Newton

1
Newtons Laws Of Motion
2
Objectives
By the end of this lesson you should

• Be able to state, in words, Newtons three laws
  of motion
• Understand the difference between mass and weight
• Be able to define the term forceBe able to state
  what is meant by the term free-body diagram
  (FBD).
• Be able to construct FBDs and use them to aid in
  solving problems
• Be able to apply Newtons Laws of Motion in a
  systematic way to solve problems.
• Be able to state what is meant by the term Normal
  Force, and incorporate this definition in solving
  problems.

3
A Shift In Focus

• Up to this point in the term, we have analyzed
  motion (DESCRIBED) without worrying about what
  was causing the motion to occur. We said that
  such a study of motion was referred to as
  kinematics.
• We now concern ourselves with why the object is
  accelerating (or not). In other words, we look
  for the cause of the motion. This type of a
  study of motion where the cause of motion is
  considered is called dynamics.

4
Introduction

• Central to this discussion are a set of laws
  called Newtons Laws of Motion. This set of laws
  is considered to be of fundamental importance to
  the study of classical mechanics. Once
  introduced, you should be able to state these
  laws and apply them correctly even if stirred
  from a deep, restful sleep at 2 oclock in the
  morning!

5
Introduction

• In the slides that follow, there are words that
  are highlighted in the statements of Newtons 3
  Laws of Motion. This highlighting is to indicate
  that these words are critical to the statement of
  the law, and you should keep them in mind when
  applying these laws so that difficulties can be
  avoided.
• We begin with Newtons first law of motion.THE
  LAW OF INERTIA

6
Newtons First Law Of Motion

• An object in motion with a constant velocity will
  remain in motion with that constant velocity
  until the object is acted upon by a net, external
  force.
• This law is also called the Law of Inertia.
• Inertia The property of an object to resist a
  change in velocity. Mass is a quantification of
  the inertia of a body.

7
Inertia Newtons First Law

• By the end of this section you will understand
  the following statement and its implications in
  physicsAn object in motion with constant
  velocity will continue with the same constant
  velocity unless acted upon by an unbalanced
  outside force and,
• An object at rest will continue at rest unless
  acted upon by an unbalanced outside force.

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8
Balanced Forces cause what?

• The statement of this law raises a question What
  do you think will happen to the motion of the
  object if there is an unbalanced outside force?

9
Balanced Forces Cause What?
Balanced forces cause an inertial state of motion
called CONSTANT VELOCITY
UNBALANCED FORCES CAUSE WHAT? AN ACCELERATION!
10
FBD.Free Body Diagrams

• The forces acting on the object of interest must
  be identified.
• Then a special diagram called a free body diagram
  can be constructed. All static and dynamics
  problems begin in this fashion.

11
Our Problem Solving Model

• The first three steps in constructing a model
  are 
• 1. Identify the object or system.
• 2. Identify the forces acting on the object or
  system.
• 3. Draw a force (or free-body) diagram assuming
  the object or system as a point particle.

12
Approaching FBDs

• One cardinal rule is that once you identify the
  object, it cannot be changed unless you start all
  over with step one again and go through all of
  the steps with the new object.

13
On the sketch, circle the object or system with a
dotted line.

• In order to make a conscious decision to choose
  the object or system, and to avoid changing it
  midway through the activity, you will need to
  draw a rough sketch of the important parts in the
  situation being investigated.
• This is the real- world representation. (At
  first, the sketch will be provided for you, but
  later in the laboratory and in word problems you
  will need to complete the sketches on your own.)

14

• Draw all of the forces on the tree in picture
  below. Use an arrow (?) to represent each force
  and to indicate the direction of each force.
  Identify each force by what is causing it. Write
  the statement, force caused by _frictional
  force, etc________, next to each arrow. Put
  the tail of the arrow at the place on the object
  where the force is being applied.

15
Identifying the Forces Acting on the Object

• The basic definition of a force is a push or a
  pull. While this definition is correct, it does
  little in helping to identify the necessary
  forces.

16
What are the forces?

• The forces that need to be identified are those
  forces acting on the object or system.
• Each of these forces has to be caused by an
  object outside of the dotted line circle. It is
  important to identify the agents outside the
  object or system that are exerting forces on the
  system.

17
Remember your units!

• The metric unit for force is the Newton (N).
• The English unit is the pound (lb).
• Since the world is converting to metrics at a
  slow but sure rate, we will only deal with
  Newtons. This is part of the Standard
  International System of Units. (SI)

18
Weight and Mass are not the same!!!

• Mass is an inherent quantity that all objects
  have. It is measured in kilograms (kg). In this
  lecture we only need to deal with the weight
  vector.
• Weight (W) in N mg 9.8 m 
• Units m/s2 (kg) N
• The direction of the gravitational force is
  always toward the center of the Earth.

19
Forces on the object caused by something outside
the object are the only forces that are used.

• Forces at a distance vs. Forces from contact
• Weight --- DISTANCE
• Normal--- CONTACT
• Friction--- CONTACT
• Tension--- CONTACT
• Thrust --- CONTACT
• Drag --- CONTACT

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Types of Forces

• There are two categories of forces to consider
• contact forces
• forces at a distance.

21
Forces at a Distance

• They arise when the object is in the field
  caused by another object, but not in contact with
  the object.
• Examples of fields are electrical, magnetic,
  and gravitational fields. Since we are only
  dealing with mechanics in this module, the only
  force at a distance we will deal with is the
  gravitational force. Gravitational force is
  often called weight.

22
Put the tail of the arrow at the center of the
object. Label this force with the symbol W and
the statement "force caused by Earth."
23
FBD Representations

• On the sketch, represent the force by an arrow.
  The tail of the arrow will be at the place of
  contact and the tip will point in the direction
  of the force. Label each force with an
  appropriate symbol and force caused by
  ________.

24
Contact Forces

• The contact forces acting on the system of
  interest are identified by going around the
  dotted circle that defines that object or system.
  There is the likelihood of a force at any point
  where something outside the dotted circle is
  touching something inside the circle.

25
Contact Forces

• There are three contact forces that deserve
  special attention.
• These contact forces are tension, normal force,
  and friction.

26
TensionTension forces are caused by ropes or
cables. Tension can only be a pull. Therefore,
the direction is always known. Tension is given
the symbol T.
27
Normal ForceAny time an object exerts a force
on a surface, the surface also exerts a force on
the object. One common example is when the
object rests on something that supports or helps
to support the object. This supporting force is
called the normal force. The direction of the
normal force is always perpendicular to the
surface that is causing the force. Normal force
is given the symbol N.
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• The last special contact force to be discussed
  is surface friction. Friction is designated by
  the lower case letter f. Surface friction occurs
  whenever two surfaces rub together. It also can
  occur when two surfaces are touching but not
  moving with respect to each other.

29
This relationship between magnitude and the
direction of the force is true for any two
surfaces of the same material when rubbed
together.
30
Types of Friction

• There are two types of friction. When one
  surface slides on a second surface, it is called
  kinetic friction. When one surface tries to
  slide on a second surface but does not move, it
  is called static friction.

31
Static Friction

• When an object is at rest with respect to a
  surface, the frictional force can be greater than
  when the objects move across each other. In our
  model, imagine that the bumps (or grooves)
  are deeply interlaced.
• If a small force is applied to the object, the
  static friction fs will equal the applied force
  and cause the object to remain in equilibrium (a
  0).

32
Kinetic Friction

• In our model, when the object moves, the grooves
  of the object bounce along the grooves of the
  surface, and never go as deep as they do in the
  static case. Thus, the kinetic friction force fk
  has a smaller magnitude than the static friction
  force.

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Graph of Frictional Force vs. Applied Force
34
General Rules of Friction in the Model

• 1.  The frictional force has a direction opposite
  to the force that is causing, or trying to cause,
  the object to slide. Friction is parallel to the
  surface therefore, it opposes the sliding
  motion.
• 2.  The force trying to cause the object to slide
  (F) must be greater than fsmax for sliding to
  occur. When F is smaller than fsmax, the object
  will not slide.
• 3.   Once the object starts to slide, the static
  friction (fs) becomes kinetic friction (fk).
  Kinetic friction is always smaller than maximum
  static friction.
• 4.   Both static friction (fs) and kinetic
  friction (fk) are proportional to the normal
  force.
• 5.  The area of contact between the surfaces does
  not influence the magnitude of the frictional
  force.
• The speed of the object (assuming a low
  speed) does not influence the magnitude of the
  kinetic friction.

35
This is the big idea

• Isolate the system
• Figure out the forces
• Label each force
• Ask yourself this question
• Are the forces balanced?

36
             A soccer player starts running to
the right. On the sketch of the player, show the
point of application and direction of the forces
(W, N, fs) on the player.
37

• A car is at rest on a horizontal road. What is
  the value of the frictional force? Explain your
  answer.
•              For the car in question, show the
  forces on the car and the points of application.

38

• A woman pushes a book (the object) across a table
  to the left. On the sketch below, show the point
  of application and the direction of the four
  forces
• (W, N, fk, F).
• (F is the force of the woman on the book.)

39
Make a real world to FBD representation

• Recall we are modeling the forces on an object.
• We need to examine if the forces are balanced or
  if there is a net force to determine the type of
  motion present.

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Section Summary

• What is inertia?
• What is a net force?
• What is equilibrium?
• What is moving equilibrium?

42
Newtons Second Law Of Motion

• The acceleration of an object is directly
  proportional to the unbalanced, external force
  acting on the object and inversely proportional
  to the mass of the object. The acceleration of
  the object is in the same direction as the
  unbalanced, external force.
• Forces produce accelerations accelerations do
  not produce forces!

43
Newtons Second Law Of Motion

• In the expression on the previous slide, m
  represents the mass of the object experiencing
  the acceleration and F represents force.
• Force A push or a pull any influence that
  causes an object to change its velocity. The unit
  of force is the unit of mass times the unit of
  acceleration and is measured in Newtons. 1 Newton
  is the force required to give a 1.0 kg object an
  acceleration of 1.0 m/s2.
• Newtons Second Law is also referred to as the
  Law of Acceleration.

44
Newtons Third Law Of Motion

• If an object A exerts a force on object B, then
  object B exerts a force on A which is equal in
  magnitude and opposite in direction.
• It is important to remember that the forces in
  the action-reaction pair mentioned act on
  different objects.
• Newtons Third Law is also called the Law of
  Interaction.

45
Newtons Third Law Of Motion

• Newtons third law tells us that forces always
  come in pairs and that the forces in each pair
  are of equal magnitude, are opposite in
  direction, and act on different objects. You can
  never have a single force without a counterpart
  somewhere in the universe.

46
Forces come in two types.

• Contact forces
• Field forces
• How about forces in Pairs!

47
Newtons Third Law

• There is one more important piece to the dynamic
  and static model. It is called Newtons Third
  Law. Forces come in pairs. Understand Newtons
  Third law, we can ignore internal forces, and
  then only search for external forces acting on
  the object.

48
Push Me and I Push Back!!!
49
Push me and I push back!

• For example, with the palm of your hand, push on
  a book, desk or table. You are exerting a force
  on the object you are pushing. At the same time,
  you can feel a force on your hand. There seems
  to be two forces the one your hand exerted on
  the object, and another force on your hand.
• What is the relationship between these forces?

50
The man weighs 700 N. The force exerted by the
table on the man is

•             
• a)        Larger than 700 N
• b)        Equal to 700 N
• c)        Smaller than 700 N
• d)        There is no force.

51
    A hand pushes on a balloon against a wall
with a force of 10 N. The force exerted by the
balloon on the hand is

• a)        Larger than 10 N
• b)        Equal to 10 N
• c)        Smaller than 10 N
• d)        There is no force.

52
A building is being torn down. The wrecking ball
smashes through a wall. Does the ball put a
larger force on the wall than the wall puts on
the wrecking ball? Explain your answer.
53
Imagine that you hold the two force probes, one
probe in each hand. You will notice that each
force probe has a hook on it. Connect the two
force probes together and pull as seen in the
following figure.
54
Newton's Third Law

• Why does it seem that a bug hits a windshield
  with more force than the windshield hits the bug?
• The effect on the bug is worse than the effect on
  the windshield but the force is still the same!

55
Forces come in pairs. But which pair?

• Forces come in pairs
• An example would be the weight and normal force
  pairs in the left figure.
• Fg vs. Fg and Fn vs. Fn
• The Weight of an object and Normal Force are
  sometimes equal but they are not Force Pairs!!!

56
Mass and Weight

• For good reason, many people think of mass and
  weight as the same thing. It is difficult to
  distinguish between the two if your experience is
  restricted to on location on the earth. Mass and
  weight, however, are not the same. Mass is the
  quantification of an object inertia. That is,
  mass is a measure of an objects resistance to
  change in state of motion. Weight is a force.
  Weight is the force of attraction toward the
  earth. Mass is a scalar Weight (Force) is a
  vector.

57
Virtual Field Trip!

• Suppose we hopped a shuttle and went to a remote
  area in space where there was nothing around.
  Since we are in empty space, we would all be
  weightless. Even the 50 lb (weight on earth)
  cannon ball I brought with us would be
  weightless.

58
Virtual Field Trip

• Now, I am going to put the cannon ball into a
  cannon and fire it at 100 mph. I would like a
  volunteer from the class to stand directly in
  front of the cannon and catch the (weightless)
  cannon ball for me. What? No takers? And you are
  wise not to stand in front of the cannon. The
  cannon ball is still going to resist a change in
  state of velocity just the same as if it were on
  the earth. The cannon ball still has inertia, or
  mass, even though it has no weight!

59
Virtual Field Trip

• I hope this example helps you to start to see
  that there is a difference between mass and
  weight. We will explore mass and weight in more
  detail as we go through this and the next
  chapter.

60
Foreshadowing

• We move from a virtual field trip to a thought
  experiment in the next slide. I ask you to take
  some time and think about the question posed as
  it is quite complex. A class of 50 students will
  generally spend between 5-10 minutes stating
  wrong answers to the question before someone
  stumbles upon the correct answer. It is
  important for you to go through the same thinking
  process.

61
Try It On Your Own

• A person stands on a skateboard and pushes
  against the wall. The wall pushes back on the
  person and the skateboard moves (accelerates).
  According to Newtons 3rd law, the force exerted
  by the person on the wall and the force exerted
  by the wall on the person add to zero. If these
  two forces add to zero, why is it that the
  skateboard accelerates? (The correct answer does
  not involve the mass of the earth nor frictional
  forces.)

62
Free Body Diagrams

• A free body diagram (FBD) differs from your
  picture of the problem. In a FBD, you isolate
  the object that you are interested in by drawing
  it as a single point. Then, draw on this
  isolated object only those forces that act
  directly on the object. Do not include forces
  that the isolated object exerts. Also, include
  your sign convention in the FBD.
• A well drawn FBD is crucial to the successful
  solution of a problem involving Newtons Laws of
  Motion.

63
Free Body Diagrams

• The reason that I had you go through the
  skateboard problem was to illustrate the
  importance of the FBD. When you consider only
  the forces acting directly on the skateboarder,
  the force provided by the wall is the only
  external force acting on the skateboarder. Since
  there is an unbalanced, external force acting on
  the skateboarder, the skateboarder will
  accelerate according to Newtons second law of
  motion.

64
Example

• A car is traveling at a constant velocity
  straight ahead on a flat,frictionless road. Draw
  a free-body diagram for the car.

65
Try It On Your Own

• The driver in the car fires retro rockets so that
  the car is decelerating while traveling on a
  straight, flat, and frictionless road. Describe
  the free body diagram of the car.

66
Normal Force

• The last two situations had a force exerted by a
  surface on an object. A surface will always push
  on an object in a direction that is
  perpendicular, or normal, to the surface. Such a
  force exerted by a surface is called a normal
  force.

67
Example

• A 4.0 kg object is pulled along a frictionless
  surface to the right by a 6.0 N force. How long
  does it take the object to travel a distance of
  25.0 m assuming the object starts at rest?

68
Solution To Example

• Use Fma to find acceleration.6 Newtons a4kg
  or 1.5 m/s2then use the acceleration in the
  equationx1/2a8 t2 and solve for time.25
  .51.5t2.

69
Try It On Your Own

• A 4.0 kg object is pulled along a frictionless
  surface to the right by a 6.0 N force, directed
  30? above the horizontal. How long does it take
  the object to travel a distance of 25.0 m
  assuming the object starts at rest?

70
Example

• An 85.0 kg person stands on a scale that reads
  weight in Newtons while standing in an elevator.
  What is the reading on the scale when
• (a) The elevator is stopped?
• (b) The elevator is accelerating
  upward at 3.5 m/s2?

71
Solution

• Normal Up is larger than the weight down. Hence
  the scale reading would be Greater than if it
  was not accelerating at all.Answer for part b
  is 1130.5 newton's

72
Try It On Your Own

• An 85.0 kg person stands on a scale that reads
  weight in Newtons while standing in an elevator.
  What is the reading on the scale when the
  elevator is moving upward at a constant speed of
  5.0 m/s?

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Summary

• A correctly drawn free body diagram is essential
  to solve problems involving Newtons Laws of
  Motion.
• Newtons Laws of Motion are useful in a wide
  variety of situations ranging from the motion of
  a baseball when struck by a bat to the motion of
  the planets in the solar system. This wide range
  of applicability is why Newtons Laws are so
  highly regarded.