Chapter 4- Newton�s laws of Motion by 594F8exy

VIEWS: 3 PAGES: 30

									     Chapter 4-
Newton’s laws of Motion
• Kinematics
  – the study of how objects move
• Dynamics
  – the study of why objects move
• Force
  – a push or a pull; symbol is F; SI unit is the
    Newton, or N
  – One Newton is the force necessary to cause a
    one kilogram mass to accelerate at the rate of
    1 m/s2
  – 1 N = 1 kg m/s2
• Statics
  – Statics is the study of the forces acting on and within
    structures that are in equilibrium. Statics means that
    the body is at rest.
• Conditions for static equilibrium
  – The sum of the forces acting on the body must add up
    to zero. (Remember, if a force component points in
    the negative x, y, or z direction, it is assigned a
    negative value.
      SFx = 0
      SFy = 0
      SFz = 0
  – The sum of all the torques acting on the object
    (calculated along any axis) must be zero. St = 0
• Four basic forces:
  – Gravitational force -an attractive force that exists
    between all objects with mass; an object with mass
    attracts another object with mass; the magnitude of
    the force is directly proportional to the masses of the
    two objects and inversely proportional to the square
    of the distance between the two objects. Stated
    mathematically:
  – Where G is the universal gravitational constant
    (meaning it has the same value throughout the
    universe), m1 and m2 are the masses of the objects
    in kilograms, and d is the distance between them in
    meters
  – G = 6.67 x 10-11 N m2 / kg2
  – Cavendish found the universal gravitation constant,
    allowing the earth to be "weighed."
  – Check out Black Holes, Gravitational Waves, and
    Escape Velocity under Advanced
      Newton’s Laws of Motion:
• Newton’s First Law – an object in motion remains in
  motion at constant speed and moving in a straight line
  and an object at rest remains at rest unless acted upon
  by an outside force; called the law of inertia.
• You do not need a force to keep a body moving at a
  constant velocity. Also, a body at rest in one frame of
  reference could be moving at constant speed relative to
  another frame of reference.
   – Equilibrium
        an object is in equilibrium when its velocity is zero or its
     velocity is constant
   – Inertia
        a measure of how an object resists changes in motion; it is a
     measure of an object’s mass
Electromagnetic force
an attractive or a repulsive force between
  charged particles; when charged particles
  are in motion, they produce magnetic
  forces on each other; the magnitude of the
  force is directly proportional to the
  magnitudes of the charges and inversely
  proportional to the square of the distance
  between the two charges
Strong nuclear force
an attractive force between the particles in
  the nucleus; it is the strongest of the four
  forces, but only acts over very small
  distances (does not obey inverse square
  law for distances)
Weak nuclear force
a force involved in the radioactive decay of
  some nuclei (in the 1960’s, Weinberg
  theorized the existence of the electroweak
  force, combing the electromagnetic and
  the weak nuclear force)
• Newton’s Second Law – An unbalanced force
  (or net force, S) causes an object to accelerate;
  this acceleration is directly proportional to the
  unbalanced force and inversely proportional to
  the object’s mass; called the law of acceleration
  – a = SF / m or S F = m a
  – Equilibrium
     • an object is in equilibrium when no unbalanced force (or net
       force) acts on it
  – Mass
     • A measure of the inertia of a body. (SI unit is the kilogram);
       Mass is a property of a body itself. It should not be confused
       with weight, which is a force (the force of gravity acting on an
       object).
  – An excellent Newton's Second Law Applet that allows
    you to conduct a simulated Second Law experiment.
• Newton’s Third Law – When one object
  exerts a force on another object, the
  second object exerts a force on the first
  object that is equal in magnitude, but
  opposite in direction; for every action,
  there is an equal, but opposite reaction;
  called the law of action-reaction
• A good site that tests your understanding
  of action/reaction pairs of forces
          Advanced Look at the 3rd Law
• Where do forces come from? A force is exerted
  on an object and is exerted by another object.
  The "action" force acts on a different body than a
  "reaction" force. To experience the 3rd law, push
  on a desk with your hand. Your hand's shape is
  distorted, showing that a force is acting on it.
  You can feel the force that the desk exerts on
  your hand. The harder that you push on the
  desk, the harder that the desk pushes back on
  your hand. You only feel the forces exerted on
  you; you do not feel the forces that you exert on
  something else.
     Applications of Newton's Laws
• Free-body diagrams represent forces (their magnitudes
  and their directions). In a free-body diagram, all forces
  are represented using arrows. The direction of motion is
  considered positive (usually assigned the right direction);
  the direction opposite the motion is negative (typically
  assigned the left direction); up is positive and down is
  negative
• If the sum of all the horizontal forces acting on an object
  is zero, then the object is in equilibrium horizontally. If
  the sum of all the vertical forces acting on an object is
  zero, then the object is in equilibrium vertically. If the
  sum of the forces in a direction is not zero, then the
  forces in that direction are not balanced. We say that an
  unbalanced force acts in that direction. An object can be
  in equilibrium in one direction and not in equilibrium in
  another direction.
     Forces that act horizontally are
 independent of forces that act vertically.
To work free-body diagram problems:
• Draw the free-body diagram labeling all forces (their magnitudes and
   directions). Remember to use the appropriate positive and negative
   signs.
• Add all the forces in the vertical direction. If the sum is zero, the
   forces are balanced, and there is no acceleration. If the sum is not
   zero, the forces are unbalanced, and there is acceleration in the
   vertical direction. This sum equals the product of mass times
   acceleration.
• Add all the forces in the horizontal direction. If the sum is zero, the
   forces are balanced, and there is no acceleration. If the sum is not
   zero, the forces are unbalanced, and there is acceleration in the
   horizontal direction. This sum equals the product of mass times
   acceleration.
Common types of forces involved in motion:
1. Weight – a measure of the gravitational force
  acting on an object; direction is down (toward
  the earth’s center); symbol is Fg
  – Fg = m g
  – Where Fg is the weight of the object in Newtons, m is
    the mass of the object in kilograms, and g is the
    acceleration due to gravity.
  – Letting the gravitational force equal represent the
    weight of an object yields,
    Fg = (G m1 m2) / d2
    or m1 g = (G m1 M) / d2
    or g = (G M) / d2
    where M is the mass of the earth
     Advanced Look at Weight
It is easy to see that the force of gravity acts on an
  object when it is falling. When an object is at rest
  on a surface, the gravitational force still
  continues to act. According to the second law,
  only a net force would cause the motion of the
  object to change. Since the object remains at
  rest, the net force acting on it must be zero.
  Another force (the normal force) balances the
  gravitational force. This is not an example of an
  action/reaction pair of forces! Both forces
  (gravitational and normal) act on the same
  object. Action/reaction pairs of forces act on
  different objects.
              2. Normal force
the force exerted by a surface to support an object; symbol
   is FN; direction is always upward; when an object rests
   on a horizontal surface, the normal force equals the
   object’s weight; when an object is being pushed or pulled
   by a horizontal force, the normal force equals the
   object’s weight. When a push or a pull is something
   other than horizontal, a free-body diagram is used to
   determine the normal force (taking into account the
   vertical component of the push or the pull). A normal
   force is a "response" force. In other words, a surface
   responds to a weight resting on it by acting to oppose it
   to the extent necessary to "cancel out" these forces. For
   our purposes, normal forces only exist on a surface (if
   the object is in the air, there is no normal force). The
   normal force is not an action/reaction pair of forces with
   the weight.
Advanced Look at the Normal Force
Returning to our weight example ... An
 upward force (the normal force) is exerted
 by the table on the object. The reaction to
 this is the downward force exerted by the
 object on the table. Since these forces act
 on different objects, they are
 action/reaction forces described by
 Newton's Third Law. What is the reaction
 force acting in response to the
 gravitational force? The object exerts a
 gravitational force on the earth!
  Advanced Look at these forces
     in terms of the third law
The object rests on the table and is in the Earth's
  gravitational field. The Earth exerts a downward
  gravitational force on the object equal to the object's
  weight. The object exerts an equal gravitational force on
  the Earth. The downward gravitational force exerted by
  the Earth and the upward gravitational force exerted by
  the object represent an action/reaction pair of forces.
  The table exerts an upward force on the object. The
  object exerts an equal downward force on the table.
  These also represent an action/reaction pair of forces.
  An action/reaction pair of forces never act on the same
  object. Action/reaction pair of forces represent the mutal
  interaction of two bodies.
     Famous Physics Puzzle:
A man hitches a horse to a cart. The horse
  refuses to pull the cart, telling the man,
  "No matter how hard I pull, the cart pulls
  back with an equal force, and it will be
  impossible for me to ever pull the cart!"
             Answer to puzzle:
• The horse exerts a force on the cart (action) and the cart
  exerts an equal and opposite force on the horse
  (reaction). The horse exerts a force on the ground
  (action) and the ground exerts an equal and opposite
  force back on the horse (reaction). There are two sets of
  action forces acting (for the horse). If the reaction force
  exerted by the ground on the horse is larger than the
  reaction force exerted by the sled on the horse, the
  horse will move forward. The cart will move forward
  when the force exerted by it by the horse is greater than
  the frictional force between the cart and the ground.
  Remember, there are two sets of forces acting on the
  cart: the force exerted by the horse on the cart
  (action)/the force exerted by the cart on the horse
  (reaction) and the force exerted by the cart on the
  ground (action)/the frictional force exerted by the ground
  on the cart (reaction).
                        Friction
• a force that usually opposes the motion of an
  object; symbol is Ff; direction is negative; friction
  is an electromagnetic force between surface
  atoms
• Characteristics of friction:
   – Friction acts parallel to the surfaces in contact
   – Friction usually acts opposite the direction of the
     motion. Friction opposes the applied force.
   – Friction depends upon the types of surfaces in
     contact (All surfaces are described by a coefficient of
     friction, m , which is a characteristic of that surface. m
     has no units.)
   – Friction is independent of the surface area in
     contact.(for hard surfaces)
             3. Types of friction:
• Starting friction (Static Friction) opposes the
  beginning of motion of an object; is always greater than
  sliding friction
• Advanced Look at Static Friction If an object is resting
  on a surface, there is no frictional force because there is
  no horizontal force. A person now pushes horizontally on
  the object, but not hard enough to make it move. The
  force of static friction exerted by the surface on the
  object prevents it from moving. The object does not
  move until you push hard enough (Fmax)to overcome
  static friction.
   – Fmax = msFN where ms is the coefficient of static friction.
Sliding friction (Kinetic Friction)
   – opposes the motion of an object
• Friction can be described mathematically:
   – Ff = m FN
• Advanced Look at Kinetic Friction When a
  body is in motion along a rough surface, the
  force of kinetic friction acts opposite the direction
  of the motion.
   – Ff = mkFN In AP Physics, we will refer to a smooth
     surface as one without friction and a rough surface as
     one with friction.
   – Interactive Frictional Force Site
4. Applied force – the push or pull that
   "you" use to move an object; symbol is
   Fapp
5. Unbalanced force (or net force ) – the
   sum of all the forces in a direction; it is
   what causes the acceleration of an
   object
         SF=ma
6. Tension - a force usually associated
  with a rope or a cable; it is a "response"
  force. In other words, if one pulls on a
  rope, the rope "fights back" by resisting
  being stretched. If the rope has negligible
  mass, the force exerted at one end is
  transmitted undiminished to each adjacent
  piece of rope along its entire length to the
  other end. Note: ropes, cords, and string
  can only pull. They cannot push because
  they bend.
• AP example
• Two boxes, mass 10 kg and mass 20 kg, are connected by a
  massless string on a smooth surface. A horizontal force, Fapp pulls
  the 20 kg box. How would you find the acceleration of each and the
  tension in the cord? First, draw a free diagram for each box. Four
  forces are involved in the free body diagram for the 20 kg box: Fapp
  pulls the box horizontally to the right, the Tension (T)pulls to the left,
  the normal force acts up, and the gravitational force (the weight)
  acts down. Only the tension and the applied force act parallel to the
  motion. Apply Newton's second law to the 20 kg box: SF = Fapp - T
  = (20 kg)a. Draw a free body diagram for the 10 kg box. Three
  forces are involved in the free body diagram for the 10 kg box: the
  Tension (T)pulls to the right, the normal force acts up, and the
  gravitational force (the weight) acts down. (Since we said the
  surface was smooth, there is no friction). Only the tension acts
  parallel to the motion. Apply Newton's second law to the 10 kg box:
  SF = T = (10 kg)a. Since the boxes are connected, the two boxes
  have the same acceleration. We "add" the two equations and get
  Fapp =(30 kg)a. Once the acceleration is known, you can solve for
  the tension.
7. Forces involved in springs: Most
  mass/spring systems obey a simple
  relationship between force and displacement
  (x), known as Hooke's Law. The restoring
  force (F) is proportional to the displacement
  (x). The spring constant (k) is the
  proportionality constant. Felastic = -kx
Forces on an Inclined Plane
– The normal force exerted by the incline to
  support the weight, W. The parallel force is
  the part of the object's weight that tends to
  make it slide down the incline.
   • FN = W cos q
   • FP = W sin q
Inclined plane problems are easier to work if
  one chooses the direction parallel to the
  incline surface as your x-axis. The y-axis
  is then perpendicular to the incline
  surface. If an object slides down an
  incline, three forces act on it: the normal
  force, the frictional force, and the
  gravitational force (or the object's weight).
• The gravitational force
  can be resolved into its
  x and y components.
  Its x component is
  called the parallel
  force. Its y component
  is equal in magnitude
  and opposite in
  direction to the normal
  force exerted by the
  surface on the object.

								
To top