Chapter 6: Work and Energy

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Chapter 6 Work and Energy

• Christopher Chui

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Work Done by a Constant Force

• Work is defined to be the product of the
  magnitude of the displacement times the component
  of the force parallel to the displacement, or W
  Fd cos q
• Unit for work is joule, or 1 J 1 N-m
• In British units, work is in ft-lb.
• 1 J 107 ergs 0.7376 ft-lb.
• A force can be exerted on an object and yet do NO
  work

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Problem Solving for Work

• Choose an xy coordinate system // to the plane
• Draw a free body diagram showing all forces
• Determine any unknown force
• Find the work done by a specific force on the
  body by using W Fd cos q
• Find the net work done on the body either adding
  algebraically work done by each force, or find
  the net force on the object, and use Wnet Fnetd
  cos q

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Translational Kinetic Energy

• KE ½ mv2
• Work-Energy Principle Wnet DKE
• The net work done on an object is equal to the
  change in its kinetic energy
• If the net work done on an object is positive,
  then the objects kinetic energy increases if
  the net work done is negative, then the KE
  decreases if the work done is 0, then the KE is
  constant (its speed is constant)

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Potential Energy

• Potential energy is the energy associated with
  forces that depend on the position of a body
• The most common PE is gravitational PE
• PEgravitation mgy
• Change in PE is physically meaningful
• Change in PE is the work required of an external
  force to move the object without acceleration
  between the two points
• Spring equation (Hookes law) Fs - kx
• Elastic PE ½ kx2

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Conservative and Nonconservative Forces

• Conservative forces gravitational, elastic,
  electric
• Nonconservative forces friction, air resistance,
  tension in a cord, motor or rocket propulsion,
  push or pull by a person
• PE can be defined only for a conservative force
• WNC DKE DPE

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Conservation of Mechanical Energy

• If only conservative forces are acting, the total
  mechanical energy of a system neither increases
  nor decreases in ANY process. It stays
  constantit is constant
• KE2 PE2 KE1 PE1
• Conservation of energy when PE is elastic
• Conservation of energy when only gravity acts
• Frictional forces are dissipative forces, because
  they reduce the total mechanical energy

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Problem SolvingConservation of Energy

• Draw a force diagram
• Determine the system for which energy will be
  conserved
• Decide the initial and final locations
• If the body changes height, choose the lowest
  point to be 0
• If springs are involved, choose the unstretched
  spring position to be x (or y) 0
• If no friction or other nonconservative forces
  act, then apply conservation of mechanical energy
• Solve for the unknown quantity
• If friction is present, add WNC DKE DPE

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Power

• Power is the rate at which work is done
• Average power work / time energy transformed
  / time
• 1 watt 1 J/s
• 1 horsepower 550 ft-lb/s 746 W