Chapters 4

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Chapters 4 5

• Newtons Laws of Motion
• (continued)

2
Chapter 4

• Newtons Second Law of Motion

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Newtons Second LawThe Law of Acceleration

• Forces cause acceleration
• Net force must be greater than zero
• Masses resist acceleration due to inertia
• This is, in part, why it is harder to start
  something moving than to keep it moving
• Hence we say that acceleration is directly
  proportional to net force and inversely
  proportional to mass

4
Newtons Second LawThe Law of Acceleration

• The acceleration of an object is in the direction
  of the force applied.
• Acceleration is directly proportional to the
  force applied.
• The harder you push an object the faster it goes
• Acceleration is inversely proportional to the
  mass of the object.
• The heavier the object, the less affect a push
  has.

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Sample Problem

• What force is required to accelerate a 10 kg
  object horizontally at 6 m/s2?

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Solution

• F ma (10 kg)(6 m/s2) 60 Newtons

7
Friction

• Forces always come in pairs, hence the Normal
  force, which is perpendicular to the contact
  surface, has a companion force that is parallel
  to the contact surface, this force is friction
• Friction always opposes motion
• Friction depends upon two things
• The nature of the contact between two objects
• How strong the force of contact is (The Normal
  Force)

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Friction

• Friction also occurs in gases and liquids both of
  which are referred to in physics as fluids.
• In fluids we call friction drag and in air we
  refer to it specifically in air as air
  resistance.

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Sample Problem

• If a 200 Newton force is applied to a box that
  undergoes a 100 Newton resistive force
  (friction). What is the net force on the box?
  If it is a 30 kg box, what is its acceleration?

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Solution

• Fnet 200 N 100 N 100 N
• Fnet ma so a Fnet/m
• 100 N/30 kg
• 3.3 m/s2

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Mass A Measure of Inertia

• Mass is measured in kilograms
• Mass is not Weight
• Mass is a built in property of matter
• Just because you leave earth, you dont change
  your mass, but you do change your weight
• Weight is an force caused by the acceleration due
  to gravity on the mass

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Weight

• Mathematically
• Weight mass x gravity
• Or
• Fw mg
• So the force of weight on one kilogram of mass on
  planet earth is given by
• Fw (1 kg)(9.8 m/s2) 9.8 Newtons

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Sample Problem

• What is the weight of a 10 kg object
• a) on earth
• b) on the moon (g 1/6 that of earth)

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Terminal Velocity

• When an object is in free fall where there is no
  atmosphere, there is no friction, hence no
  opposing force and it will continue to accelerate
  until it reaches the ground.
• However, when there is atmosphere, there is
  friction called drag which opposes the motion.
  
• When the force of the drag force of gravitation
  (weight) then Fnet 0, and the acceleration of
  the object becomes zero. This is called terminal
  velocity.
• Terminal velocity - is then the highest speed
  reached by a falling object in the presence of
  air resistance. It is different for every object
  based on its mass and shape.

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Chapter 5

• Vector Addition

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Vectors and Scalars

• Vector vs. Scalars
• Vectors have both magnitude and direction
• Displacement, Velocity, Acceleration, Force, and
  Momentum
• Scalars have only magnitude
• Mass, Time, and Temperature

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Mathematical Addition

• Mathematical Addition of Vectors Requires a basic
  knowledge of Geometry You must know
• Sin ? Opposite/Hypotenuse
• Cos ? Adjacent/Hypotenuse
• Tan ? Sin ?/ Cos ? Opposite/Adjacent
• ArcSin, ArcCos, ArcTan

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Mathematical Addition

• Mathematical addition requires that you be able
  to
• Draw a rough sketch of the original vectors
• Draw a parallelogram
• Draw the Resultant
• Use Triangle geometry to find the magnitude and
  direction of the resultant

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Example

• What is the result of adding two vectors if the
  first vector is 100 km to the west and the
  second vector is 50 km to the north?

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Mathematical Addition
Step One Sketch the vectors Step Two Put
vectors on the same axis and draw the
parallelogram

100 Km West
50 Km North
Step One
Step Two
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Mathematical Addition
Step Three Draw the Resultant
Step Four Since this is a right triangle you can
find the resultant using Pythagorean
theorem Pythagorean Theorem C2 A2 B2
50 Km
100 Km
111.8 Km
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Components of Vectors

• Often we need to change a single vector into two
  vectors in order to make addition easier. These
  two vectors will be a right angles to each other
  and are called component vectors or just
  components for short.
• The breaking down of a vector this way is called
  resolution.

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Vector Resolution
Step One Draw Original Vector
45º
100 Km 45 North of West
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Vector Resolution
Step Two Draw parallelogram
100 Km 45 North of West
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Vector Resolution
Step Three Label and measure
components
Sin 45 N/100 100 Sin 45 N North component
70.7 km
45
Cos 45 W/100 100 Cos 45 West West component
70.7 km
100 Km 45 North of West
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Chapter 10

• Part I Projectiles

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Projectile Motion

• A projectile is any object thrown or launched
• Uses the same kinematic equations you have
  already learned
• Requires that you use two sets of equations one
  in the horizontal and one in the vertical
• These two sets are related only by time

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Projectile Motion

• A projectile which is dropped or thrown
  horizontally has an initial velocity in the Y
  direction (V0y) 0
• Acceleration in the horizontal direction (ax)
  0 hence Velocity in the horizontal direction
  (Vx) is constant
• This means that only one kinematic equation
  applies in the horizontal direction
• Xx Vxt

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Projectile Motion

• While it is moving forward, it is also falling
  just as if you had dropped it.
• So in the Y direction
• x ½ at2
• Where a is the acceleration due to gravity.
• The one thing that both motions have in common is
  time. When the projectile hits the ground it
  stops moving in both directions!

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Projectile Motion

• A ball is thrown horizontally off a building
  which is 200 m high with a velocity of 10 m/s
• How long does it take to reach the ground?
• How far from the building will it land?
• What is its velocity just before it hits the
  ground (remember magnitude and direction)

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Chapter 5

• Newtons Third Law

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Newtons Third LawAction - Reaction

• For every action there is an equal and opposite
  Reaction.

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34
Sample Problem

• If a 0.4 kg shotgun shell undergoes a 100 Newton
  force when it is fired, what is its acceleration?
• If it was fired from a 2 kg shotgun what is the
  recoil acceleration of the shotgun?

35
Solution

• Since F ma a F/m So
• a 100 N/0.4 kg 250 m/s2
• Since the recoil force is equivalent to the
  firing force according to Newtons Third Law the
  same equation applied however now you use the
  mass of the shotgun
• a 100 N/2 kg 50 m/s2
• Demonstrating that it is the mass of the shotgun
  that keeps it from doing the same damage as the
  bullet