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