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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

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

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

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

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?)