NEWTONS LAWS

1
LECTURE-4

• NEWTONS LAWS
• AND
• FORCES

2
Inertia

• Aristotles views
• World composed of 4 elements
• Earth
• Water
• Air
• Fire
• If the hierarchical order is disturbed, there
  will
• be a natural motion establishing order

3
Fig. 3-1a, p.34
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Fig. 3-1b, p.34
5

• The motion will be in straight line away from or
• towards the earths center
• Practically this view is not very suitable as it
• implies perpetual motion of any object in air
• and no motion at all in vacuum
• Galileo came up with his own idea
• Proposed the Law of Inertia

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Galileos thought

• Perfomed a thought experiment
• Questioned himself as to what is going on
• Found that one need some sort of an interaction
  to change the state of rest or motion of an
  object
• Suggested that constant speed straight line
  motion is just as natural as rest-motion
• Laid down the concept of Inertia

7
Fig. 3-2, p.35
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Sir Isaac Newton Inertia

• According to Galileo without any external
• interaction it is not possible to move a body
• neither it is possible to stop it ,if it is
  already in
• Motion.
• Sir Isaac Newton formulated this idea and laid
• down the statement for Law of Inertia. To
• respect him this law was named after him and
• is known as Newtons First Law

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p.37
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What is a Law ?

• A Law is a rule of nature which cannot be
• derived through some mathematics. It is
• understood on basis of intuition and
• stated in an ad-hoc basis and can be
• proved through the different things
• happening in nature.

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Inertia in terms of Cartoon Laws of Physics

• Cartoons have a good knowledge of Inertia
• believe it or not !! According to them the law
• Says
• Any one suspended in space will remain
• suspended until and unless made aware of the
• situation

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Newtons First Law

• The velocity of an object remains constant
• unless an unbalanced force acts on the object.
• It actually means that
• Any object in rest will remain to be in rest and
• any object in motion will remain to be in
• motion until and unless some external
• unbalanced Force acts on it to change its state
• of rest or motion.

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Force

• While stating the First Law of Motion
• Newton said something known as Force
• What is a Force ?
• It is an abstract concept, a Human perception
• which cannot be seen.
• Hmmmm it seems to be scary.. !!!!

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• Is it ghostly ??

Forces ??
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• No way !!
• What ever they are ,atleast they r not GHOST.
• Force is a feel, in the simplest way it can be
• explained as a Push or Pull. We dont see it , we
• feel it. We can only see the changes that takes
• place under its influence. One example of Force
• is the friction force.

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Fig. 3-4, p.38
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Fig. 3-5, p.38
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• Force Has a Direction and Magnitude
• Force is a Vector Quantity
• It follows the rule for addition of Vector
• Be Careful
• The first Law says that there is a change in
• state of rest or motion only under the influence
• of an UNBALANCED FORCE. So the net force
• have to be non zero to have influence.

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Adding Vectors

• Vectors are Geometrical representations
• of physically measurable quantities.
• Mathematicians have developed rules for
• combining vector quantities such as
• displacements, velocities, accelerations,
• or forces.

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Vector Shorthand

• In texts, vectors are represented by boldface
  symbols (such as F).
• When writing by hand about vectors, you use an
  arrow over the symbol (such as F ).
• The magnitude of the vector quantity is
  represented by an italic symbol. Therefore, a
  force is written as F, and its magnitude is
  written as F.

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Fig. 3-7, p.39
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Fig. 3-8c, p.40
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• The Second Law of Motion

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Newtons Second Law

• Daily Life experience gives us
• Acceleration a of any object is proportional to
  Applied
• Force
• Acceleration a of any object is inversely
  proportional to
• the amount of matter contained in the object also
  
• known as Mass
• Newton gave this two ideas a mathematical
• formulation which came to be known after his name
  as
• Newtons Second Law of Motion

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• The mathematical formulation is
• a F/m ,
• F m x a
• Both F, a are vectors. They have magnitude and
• directions and follows the addition rule of
  vectors
• In words the Law says
• The net force on an object is equal to its mass
  times its
• acceleration and points in the direction of the
• acceleration

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Unit of Force

• The unit of force is also Named after Sir Isaac
  Newton.
• It is said to be Newton in Metric and Pound in US
  
• systems
• 1 Newton is defined as
• The force needed to accelerate an object of 1
  kilogram
• mass at 1 m/s2
• The gravitational force on a very small apple is
  almost
• equal to a newton.
• In US system it is defined as
• The force required to accelerate an object of 1
  slug
• mass at 1 ft/s2

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Some Examples

• If acceleration of an object is given by 2 m/s2
  and mass is 4 kilogram. What is the force on this
  object ?
• If net unbalanced force acting on an object is
  19.6 Newton, and mass of the object is 2 kilogram
  what is the acceleration of that object ?
• give your answers in both metric and US units

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Mass and Weight

• Mass and weight are proportional but they are not
  the
• same !!
• Weight is the measure of Gravitational attraction
  and
• varies from Place to Place.
• Mass on the other hand is quantity of matter a
  object
• contains. It is independent of wherever you are
  in the
• Universe. It is an intrinsic property.
• Mass of you in Earth and Moon are same , but in
  Moon
• you weight less than in Earth.

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p.43
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• If you are not under the influence of
  Gravitational
• Attraction you can have a feel of Weightlessness
  but
• you can never be Massless.
• You can experience Weightlessness while going up
  in a
• high speed elevator in a tall building.
• W m X g , Unit of weight is also Newton in
  Metric
• system and Pound in US system.

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Free Body Diagram

• This is a diagram used to pictorial visualize the
  different
• forces acting on a object in motion. It helps us
  to figure
• out which are the forces responsible for its
  motion and
• then we can calculate the total unbalanced force
  to find
• out the acceleration of the moving object using
• Newtons Second Law.
• As the name suggest we isolate , or free , the
  object in
• question from everything else and represent it by
  a dot.
• We then draw all the forces acting on the object
  with
• each tail starting on the dot.

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Fig. 3-10, p.45
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Friction

• It is a force which always acts against any
  motion. It is
• resistive in nature.
• Whether you move or not friction is always
  present
• Frictional Forces are of two types
• Static
• Kinetic
• Static Friction is always Greater than Kinetic
• friction.

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• NEWTONS THIRD LAW OF MOTION

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Statement of the Law

• If an object exerts a force on a second object,
• the second object exerts and equal force back
• on the first object.
• Or simply it can be stated as
• To every action there is an equal and opposite
• reaction
• Dont believe it ?? Just slap the guy seating
  beside
• you and you will believe it.. !!!!

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It doesnt applies to a Journalist
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• This forces are known as actionreaction pair.
• They never act on the same body
• Effect depends on mass of the body
• Third Law forces never appear on the same body in
  a free body diagram
• Have you ever thought why do you stand ? What
  stops
• you from going inside the ground if Newtons
  Second
• Law of Motion was only there ?
• When you fire a rifle you experience a recoil,
  what is
• this ?

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Fig. 3-14, p.49
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Fig. 3-15, p.49
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• CIRCULAR MOTION

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• Till now we have been talking about motions in
• a straight line. Let us now discuss what
• happens when motion is along a circular path.
• What are the forces acting ? How do they lead
• to motion. What about the acceleration.

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• Some examples of Circular Motions
• Motion of Earth about Sun
• Runner in a race track
• Ball swinging on the end of a rope
• Whirlpool
• Centrifuge

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• While moving in a circular path. Even if you are
  moving
• at a constant speed you are still accelerating.
• The force that leads to circular motion is known
  as
• Centripetal Force.
• As the name suggest. It is a center seeking force
  and
• always acts towards the center of the circle.
• The generation of this force can be understood
  from
• Newtons first law.

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Fig. 4-1, p.57
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Fig. 4-2, p.57
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Fig. 4-3, p.58
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• Circular Acceleration
• While one is moving in a circular path even if
  the speed
• remain constant he is constantly changing
  direction.
• Hence we can say that the velocity is changing.
• This change in velocity gives rise to the
• acceleration.
• Since acceleration is also a Vector quantity .
  Then from
• Newtons second law of motion we get that in a
  circular
• motion the acceleration is also towards the
  center
• and is known as Centripetal Acceleration

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Fig. 4-4, p.58
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How Do You Diagram This?

• Two students have different opinions about the
  appropriate free-body diagram for Billy when he
  is at the location shown in this figure.

At the county fair Billy finds himself pressed up
against the wall of the Rotor, a circular room
that spins about a vertical axis. When the room
is spinning fast enough, the floor drops from
under the people.
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Isabels Argument

• The gravitational force is pulling down on
  Billy, and the frictional force of the wall is
  keeping him from falling. The wall is exerting a
  normal force inward and the centrifugal force is
  acting outward, pinning Billy to the wall.

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Caitlins Argument

• I agree with you except for the centrifugal
  force. Billy would travel in a straight-line path
  if it werent for the inward centripetal force
  pushing him into a circular path.

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Fig. 4-7, p.61
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Fig. 4-8, p.61
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Working It Out Centripetal Acceleration

• Find the centripetal acceleration of a 0.2-kg
  ball traveling in a 1-m radius circle at 1
  revolution per second.
• Because this circle has a circumference of 2 r
  6.3 m, the ball has a speed of 6.3 m/s
• Because Fnet ma is always valid, we can use
  this result to find the centripetal force.

p
55
Banking Corners

• By banking the road, the demands on the
  frictional forces can be reduced.
• Lets first consider the case when there is no
  frictional force.
• As shown in the figure, the cars weight acts
  vertically downward, pushing the car against the
  road. Because there is no frictional force, the
  road can only exert a force on the car that is
  perpendicular to the road.

The horizontal unbalanced force provides the
centripetal acceleration that makes the car go
around the curve.
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Design Considerations

• The design speed of such a banked curve is that
  speed which does not require any frictional
  forces between the tires and the road while you
  are turning.
• This is the speed you want to use if the road is
  icy.
• At highway speeds, you would need a 40 bank
  angle to dispense with friction for a curve with
  a radius of 100 meters.
• The centripetal force experienced by a car going
  around a curve increases as the weight of the car
  increases. This is fortunate, because the larger
  mass of the car requires a greater centripetal
  force to make the car go around the corner.
• Therefore, the design speed of the curve is the
  same for all cars.

57
Projectile Motion

• When something is launched near Earths surface,
  it experiences a constant vertical gravitational
  force.

• Motion under these conditions is called
  projectile motion. It occurs whenever an object
  is given some initial velocity and thereafter
  travels in a trajectory subject only to the force
  of gravity.

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Projectile Motion

• Strobe drawing of a thrown balls motion. Note
  that the horizontal motion has a constant speed.

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A Trip to Narang

• The same experiment, only now with the bullet
  fired at an upward angle, shows the same results.
  
• Horizontal movement is unaffected by the presence
  or absence of gravity.
• The distance d is equal to free-fall.

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Launching an Apple into Orbit

• On our first attempt, we throw the apple with an
  ordinary speed.
• The apple follows a projectile path.
• On our next attempt, imagine that we throw the
  apple much faster.
• The apple still falls to the ground, but the path
  is unlike the first one. If the apple travels
  very far, Earths curvature becomes important.
  The force of gravity points in slightly different
  directions at the beginning and end of the path.

An unsuccessful launch results in projectile
motion.
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Launching an Apple into Orbit

• Normally, we are not aware of the curvature of
  Earths surface, because Earth is so huge.
• If we were to construct a large perfectly
  horizontal plane resting on the surface of a
  perfectly spherical Earth, Earths surface will
  be 5 meters below the plane at a distance of 8
  kilometers.
• Imagine what would happen if on our next attempt
  to launch the apple, we throw it with a speed of
  8 km/sec (18,000 mph!) During the first second,
  the apple drops 5 meters.

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Launching an Apple Into Orbit

• The result is that the motion during the next
  second is a repeat of that during the first. And
  so on. The apple is in orbit.
• By throwing the apple far enough, we have changed
  the motion from projectile to circular.

This illustration was used in Newtons Principia
in the discussion of launching an object into
orbit around Earth.
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Flawed Reasoning about Orbits

• A newspaper report reads in part, The space
  shuttle orbits Earth at an altitude of nearly 200
  miles and is traveling at a speed of 18,000 mph.
  The shuttle remains in orbit because the
  gravitational force pulling it toward Earth is
  balanced by the centrifugal force (the force of
  inertia) that is pulling it away from Earth.
• Explain why this newspaper should hire a new
  reporter.

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• At last we are done with motion
• Just hope if Newton would have born at
• this age. I wouldnt had to talk that much
• neither you guys had to bear with it
• Well folks he is not going to Let us live
• happily Here he comes again with
• GRAVITATION