Chapter 6 Forces

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Chapter 6 Forces

• 6.1 Force and Motion
• A object that experiences a push or a pull has a
  force exerted on it.
• The object is called the system
• The world around the object that exerts forces on
  it is called the environment.
• Force (F)is a vector quantity that has magnitude
  (F) and direction.

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The Two Types of Forces

• CONTACT FORCE acts on an object only by touching
  it.
• LONG RANGE FORCE is exerted without contact. For
  example the force of gravity is an attractive
  force that exists between all objects without
  touching, Electric Forces and Magnetic forces.

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Newtons Second Law of Motion

• The acceleration of an object as produced by a
  net force is directly proportional to the
  magnitude of the net force, in the same direction
  as the net force, and inversely proportional to
  the mass of the object being accelerated.
• Fnet m a
• a Fnet/m
• The unit of force in the SI unit is the Newton
• 1N 1kg.m/s2

Net force Sum of all the forces on an object
.
.
Fnet
Fnet
Fnet
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Newton's second law of motion pertains to the
behavior of objects for which all existing forces
are not balanced.As the net force increases, so
will the object's acceleration. However, as the
mass of the object increases, its acceleration
will decrease
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• Practice
• A net force of 16 N causes a mass to accelerate
  at a rate of 5 m/s2. Determine the mass.
• Two forces, 225 N and 165 N are exerted in
  opposite directions on a crate, what is the net
  horizontal force on the crate? Indicate the
  direction of the net force.
• The 225-N force is exerted on the crate toward
  the north and the 165-N force is toward the east.
  Find the magnitude and direction of the net
  force.

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Newtons First Law of Motion or Law of Inertia

• An object that is at rest will remain at rest or
  an object that is moving will continue to move in
  a straight line with constant speed, if and only
  if the net force acting on that object is zero.

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• Inertia is the tendency of an object to resist
  change.
• Equilibrium if the net force on an object is
  zero, then the object is in equilibrium.

collision of a motorcycle with a wall
The person is at equilibrium
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6.2 Using Newtons Laws

• The second law is not true for velocities close
  to the speed of light, nor for objects the size
  of atoms. Einsteins theory of relativity and
  quantum mechanics should be used instead.
• The weight (or gravitational) force is
• Fg mg (g is the acceleration the object would
  have if it was falling freely)
• Weights vary from planet to planet, but masses
  will not change.

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The forces acting upon the sled from point B to
point C would be the normal force (the snow
pushing up on the sled) and the gravity force

• Without friction or air resistance to slow it
  down,
• the sled would continue in motion with the same
• speed and in the same direction.

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• Example 1 Weighing Yourself in an Accelerating
  Elevator (pg 128)
• Your mass is 75 kg. You stand on a bathroom scale
  in an elevator. Going up! Starting from rest,
  the elevator accelerates at 2.0 m/s2 for 2s, then
  continues at a constant speed. What is the scale
  reading during the acceleration? Is it larger
  than, equal to, or less than the scale reading
  when the elevator is at rest?
• Weightlessness doesnt mean that your weight is
  zero, but that there are no contact forces
  pushing up on you. It means that you apparent
  weight is zero.

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Example 2Lifting a bucket

• A 50-kg bucket is being lifted by a rope. The
  rope is guaranteed not to break if the tension is
  500 N or less. The bucket started at rest, and
  after being lifted 3.0 m, it is moving at 3.0
  m/s. Assuming that the acceleration is constant,
  is the rope in danger of breaking?

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The Friction Force

• Static Friction Force is exerted on one surface
  by the other when there is no relative motion
  between the two surfaces.
• Kinetic Frictional Force (Ff,kinetic) is the
  force exerted on surface by the other when the
  surfaces are in relative motion.
• Friction depends on the surfaces in contact, but
  not on the area of the surfaces nor the speed of
  their relative motion.
• Ff,kinetic ?K FN
• Where ?K is proportionality constant called the
  kinetic coefficient of friction.
• FN is the normal force
• Static Friction Force 0? Ff,static ? ?s FN? is
  the maximum static friction force that must by
  balanced before motion can begin.

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Typical Coefficients of Friction
Practice The net force is the vector sum of all
the individual forces 1. You push a 25-kg
wooden box across a wooden floor at a constant
speed of 1.0 m/s. How much force do you exert on
the box. 2. if the force you exert on the box is
doubled, what is the resulting acceleration of
the box?
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Practice 1

• An applied force of 50 N is used to accelerate an
  object to the right across a frictional surface.
  The object encounters 10 N of friction. Use the
  diagram to determine the normal force, the net
  force, the mass, and the acceleration of the
  object. (Neglect air resistance.)

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Practice 2

• An applied force of 20 N is used to accelerate an
  object to the right across a frictional surface.
  The object encounters 10 N of friction. Use the
  diagram to determine the normal force, the net
  force, the coefficient of friction (µ) between
  the object and the surface, the mass, and the
  acceleration of the object. (Neglect air
  resistance.)

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Practice 3

• A 5-kg object is sliding to the right and
  encountering a friction force which slows it
  down. The coefficient of friction (µ) between the
  object and the surface is 0.1. Determine the
  force of gravity, the normal force, the force of
  friction, the net force, and the acceleration.
  (Neglect air resistance.)

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Falling with Air Resistance

• As an object falls through air, it usually
  encounters some degree of air resistance. Air
  resistance is the result of collisions of the
  object's leading surface with air molecules.
• Air resistance encountered by an object depends
  upon the speed of the object and the
  cross-sectional area of the object.
• Increased speeds result in an increased amount of
  air resistance. Increased cross-sectional areas
  result in an increased amount of air resistance.

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Terminal Velocity

• The constant velocity that is reached when the
  drag force equals the force of gravity is called
  the terminal velocity.
• Object Terminal velocity
• Tennis ball in air 9 m/s
• Basketball 20 m/s
• Baseball 42 m/s

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The feather quickly reaches a balance of forces
and thus a zero acceleration (i.e., terminal
velocity). On the other hand, the elephant never
does reach a terminal velocity during its fall
the forces never do become completely balanced
and so there is still an acceleration. If given
enough time, the elephant would finally
accelerate to high enough speeds to encounter a
large enough upward air resistance force in order
to achieve a terminal velocity.
an elephant and a feather are dropped off a very
tall building from the same height at the same
time.
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As the skydiver falls, he encounters the force of
air resistance. The amount of air resistance
depends upon the speed of the skydiver, and the
cross-sectional area of the skydiver. A skydiver
in the spread eagle position (or with open
parachute) encounter more air resistance than a
skydiver who assumes the tuck position or who
falls feet (or head) first. The greater
cross-sectional area of a skydiver in the spread
eagle position leads to a greater air resistance
and a tendency to reach a slower terminal
velocity
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Periodic Motion

• A plucked guitar string continues to move rapidly
  back and forth in simple harmonic motion.
• Whenever the object is pulled away from its
  equilibrium position, the net force becomes
  nonzero and pulls it back toward equilibrium. If
  the force that restores the object to its
  equilibrium position is directly proportional to
  the displacement of the object, the motion that
  results is called simple harmonic motion.
• Simple harmonic motion is described by two
  quantities The period is the time needed to
  repeat one complete cycle of motion, and
  amplitude is the maximum distance the object
  moves from equilibrium

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• Other example of harmonic motion is pendulum, a
  metal block bobbing up and down on a spring. The
  swing of the pendulum demonstrates simple
  harmonic motion.
• The period of a pendulum (T) is given by the
  following equation
• This formula is valid only for small angles (less
  than 15?)
• l is the length of the pendulum in meters and g
  is the acceleration due to gravity.
• Period depends only upon the length of the
  pendulum and the acceleration due to gravity, not
  on the mass of the bob or the amplitude of
  oscillation.

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A simple pendulum consists of a string, cord, or
wire that allows a suspended mass (called bob) to
swing back and forth. The longer the pendulum,
the longer is the time of its swing
pendulum
Pendulum animation
http//online.cctt.org/physicslab/content/applets/
JavaPhysMath/java/pend1/index.html
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The forces acting on the mass are gravity and the
tension in the string.  Only gravity provides a
restoring force towards the equilibrium
position.  The magnitude of this force Fnet FT
Fg mgsin?
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6.3 Interaction Forces

• Newtons Third Law For every action, there is an
  equal and opposite reaction."
• In every interaction, there is a pair of forces
  acting on the two interacting objects. The size
  of the force on the first object equals in size
  and opposite to the direction of the force on the
  second object.

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Action-reaction force pairs make it possible for
birds to fly.

• A bird flies by use of its wings. The wings of a
  bird push air downwards. In turn, the air reacts
  by pushing the bird upwards. The size of the
  force on the air equals the size of the force on
  the bird the direction of the force on the air
  (downwards) is opposite to the direction of the
  force on the bird (upwards)