Newton's Laws of Motion

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Newton's Laws of Motion

• By Sandrine Colson-Inam, Ph.D

• References
• Conceptual Physics, Paul G. Hewitt, 10th edition,
  Addison Wesley publisher
• http//www.glenbrook.k12.il.us/gbssci/Phys/Class/v
  ectors/u3l2a.html

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Outline

• Intro
• Newton's First Law of Motion
• Forces and Free-Body Diagrams, Net Force
• Newton's Second Law of Motion
• Newton's Third Law of Motion
• Friction

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INTRODUCTION

• Newton's Laws of Motion are the most fundamental
  laws that explain the physical world around us.

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Newton's First Law of Motion

• An object at rest tends to stay at rest and an
  object in motion tends to stay in motion with the
  same speed and in the same direction unless acted
  upon by an unbalanced force.

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Inertia and Mass

• Inertia the resistance an object has to a change
  in its state of motion.
• The tendency of an object to resist changes in
  its state of motion varies with mass. Mass is
  that quantity which is solely dependent upon the
  inertia of an object.
• Inertia tendency of an object to resist changes
  in its velocity.
• Inertia tendency of an object to resist
  accelerations.

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Check your understanding

• 1. Imagine a place in the cosmos far from all
  gravitational and frictional influences. Suppose
  that you visit that place (just suppose) and
  throw a rock. The rock will
• a. gradually stop.
• b. continue in motion in the same direction at
  constant speed.
• 2. Ben Tooclose is being chased through the woods
  by a bull moose which he was attempting to
  photograph. The enormous mass of the bull moose
  is extremely intimidating. Yet, if Ben makes a
  zigzag pattern through the woods, he will be able
  to use the large mass of the moose to his own
  advantage. Explain this in terms of inertia and
  Newton's first law of motion.
• 3. The group of physics teachers are taking some
  time off for a little putt-putt golf. The 15th
  hole at the Hole-In-One Putt-Putt Golf Course has
  a large metal rim which putters must use to guide
  their ball towards the hole. Mr. S guides a golf
  ball around the metal rim When the ball leaves
  the rim, which path (1, 2, or 3) will the golf
  ball follow?

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Answers

• 1. According to Newton's first law, the rock will
  continue in motion in the same direction at
  constant speed.
• 2. The large mass of the bull moose means that
  the bull moose has a large inertia. Thus, Ben can
  more easily change his own state of motion (make
  quick changes in direction) while the moose has
  extreme difficulty changing its state of motion.
  Physics for better living!
• 3. The answer is 2. Once leaving the rim, the
  ball will follow an "inertial path" (i.e., a
  straight line). At the instant shown in the
  diagram, the ball is moving to the right once
  leaving the rim, there is no more unbalanced
  forces to change its state of motion. Paths 1 and
  3 both show the ball continually changing its
  direction once leaving the rim.

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About Force

• A force is a push or pull upon an object
  resulting from the object's interaction with
  another object. Whenever there is an interaction
  between two objects, there is a force upon each
  of the objects. When the interaction ceases, the
  two objects no longer experience the force.
• A force is a vector quantity.
• Forces only exist as a result of an interaction.
• Force is a quantity which is measured using the
  standard metric unit known as the Newton (N).
• For simplicity sake, all forces (interactions)
  between objects can be placed into two broad
  categories
• contact forces, and
• forces resulting from action-at-a-distance

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Contact Forces

• Those types of forces which result when the two
  interacting objects are perceived to be
  physically contacting each other. Examples of
  contact forces include frictional forces,
  tensional forces, normal forces, air resistance
  forces, and applied forces.
• Contact Forces
• Frictional Force
• Tension Force
• Normal Force
• Air Resistance Force
• Applied Force
• Spring Force

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Actions at Distance

• Those types of forces which result even when the
  two interacting objects are not in physical
  contact with each other, yet are able to exert a
  push or pull despite their physical separation.
  Examples of action-at-a-distance forces include
  gravitational forces. Electric forces are
  action-at-a-distance forces. magnetic forces are
  action-at-a-distance forces.

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Balanced Forces

• The book is said to be at equilibrium.

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Unbalanced Forces

• In this case, an unbalanced force acts upon the
  book to change its state of motion.

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Check your understanding

• Several of Luke's friends were watching the
  motion of the falling cat. Being "physics types",
  they began discussing the motion and made the
  following comments. Indicate whether each of the
  comments are correct or incorrect? Support your
  answers.
• a. Once the cat hits the water, the forces are
  balanced and the cat will stop.
• b. Upon hitting the water, the cat will
  accelerate upwards because the water applies an
  upward force.
• c. Upon hitting the water, the cat will bounce
  upwards due to the upwards force.

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Answers

• a. False.
• Once the cat hits the water, the forces are
  balanced (50 N down and 50 N up). However, an
  object in motion (such as the cat) will continue
  in motion at the same speed and in the same
  direction. When the cat strikes the water, it
  stops accelerating yet it does not stop moving.
• b. False.
• Once the cat hit the water, the forces are
  balanced (50 N down and 50 N up). The upward
  force of the water on the cat is balanced by the
  downward pull of gravity. The cat will continue
  in motion at constant speed.
• c. False.
• Once the cat hits the water, the forces are
  balanced (50 N down and 50 N up). The cat would
  only bounce upwards if the water applied an
  upward force greater than 50 N. As stated in the
  problem, the water applies only 50 N of upward
  force. Furthermore, the upward force would first
  contribute to slowing the cat down (an upward
  acceleration) before it could begin to actually
  move it upward.

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Types of Forces 1/2
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Types of Forces 2/2
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Confusion of Mass and Weight

• Many students of physics confuse weight with
  mass.
• The force of gravity acting upon an object is
  sometimes referred to as the weight of the
  object.
• The mass of an object refers to the amount of
  matter that is contained by the object.
• The weight of an object is the force of gravity
  acting upon that object. Mass is related to how
  much stuff is there and weight is related to the
  pull of the Earth (or any other planet) upon that
  stuff.

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Weight

• Weight is the magnitude of the force of gravity
  acting on an object.
• Weight Fgrav
• Fgrav mass x gravity

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Normal Force

• Normal Force is a force exerted by one object on
  another in a direction perpendicular to the
  surface of contact.
• The normal force is always perpendicular to the
  surface but is not always opposite the force of
  gravity.

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Normal Force at an angle

• On an angle, the normal force is calculated using
  Fn mgcos?.
• The ? is the angle of the ramp.

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FRICTION

• Friction opposes the applied force.
• The force of friction is proportional to the
  normal force.
• It is easier to push a chair across the floor at
  a constant speed than to push a heavy desk across
  the floor at the same speed.
• Because the desk is heavier than the chair, the
  desk experiences a greater normal force and
  therefore greater friction.
• Two types of friction Static and Kinetic

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STATIC FRICTION

• The resistive force that keeps objects from
  moving is called the force of static friction.
• Static Friction Fs
• As long as the object doesnt move, the static
  friction is always equal to the opposite in
  direction to the applied force.
• Fs -Fapplied
• When the applied force is as great as it can be
  without moving the object, the force of static
  friction reaches its maximum value, called Fsmax

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KINETIC FRICTION

• Once an object exceeds Fsmax, it begins to move.
• The resistive force that opposes the relative
  motion of two contacting surfaces that are moving
  is called the force of kinetic friction (Fk)?

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Coefficients of Friction

• Friction depends on the surfaces in contact.
• The quantity that expresses the dependence on
  frictional forces on the particular surfaces in
  contact is called the coefficient of friction.
• Coefficient of friction is represented by the
  symbol µ and pronounces mu.

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Coefficient of kinetic friction

• µk Fk/Fn
• Divide the Force of kinetic friction by the
  normal force

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Coefficient of static friction

• µs Fsmax / Fn
• Divide the maximum value of static friction by
  the normal force

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Finding Friction

• If the value of µ is known and the normal force
  is known, then the magnitude of the force of
  friction can be calculated.
• Ff µFn
• The kinetic friction is always less than or equal
  to the maximum static friction.
• Think about pushing a car that is sitting still
  or pushing a car that is already moving.
• The coefficient of kinetic friction is always
  less than or equal to the coefficient of static
  friction.

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Materials µs µk
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Air Resistance

• Whenever an object moves through a fluid medium,
  like air or water, the fluid provides a
  resistance to the motion.
• When an object falls through the air, its
  velocity increases until the air resistance
  balances the downward force of gravity.
• The object falls with a constant speed, called
  terminal speed.

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Check Your Understanding

• A 24 Kg crate initially at rest on a horizontal
  floor requires a 75 N horizontal force to set it
  into motion. Find the coefficient of static
  friction.
• Knowns?
• m 24 kg, Fsmax 75 N
• Unknown?
• Coefficient of static friction ?
• Equations?
• µs Fsmax / Fn and Fn mg

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ANSWER

• Fn 24(9.8) 235.2 N µs 75/235.2 .32

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More Practice

• A student moves a box down the hall with a rope
  by pulling with a force of 185 N at an angle of
  25 degrees to the horizontal. The box has a mass
  of 35 kg and a coefficient of kinetic friction
  of .27. What is the acceleration?
• On Board
• Draw it first and find the resultant force.
• Write knowns, unknowns, equations, and work it.

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ANSWER

• 2.7 m/s2 in the positive x direction

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Drawing Free-Body Diagrams

• Free-body diagrams are diagrams used to show the
  relative magnitude and direction of all forces
  acting upon an object in a given situation. A
  free-body diagram is a special example of the
  vector diagrams.

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Check your understanding

• A book is at rest on a table top. Diagram the
  forces acting on the book.
• A girl is suspended motionless from the ceiling
  by two ropes. Diagram the forces acting on the
  combination of girl and bar.
• An egg is free-falling from a nest in a tree.
  Neglect air resistance. Diagram the forces acting
  on the egg as it is falling.
• A flying squirrel is gliding (no wing flaps) from
  a tree to the ground at constant velocity.
  Consider air resistance. Diagram the forces
  acting on the squirrel.
• A rightward force is applied to a book in order
  to move it across a desk with a rightward
  acceleration. Consider frictional forces. Neglect
  air resistance. Diagram the forces acting on the
  book.

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Answers
3
1
2
5
4

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Determining the Net Force (or Unbalanced Force)?

• The unbalanced force refers to that force which
  does not become completely balanced (or canceled)
  by the other individual forces. If either all the
  vertical forces (up and down) do not cancel each
  other and/or all horizontal forces do not cancel
  each other, then an unbalanced force exists.
• The existence of an unbalanced force for a given
  situation can be quickly realized by looking at
  the free-body diagram for that situation.
• Free-body diagrams for three situations are shown
  below. Note that the actual magnitude of the
  individual forces are indicated on the diagram.
  What is the net force?

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Answer

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Summary for Net Force/Newton's 1st Law

• The net external force is the vector sum of all
  the forces acting on an object.
• A simple problem occurs when all forces act
  directly along the x and y axis. You would just
  add and subtract and use Pythagorean theorem.
• However, most of the time, we must use vector
  component method.
• Newtons 1st law states one condition must be
  true for equilibrium the net external force
  acting on a body in equilibrium must be equal to
  zero.

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Newtons 2nd Law of Motion

• Force is proportional to mass and acceleration.
• Force Mass x Acceleration (Fma)?
• a (Vf Vi)/ (tf ti)?

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Newtons 3rd Law of Motion

• Forces always exist in pairs.
• Every action has an equal and opposite reaction.

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Check your understanding

• The net external force on the propeller of a 3.2
  kg model airplane is 7 N forward. What is the
  acceleration of the plane?
• Knowns?
• m 3.2 kg, F 7 N
• Unknown?
• a ?
• Equation?
• Fma
• Answer?
• 7 3.2a, a 2.2 m/s2 Forward (vector need
  direction)?

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THE END!