1. Conservation of Mechanical Energy

2. Mechanical Energy KE and PE = total mechanical energy E = KE + PE
Actually there are other forms of energy to include, but we haven’t met them yet in the book

3. Work Energy Theorem (again)
Wnc = (KEf – KEi) + (PEf – PEi)
Rearrange
Wnc = (KEf + PEf) – (KEi + PEi)
Wnc = Ef – Ei
Nonconservative forces change the total mechanical energy of the system
Noneconservative forces = friction
Air resistance

4. Wnc = 0
Wnc = Ef – E0
If Wnc = 0 like if friction or air resistance is negligible
0 = Ef – E0
Ef = E0
If all forces are conservative, then the total mechanical energy does not change

5. Conservation of Mechanical Energy
If there is no work done by nonconservative forces
Total mechanical energy is constant
KEi + PEi = KEf + PEf

6. Conceptual Example
A rope is tied to a tree limb and used by a swimmer to swing into the water below. The person starts from rest with the rope held in the horizontal position, swings down and then lets go of the rope. Three forces act on him; W, T, and air resistance. Can conservation of mechanical energy be used to find the speed when he lets go of the rope?
Insert figure 6.19

7. Conceptual Example
In order to use conservation of mechanical energy, Wnc = 0
Nonconservative force in example
Tension  perpendicular to the motion so W = 0
Air Resistance  opposite and parallel to motion
Work does not equal 0
Cannot use conservation of ME
However, since the air resistance is small, you can usually say that the air resistance is negligible.

8. Reasoning Strategy for Conservation of ME
Identify the external conservative and nonconservative forces that act on the object. For this principle to apply, the total work done by nonconservative forces must be zero.
Choose the location where the PE is taken to be zero.
Set the final total ME equal to the initial total ME.