Download Total Mechanical Energy

Total Mechanical Energy
• The total mechanical energy of a system is
defined to be the sum of:
• The total potential energy of the system
• The total kinetic energy of the system
• The symbol used for total mechanical energy
is ME. The units of ME are joules.
• The total mechanical energy of a system can
be negative if and only if the total potential
energy is negative and has a greater
magnitude than the total kinetic energy.
Law of Conservation of
Energy
Law of Conservation of Energy
• When a ball flies
through the air it does
not lose energy even
though it slows down
and speeds up
• The energy in the ball
changes from kinetic
to potential and then
back to kinetic energy
Example
A 50.0 gram tennis
ball is at rest on the
ground.
The tennis ball is then
thrown upward…
A 50.0 gram tennis ball is
thrown upward – when
it is at a height of 0.75
meters above the
ground…
The change in
gravitational potential
energy of the tennis ball
is:
PE  PE f  PEi
0.75 m
PEg  mgh f  mghi
PE  (0.0500 kg)(9.80
m
m
)(
0
.
75
m)
(
0
.
0500
kg
)(
9
.
80
)(0.00 m)
2
2
s
s
PE  0.37 J
A 50.0 gram tennis ball is
thrown upward – when
it is at a height of 0.75
meters above the
ground…
When the ball reaches the
height of 0.75 m, it is
traveling at 1.35 m/s.
The kinetic energy of
the ball is:
1 2
KE  mv
2
1
KE  (0.050 kg)(1.35 m s) 2
2
KE  0.046 J
1.35 m/s
0.75 m
A 50.0 gram tennis ball is
lifted to a height of 0.75
meters above the
ground.
When the ball reaches the
height of 0.75 m, it is
traveling at 1.35 m/s.
What is the total
mechanical energy of
the system?
ME  KE  PE
ME  0.046 J  0.37 J
ME  0.42 J
KE  0.046 J
PE  0.37 J
1.35 m/s
0.75 m