Mechanical Energy
Conservative Forces
Conservation of Mechanical Energy

Conserved Quantities
• When a quantity is conserved, it remains constant
• The amount of a conserved quantity is the same at the beginning of a situation as it is at the end of the situation

Conservation of Energy
• The TOTAL amount of energy in a closed system will remain constant
 CLOSED SYSTEM: Nothing in or out – no interaction with the surroundings
 TOTAL ENERGY: all kinds of energy
(kinetic, PE
E
, PE
G
, chemical, heat, etc.)

Mechanical Energy
• Energy associated with the motion and position of everyday objects
• Mechanical Energy is the sum of kinetic and potential energy
• ME = KE +

PE
 ME = KE + PE
G
+ PE
E

Conservation of Mechanical Energy
• When there are only conservative forces acting on an object (gravity, springs),
MECHANICAL ENERGY IS CONSERVED

Conservative Forces
• Conservative forces DO NOT change the amount of mechanical energy of a system
• Gravity and Elastic Forces
• Conservative forces will convert one form of mechanical energy into another, but the total amount of mechanical energy remains the same

Conservation of Mechanical Energy
• When there are only conservative forces acting on an object (gravity, springs),
MECHANICAL ENERGY IS CONSERVED
• ME i
= ME f
• KE i
+ PE
Gi
+ PE
Ei
= KE f
+ PE
Gf
+ PE
Ef

Conservative Forces
Conservation of Mechanical Energy
PE
G
decreases & KE increases, but total ME remains constant (in the absence of air friction)!

Conservation of ME & Falling Objects
10000 J
5000 J
Time (s)

Conservation of ME & Pendulums
PE
G
= mgh
KE = 0
KE = ½ mv 2
PE
G
= 0

Is Mechanical Energy Conserved Here?

Nonconservative Forces
• When nonconservative forces do work on a system, mechanical energy IS NOT conserved
 W
NC
= ΔME
 This is the Work-Energy Theorem

Friction
• Friction does negative work on the system, so the mechanical energy is decreased
• While ME is not conserved when nonconservative forces (like friction) act on an object, TOTAL
ENERGY is always conserved
– Total energy would include heat energy
• Friction forces turn ME into non-ME (usually heat), but the total amount of energy stays the same

Friction & Pendulums