Newton

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Newtons Laws

• The Study of Dynamics

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Isaac Newton

• Arguably the greatest scientific genius ever.
• Came up with 3 Laws of Motion to explain the
  observations and analyses of Galileo and Johannes
  Kepler.
• Discovered that white light was composed of many
  colors all mixed together.
• Invented new mathematical techniques such as
  calculus and binomial expansion theorem in his
  study of physics.
• Published his Laws in 1687 in the book
  Mathematical Principles of Natural Philosophy.

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What is a Force?

• NO not THE Force
• A force is a push or pull on an object. It may
  be from gravity, electrical, magnetic, or muscle
  efforts.

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• A net force causes an object to accelerate
• To speed up
• To slow down
• To change direction

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• Contact Forces Field Forces
• Arise because of direct Gravity
• contact between objects. Electric
  Act over a distance.
• ex friction, tension Magnetic

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Free body diagram (FBD)

• Shows all the forces acting on an object.
• support force
• friction force Applied
  force
• weight

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Newtons First Law

• A body in motion stays in motion at constant
  velocity and a body at rest stays at rest unless
  acted upon by a net external force.
• This law is commonly referred to as the Law of
  Inertia.

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Implications of Newtons 1st Law

• If there is zero net force on a body, it cannot
  accelerate, and therefore must move at constant
  velocity, which means
• it cannot turn,
• it cannot speed up,
• it cannot slow down.

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What is Zero Net Force?
Physics
A book rests on a table.
Even though there are forces on the book, they
are balanced. Therefore, there is no net force on
the book. SF 0
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Diagrams

• Draw a force diagram and a free body diagram for
  a book sitting on a table.

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Sample Problem

• A monkey hangs by its tail from a tree branch.
  Draw an FBD representing all forces on the monkey

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Sample Problem

1. Now the monkey hangs by both hands from two
   vines. Each of the monkeys arms are at a 45o
   from the vertical. Draw an FBD representing all
   forces on the monkey.

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Mass and Inertia

• Chemists like to define mass as the amount of
  stuff or matter a substance has.
• In physics mass is a measure of inertia, which is
  the ability of a body to resist acceleration by a
  net force.

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Demonstration

• A heavy block hangs from a string attached to a
  rod. An identical string hangs down from the
  bottom of the block. Which string breaks
• when the lower string is pulled with a slowly
  increasing force?
• when the lower string is pulled with a quick jerk?

Top string breaks due to its greater force.
Bottom string breaks because block has lots of
inertia and resists acceleration. Pulling force
doesnt reach top string.
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Newtons Second Law

• A body accelerates when acted upon by a net
  external force.
• The acceleration is proportional to the net force
  and is in the direction which the net force acts.

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Newtons Second Law

• ?F ma
• where ?F is the net force measured in Newtons (N)
• m is mass (kg)
• a is acceleration (m/s2)

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Units of force

• Newton (SI system)
• 1 N 1 kg m /s2
• 1 N is the force required to accelerate a 1 kg
  mass at a rate of 1 m/s2
• 1 N.225 lb (about the weight of a stick of
  butter)

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Working 2nd Law Problems

• Draw a free body diagram.
• Set up 2nd Law equations in each dimension.
• SFx max and/or SFy may
• Identify numerical data.
• x-problem and/or y-problem
• Substitute numbers into equations.
• plug-n-chug
• Solve the equations.

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Sample Problem

• In a grocery store, you push a 14.5-kg cart with
  a force of 12.0 N. If the cart starts at rest,
  how far does it move in 3.00 seconds?

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Sample Problem

• A catcher stops a 92 mph pitch in his glove,
  bringing it to rest in 0.15 m. If the force
  exerted by the catcher is 803 N, what is the mass
  of the ball?

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Sample Problem

• A 747 jetliner lands and begins to slow to a stop
  as it moves along the runway. If its mass is 3.50
  x 105 kg, its speed is 27.0 m/s, and the net
  braking force is 4.30 x 105 N
• a) what is its speed 7.50 s later?
• b) How far has it traveled in this time?

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Newtons Third Law

• For every action there exists an equal and
  opposite reaction.
• If body A exerts a force F on body B, then body B
  exerts a force of -F on body A.

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Examples of Newtons 3rd Law
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Sample Problem

• You rest an empty glass on a table.
• a) How many forces act upon the glass?
• b) Identify these forces with a free body
  diagram.
• c) Are these forces equal and opposite?
• d) Are these forces an action-reaction pair?
  Identify the action-reaction force pairs.

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Sample Problem

• A force of magnitude 7.50 N pushes three boxes
  with masses m1 1.30 kg, m2 3.20 kg, and m3
  4.90 kg as shown. Find the contact force between
  (a) boxes 1 and 2 and (b) between boxes 2 and 3.

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Mass and Weight

• Many people think mass and weight are the same
  thing. They are not.
• Mass is the amount of matter in an object,
  measured by its inertia, or resistance to
  acceleration.
• Weight can be defined as the force due to
  gravitation attraction.
• W mg

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Sample Problem

• A man weighs 150 pounds on earth at sea level.
  Calculate his
• a) mass in kg.
• b) weight in Newtons.

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Apparent weight

• If an object subject to gravity is not in free
  fall, then there must be a reaction force to act
  in opposition to gravity.
• We sometimes refer to this reaction force as
  apparent weight.

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Elevator rides

• When you are in an elevator, your actual weight
  (mg) never changes.
• You feel lighter or heavier during the ride
  because your apparent weight increases when you
  are accelerating up, decreases when you are
  accelerating down, and is equal to your weight
  when you are not accelerating at all.

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Going Up?
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Going Down?
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Sample Problem

• An 85-kg person is standing on a bathroom scale
  in an elevator. What is the persons apparent
  weight
• a) when the elevator accelerates upward at 2.0
  m/s2?
• b) when the elevator is moving at constant
  velocity between floors?
• c) when the elevator begins to slow at the top
  floor at 2.0 m/s2?

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