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Conservation of Mechanical Energy

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Conservation of Mechanical Energy Mechanical Energy The sum of Potential and Kinetic Energies ME=PE+KE The conservation of mechanical energy states that ... – PowerPoint PPT presentation

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Title: Conservation of Mechanical Energy


1
Conservation of Mechanical Energy
  • Mechanical Energy The sum of Potential and
    Kinetic Energies
  • MEPEKE
  • The conservation of mechanical energy states that
    mechanical energy remains constant in the absence
    of air resistance or friction (non-conservative
    forces).
  • Conservation of mechanical energy is path
    independent.

PE100 J KE0 J ME100 J
PE30 J KE70 J ME100 J
PE0 J KE100 J ME 100 J
2
Conservation of Mechanical Energy(Pendulum)
PE10 J KE0 J ME10 J
PE10 J KE0 J ME10 J
PE0 J KE10 J ME10 J
Maximum potential Energy, zero kinetic energy
Maximum kinetic energy, zero potential energy
Maximum potential Energy, zero kinetic energy
Maximum kinetic Energy, zero potential energy
Maximum potential Energy, zero kinetic energy
Maximum potential Energy, zero kinetic energy
3
Conservation of Mechanical Energy (Problem
Solving)
  • ME1ME2
  • PE1KE1PE2KE2
  • mgh1 ½ mv12mgh2 ½ mv22
  • If v10 and h20 then
  • mgh1 0 0 ½ mv22
  • PE1KE2 (The initial potential energy is
    converted to the final kinetic energy. The work
    accomplished by gravity causes the change of
    potential to kinetic energy.)

1
h1
2
h2
4
Conservation of Mechanical Energy (Something to
Consider)
  • ME1ME2
  • PE1KE1PE2KE2
  • KE2-KE1-(PE2-PE1)
  • ?KE-?PE What is the interpretation of this
    equation?
  • Multiply by -1
  • ?PE-?KE (Interpret this equation)

1
h1
2
h2
5
Conservation of Mechanical Energy (More things to
consider)
  • Is mass a factor in determining height or
    velocity?
  • ME1ME2
  • PE1KE1PE2KE2
  • mgh1 ½ mv12mgh2 ½ mv22
  • gh1 ½ v12gh2 ½ v22
  • Multiply by 2
  • 2gh1v122gh2v22 (Is this equation familiar?)
  • v22v122gh1-2gh2 (Is this equation familiar?)
  • v22v122g(h1-h2) (Is this equation familiar?)
  • g-9.8 m/s2, dh1-h2
  • v22v122gd (Is this equation
    familiar?)
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