Kinetic Energy and Work

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Chapter 7 Kinetic Energy and Work
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• Energy
• What is energy?
• Energy - is a fundamental, basic notion in
  physics
• Energy is a scalar, describing state of an
  object or a system
• Description of a system in energy language is
  equivalent to a description in force language
• Energy approach is more general and more
  effective than the force approach
• Equations of motion of an object (system) can be
  derived from the energy equations

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• Some calculus
• In 1D case

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• Some calculus
• In 1D case
• In 3D case, similar derivations yield
• K kinetic energy

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• Kinetic energy
• K mv2/2
• SI unit kgm2/s2 J (Joule)
• Kinetic energy describes objects state of
  motion
• Kinetic energy is a scalar

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Chapter 7 Problem 4
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• Workkinetic energy theorem
• Wnet work (net)
• Work is a scalar
• Work is equal to the change in kinetic energy,
  i.e. work is required to produce a change in
  kinetic energy
• Work is done on the object by a force

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• Work graphical representation
• 1D case Graphically - work is the area under
  the curve F(x)

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• Net work vs. net force
• We can consider a system, with several forces
  acting on it
• Each force acting on the system, considered
  separately, produces its own work
• Since

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• Work done by a constant force
• If a force is constant
• If the displacement and the constant force are
  not parallel

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Chapter 7 Problem 14
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• Work done by a spring force
• Hookes law in 1D
• From the workkinetic energy theorem

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• Work done by the gravitational force
• Gravity force is constant near the surface of
  the Earth
• If the displacement is vertically up
• In this case the gravity force does a negative
  work (against the direction of motion)

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• Lifting an object
• We apply a force F to lift an object
• Force F does a positive work Wa
• The net work done
• If in the initial and final states the object is
  at rest, then the net work done is zero, and the
  work done by the force F is

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Chapter 7 Problem 20
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• Power
• Average power
• Instantaneous power the rate of doing work
• SI unit J/s kgm2/s3 W (Watt)

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• Power of a constant force
• In the case of a constant force

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Chapter 7 Problem 44
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Chapter 7 Problem 50
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Answers to the even-numbered problems Chapter 7
Problem 8 5.0 kJ
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Answers to the even-numbered problems Chapter 7
Problem 40 2.7 105 W