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, PEE, PEG,
chemical, heat, etc.)
Mechanical Energy
 Mechanical
Energy is the sum of
kinetic and potential energy
 ME = KE + PE
ME = KE + PEG + PEE
 “Useful” energy
 “Can the energy break the window?”
Conservative Forces
 Gravity
and elastic forces
 Conservative forces DO NOT change
the amount of mechanical energy of
a system
Energy is converted from one form
to 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
 MEi = MEf
 KEi + PEGi + PEEi = KEf + PEGf + PEEf
Conservative Forces
Conservation of Mechanical Energy
PEG 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
PEG = mgh
KE = 0
KE = ½ mv2
PEG = 0
Is Mechanical Energy Conserved
Here?
Nonconservative Forces

When nonconservative forces act on a
system, mechanical energy IS NOT
conserved
 WNC = 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 act on an object,
TOTAL ENERGY is always conserved

 Total energy would include heat energy

Non-Conservative forces turn ME into
non-ME (usually heat), but the total
amount of energy stays the same
Friction & Pendulums