Forces

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Forces the Laws of Motion

• Chapter 4

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4.1 Changes in Motion

• Objectives
• Explain how force affects the motion of an object
• Distinguish between contact forces and field
  forces
• Interpret and construct free-body diagrams

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Force

• What is a force?
• A push or pull that can change the motion of an
  object
• What is the SI unit for force?
• The newton (N)
• One newton is the force required to accelerate a
  1-kg mass at 1 m/s2
• 1N 1 kgm/s2 1N 0.225 lbf
• 1lbf 4.448 N

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Forces act through contact or at a distance

• Contact forces
• Forces that affect an object through physical
  contact with another object
• Example a baseball bat hitting a baseball
• Field forces
• Forces that affect an object without physical
  contact
• Examples gravitational, magnetic, and
  electrostatic forces

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Field Theory

• Explains how forces can affect an object without
  physical contact
• Explanation of field forces
• An object affects the space surrounding it so
  that a force is exerted on other objects in that
  space.
• The field is the region of space in which the
  force is exerted
• Example magnetic field

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Electrostatic Forces

• Example of a field force
• Stream of ethanol is attracted to an electrically
  charged probe

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Force Diagrams

• Force is a vector
• Force diagrams
• Diagram the objects involved in a situation and
  the forces acting on the objects
• Free-body diagrams
• Diagram the forces acting on a single object
• i.e. diagram the object free from influence of
  other objects and their forces

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Representing Forces

• Force is a vector
• Free-body diagrams illustrate forces acting on an
  object isolated from its surroundings

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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
• Represent object as a box with forces originating
  from center of box

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Example of a Free-Body Diagram
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Common Forces in Force Diagrams

• Applied force Fapp
• Weight Fg (mg)
• Normal force FN - to surface
• Friction Ff
• Air resistance Fair
• Tension Ftens
• Spring force Fspring

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Force Equilibrium

• Force equilibrium
• All forces cancel
• No net force acting on an object
• Can an object in force equilibrium be in motion?

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4.2 Newtons First LawLaw of Inertia

• Galileo noted that things tend to slide further
  on smoother surfaces
• Concluded that an object would slide forever on a
  perfectly smooth surface in the absence of any
  applied force
• This led to Newtons First Law of Motion

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Newtons First Law of MotionInertia

• An object at rest remains at rest, and an object
  in motion continues in motion in a straight line,
  with a constant velocity, unless acted upon by a
  net external force
• Inertia the tendency of an object to maintain
  its state of motion
• When net force on an object is zero, acceleration
  is zero (?v/?t 0)

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Newtons First Law of Motion

• An object at rest remains at rest, and an object
  in motion continues in motion with a constant
  velocity unless acted upon by a net external
  force
• A net force is required to change the state of
  motion of an object
• Net external force
• Resultant force produced from combination of all
  forces acting on an object

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Net External Force

• Typical external forces
• gravity (weight mg) 22N
• normal force - to surface 18N
• push/pull 0
• friction 11N
• A book is left on a drafting table with an
  incline of 35
• Identify forces acting on the book calculate
  Fnet
• (sum of x y components)

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Forces Acting on Inclined Planes

1. FN, normal force, surface acting on object
2. Fg, weight mg
3. Fgx, component of g, to surface
4. Fgy, component of g - surface
5. Ff, friction

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Calculating Net External Force

• Identify variables select equation
• Draw free-body diagram and apply coordinate
  system
• Calculate x y components of all vectors
• Calculate x y components of the resultant Fnet
  (Fx, Fy)
• Calculate net external force (Fnet)

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Inertia

• Inertia is tendency of an object to maintain its
  state of motion unless acted upon by a net force
• Mass is a measurement of inertia
• ? mass ? ? inertia
• As the same speed, a rolling car is more
  difficult to stop than a rolling basketball

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Equilibrium

• The state of a body in which there is no change
  in motion
• Net force acting on a body is zero

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4.3 Newtons 2nd 3rd LawsLearning objectives

1. Describe acceleration of an object in terms of
   its mass and the net external force acting on it
2. Predict direction magnitude of acceleration
   caused by a known net external force
3. Identify action-reaction force pairs
4. Explain why action-reaction pairs do not result
   in equilibrium

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Newtons 2nd Law

• The acceleration of an object is directly
  proportional to the net external force acting on
  the object and inversely proportional to the mass
  of the object
• a SFnet /m , where S means sum of
• SFnet ma

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Conceptual Question

• A grain truck filled with soy beans accelerates
  along the highway at 0.50 m/s2. If the driving
  force on the truck remains the same, what happens
  to the acceleration of the truck if soybeans leak
  from it at a constant rate?
• Answer The loss of soy beans is a decrease in
  mass. Since a SFnet /m , acceleration
  increases.

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Newtons 3rd Law

• "For every action, there is an equal and opposite
  reaction." equal magnitude and opposite direction
  
• In every interaction, there is a pair of forces
  acting on the two interacting objects.
• Action-reaction force pairs equal in magnitude,
  but opposite in direction.

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Action-Reaction Force Pairs

• Since force pairs are equal in magnitude, but
  opposite in direction, why do they not result in
  equilibrium?
• Because they act on different objects.
• If equal but opposite forces acted on the same
  object, there would be equilibrium, i.e. no net
  force.

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4.4 Everyday Forces

• Weight
• Force of gravity acting on a mass
• Fg mg W mg Fw mg
• Normal Force
• contact force exerted by one object on another
  in a direction - surface of contact
• Friction
• contact force that opposes motion.
• opposes applied force

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Weight Normal Force

• Fg mg
• Always - surface of earth
• Directed toward center of earth
• FN Fgcos (?)
• Always - surface of contact
• Always opposes Fg

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Identify Forces Acting on Inclined Planes

1. FN, normal force, surface acting on object
2. Fg, weight mg
3. Fgx, component of g, to surface
4. Fgy, component of g - surface
5. Ff, friction

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Force of Friction

• Ff opposes applied force
• Static friction Ffs .
• force exerted by environment on motionless body
  to resist applied force
• Kinetic friction Ffk .
• force exerted by environment on moving object
  to resist applied force
• Ffs gt Ffk
• Depends on surfaces in contact.
• Types and smoothness
• Proportional to FN

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Static vs. Kinetic Friction
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Relationship of Ff and Fn

• Ff is proportional to FN
• Proportionality constant is the coefficient of
  friction, µ
• µ Ff / FN
• Depends on types of surfaces in contact
• Depends on static or kinetic friction
• µs Fs / FN µk Fk / FN

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Problem 4C

• A crate of mass 24 kg is set in motion on a
  horizontal surface with a horizontal force of 75
  N. Find the coefficient of static friction, µs
• µs Fs / FN
• Fs / mg
• 75 N / (24 kg x 9.81 m/s2)
• 0.32

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Coefficients of Friction(Approximate)
Materials µs µk Materials µs µk
Steel on steel 0.74 0.57 Waxed wood on wet snow 0.14 0.10
Aluminum on steel 0.61 0.47 Waxed wood on dry snow ---- 0.04
Rubber on dry concrete 1.00 0.80 Metal on metal (lubricated) 0.15 0.06
Rubber on wet concrete ---- 0.50 Ice on ice 0.10 0.03
Wood on wood 0.40 0.20 Teflon on Teflon 0.04 0.04
Glass on glass 0.90 0.40 Synovial joints in humans 0.01 0.003
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Role of Surface in Friction

• Static friction increases with increasing force
  until overcome
• Kinetic friction is less than the maximum static
  friction

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Frictional Applied Force
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