Newtons Laws

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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 Force?

• A force is a push or pull on an object.
• Forces cause an object to accelerate
• To speed up
• To slow down
• To change direction

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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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The First Law is Counterintuitive
Aristotle firmly believed this. But Physics B
students know better!
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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 a force diagram representing all forces on
  the monkey

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Sample Problem

• Now the monkey hangs by both hands from two
  vines. Each of the monkeys arms are at a 45o
  from the vertical. Draw a force diagram
  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.
• Physicists define mass as inertia, which is the
  ability of a body to resist acceleration by a net
  force.
• Dr Julius Sumner Miller

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Sample Problem

• 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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Helicopters, Cafeterias, Airplanes and Busses

• Can a helicopter simply take off and let the
  earth bring its destination to it?
• Can you jump in the hall and let the cafeteria
  come to you?
• If luggage falls out of the overhead on the
  airplane wont it kill you?
• If you toss a ball up in the bus, will it hit the
  people in the back?
• Does a fly on the bus crash into the back when
  the bus takes off?

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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
• Pound (British system)
• 1 lb 1 slug ft /s2

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Working 2nd Law Problems

• Draw a force or 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 A exerts a force F on B, then B exerts a force
  of -F on 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?

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Sample Problem (similar to 17)

• 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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Newtons 2nd Law in 2-D

• The situation is more complicated when forces act
  in more than one dimension.
• You must still identify all forces and draw your
  force diagram.
• You then resolve your problem into an x-problem
  and a y-problem (remember projectile motion????).

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Forces in 2-D
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Forces in 2-D
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Forces in 2-D
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Forces in 2-D
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Forces in 2-D
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Sample Problem

• A surfer hangs ten, and accelerates down the
  sloping face of a wave. If the surfers
  acceleration is 3.50 m/s2 and friction can be
  ignored, what is the angle at which the face of
  the wave is inclined above the horizontal?

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Sample Problem

• How long will it take a 1.0 kg block initially at
  rest to slide down a frictionless 20.0 m long
  ramp that is at a 15o angle with the horizontal?

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Sample Problem

• An object acted on by three forces moves with
  constant velocity. One force acting on the object
  is in the positive x direction and has a
  magnitude of 6.5 N a second force has a
  magnitude of 4.4 N and points in the negative y
  direction. Find the direction and magnitude of
  the third force acting on the object.

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Mass and Weight

• Many people think mass and weight are the same
  thing. They are not.
• Mass is 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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Sample Problem

• A 5-kg salmon is hanging from a fish scale in an
  elevator. What is the salmons apparent weight
  when the elevator is
• a) at rest?
• b) moving upward and slowing at 3.2 m/s2?
• c) moving downward and speeding up at 3.2 m/s2?
• d) moving upward and speeding up at 3.2 m/s2?

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Announcements 12/7/2009
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Normal force

• The normal force is a force that keeps one object
  from penetrating into another object.
• The normal force is always perpendicular a
  surface.
• The normal exactly cancels out the components of
  all applied forces that are perpendicular to a
  surface.

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Normal force on flat surface

• The normal force is equal to the weight of an
  object for objects resting on horizontal
  surfaces.
• N W mg

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Normal force on ramp

• The normal force is perpendicular to angled ramps
  as well. Its always equal to the component of
  weight perpendicular to the surface.

N mgcos?
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Normal force not associated with weight.

• A normal force can exist that is totally
  unrelated to the weight of an object.

N applied force
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The normal force most often equals the weight of
an object
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but this is by no means always the case!
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Draw a free body diagram for the skier.
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Normal force is perpendicular to the surface.
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Gravitational force is straight down toward the
center of the earth.
W
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Free body diagram contains only two forces.
N
W
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Sample problem

• A 5.0-kg bag of potatoes sits on the bottom of a
  stationary shopping cart. Sketch a free-body
  diagram for the bag of potatoes. Now suppose the
  cart moves with a constant velocity. How does
  this affect the free-body diagram?

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Sample problem

• Find the normal force exerted on a 2.5-kg book
  resting on a surface inclined at 28o above the
  horizontal.
• If the angle of the incline is reduced, do you
  expect the normal force to increase, decrease, or
  stay the same?

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Sample problem

• A gardener mows a lawn with an old-fashioned push
  mower. The handle of the mower makes an angle of
  320 with the surface of the lawn. If a 249 N
  force is applied along the handle of the 21-kg
  mower, what is the normal force exerted by the
  lawn on the mower?

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Sample problem

• Larry pushes a 200 kg block on a frictionless
  floor at a 45o angle below the horizontal with a
  force of 150 N while Moe pulls the same block
  horizontally with a force of 120 N.
• a) Draw a free body diagram.
• b) What is the acceleration of the block?
• c) What is the normal force exerted on the block?