Conservation of Mechanical Energy

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

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

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

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

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

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.

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.