zero. As a result of this, the object moves with
constant velocity, which is called terminal
velocity.
123
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Standardized Test Practice
  • What is the acceleration of the car described by
    the graph on the right?

A. 0.20 m/s2 B. 0.40 m/s2
C. 1.0 m/s2 D. 2.5 m/s2
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Standardized Test Practice
  • What distance will the car described by the above
    graph have traveled after 4.0 s?

A. 13 m B. 40 m
C. 80 m D. 90 m
125
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Standardized Test Practice
  • If the car in the graph on the right maintains a
    constant acceleration, what will its velocity be
    after 10 s.

A. 10 km/h B. 25 km/h
C. 90 km/h D. 120 km/h
126
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Standardized Test Practice
  • In a tug-of-war, 13 children, with an average
    mass of 30 kg each, pull westward on a rope with
    an average force of 150 N per child. Five
    parents, with an average mass of 60 kg each, pull
    eastward on the other end of the rope with an
    average force of 475 N per adult. Assuming that
    the whole mass accelerates together as a single
    entity, what is the acceleration of the system?

A. 0.62 m/s2 E B. 2.8 m/s2 W
C. 3.4 m/s2 E D. 6.3 m/s2 W
127
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Standardized Test Practice
  • What is the weight of a 225-kg space probe on the
    Moon? The acceleration of gravity on the Moon is
    1.62 m/s2.

A. 139 N B. 364 N C. 1.35103 N D. 2.21103 N
128
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Standardized Test Practice
Test-Taking Tip
  • Maximize Your Score

If possible, find out how your standardized test
will be scored. In order to do your best, you
need to know if there is a penalty for guessing,
and if so, what the penalty is. If there is no
random-guessing penalty at all, you should always
fill in an answer, even if you have not read the
question.
129
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Chapter Resources
Forces Exerted on the Book
130
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Chapter Resources
Ball Tied to a String
131
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Chapter Resources
Ball Held in Your Hand
132
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Chapter Resources
The Carts Motion Shown in a Linear Relationship
133
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Chapter Resources
Acceleration of Cart
134
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Chapter Resources
Force-Acceleration Graph
135
Forces in One Dimension
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Chapter Resources
Combining Forces
136
Forces in One Dimension
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Chapter Resources
Fighting Over a Toy
137
Forces in One Dimension
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Chapter Resources
An Elevator Accelerating Upward
138
Forces in One Dimension
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Chapter Resources
A Soccer Ball on a Table on Earth
139
Forces in One Dimension
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Chapter Resources
Earths Acceleration
140
Forces in One Dimension
CHAPTER4
Chapter Resources
The Normal Force on an Object
141
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