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?)