Chapter%206%20Force%20and%20Motion%20II

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Chapter 6 Force and Motion II

•  6.2. Friction     
•  6.3. Properties of Friction     
•  6.4. The Drag Force and Terminal Speed      
• 6.5. Uniform Circular Motion      

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The Friction Force

• There are two types of friction forces
• Kinetic Friction Forces
• Static Friction Forces

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Kinetic Friction Forces

• An object is experiencing a kinetic friction
  force when the object is moving relative to a
  surface.

• Kinetic friction forces is linearly proportional
  to the normal force.
• The slope of Kinetic friction forces vs. the
  normal force is changing for different surfaces.

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Kinetic Friction Forces

• The magnitude of the kinetic friction force can
  be expressed as

The slope µkin is called the coefficient of
kinetic friction and N is the magnitude of the
normal force.
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Question

• A person has a choice of either pushing or
  pulling a sled at a constant velocity, as the
  drawing illustrates. Friction is present. If the
  angle ? is the same in both cases, does it
  require less force to push or to pull? Account
  for your answer.

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Example 1  Sled Riding

• A sled is traveling at 4.00 m/s along a
  horizontal stretch of snow, as Figure
  illustrates. The coefficient of kinetic friction
  is µk0.0500. How far does the sled go before
  stopping?

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Static Friction Forces

• An object is experiencing a static friction
  force when the object intend to move (but not
  move yet) relative to the surface.

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Properties of Static Friction Forces

• The magnitude fs of the static frictional force
  can have any value from zero up to a maximum
  value of depending on the applied force.
• The maximum static friction is

The µs is the coefficient of static friction,
and N is the magnitude of the normal force.

• The coefficient of static friction is usually
  larger than the coefficient of kinetic friction

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Example 2  The Force Needed to Start a Sled Moving

• A sled is resting on a horizontal patch of
  snow, and the coefficient of static friction is
  µs0.350. The sled and its rider have a total
  mass of 38.0 kg. What is the magnitude of the
  maximum horizontal force that can be applied to
  the sled before it just begins to move?

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Example 3

• A House on a Hill A house is built on the top
  of a hill with a nearby 45 slope (Fig. 6-42). An
  engineering study indicates that the slope angle
  should be reduced because the top layers of soil
  along the slope might slip past the lower layers.
  If the static coefficient of friction between two
  such layers is 0.5, what is the least angle f
  through which the present slope should be reduced
  to prevent slippage?

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Example 4

• Block on a Slab A 40 kg slab rests on a
  frictionless floor. A 10 kg block rests on top of
  the slab (Fig. 6-58). The coefficient of static
  friction between the block and the slab is 0.60,
  whereas their kinetic friction coefficient is
  0.40. The 10 kg block is pulled by a horizontal
  force with a magnitude of 100 N. What are the
  resulting accelerations of (a) the block and (b)
  the slab?

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Example 5

• Body A in Fig. weighs 102 N, and body B
  weighs 32 N. The coefficients of friction between
  A and the incline are and . Angle is 40.
  Let the positive direction of an x axis be up the
  incline. In unit-vector notation, what is the
  acceleration of A if A is initially (a) at rest,
  (b) moving up the incline, and (c) moving down
  the incline?

    




                                                                                    
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Drag Force

• The magnitude of the drag force is related to
  the relative speed

• C is drag coefficient
• ? is the air density (mass per volume)
• A is the effective cross-sectional area of the
  body (the area of a cross section taken
  perpendicular to the velocity ).

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Terminal Speed

• When sky diving, a terminal speed will be
  reached when drag force is equal to the gravity.

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Centripetal Force
A centripetal force accelerates a body by
changing the direction of the bodys velocity
without changing the bodys speed.



Important a centripetal force is not a special
type of force.
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Sample Problem 6

• In a 1901 circus performance, Allo Dare
  Devil Diavolo introduced the stunt of riding a
  bicycle in a loop-the-loop (Fig. 6-10a). Assuming
  that the loop is a circle with radius , what is
  the least speed v Diavolo could have at the top
  of the loop to remain in contact with it there?

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Sample Problem 7

• Curved portions of highways are always banked
  (tilted) to prevent cars from sliding off the
  highway. When a highway is dry, the frictional
  force between the tires and the road surface may
  be enough to prevent sliding. When the highway is
  wet, however, the frictional force may be
  negligible, and banking is then essential. Figure
  6-13a represents a car of mass m as it moves at a
  constant speed v of 20 m/s around a banked
  circular track of radius R190m . (It is a normal
  car, rather than a race car, which means any
  vertical force from the passing air is
  negligible.) If the frictional force from the
  track is negligible, what bank angle ? prevents
  sliding?

    


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Conceptual Questions

•  Suppose that the coefficients of static and
  kinetic friction have values such that µs2.0µk
  for a crate in contact with a cement floor. Does
  this mean that the magnitude of the static
  frictional force acting on the crate at rest
  would always be twice the magnitude of the
  kinetic frictional force acting on the moving
  crate? Give your reasoning.
• A box rests on the floor of an elevator. Because
  of static friction, a force is required to start
  the box sliding across the floor when the
  elevator is (a) stationary, (b) accelerating
  upward, and (c) accelerating downward. Rank the
  forces required in these three situations in
  ascending orderthat is, smallest first. Explain.

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• During the final stages of descent, a sky diver
  with an open parachute approaches the ground with
  a constant velocity. The wind does not blow him
  from side to side. Is the sky diver in
  equilibrium and, if so, what forces are
  responsible for the equilibrium?