5.3 The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF
ENERGY
The term conserved means constant
5.3 The Conservation of Mechanical Energy
THE PRINCIPLE OF CONSERVATION OF
MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an object
remains constant as the object moves in the absence of
friction.
Conservation of Mechanical
Energy
• The sum of KE and PE remains constant.
• One type of energy changes into another type.
– For the falling book, the PE of the book changed into KE as it
fell.
– As a ball rolls up a hill, KE is changed into PE.
5.3 The Conservation of Mechanical Energy
Wnet  KE  PE  KEf  KEi   PEf  PEi 
Wnet  KEf  PEf   KEi  PEi 
Wnet  Ef  Ei
If the net work on an object by nonconservative forces
is zero, then its energy does not change:
E f  Ei
Conservation of Energy
• Acceleration does not have to be constant.
• ME is not conserved if friction is present.
– If friction is negligible, conservation of ME is
reasonably accurate.
• A pendulum as it swings back and forth a few
times
• Consider a child going down a slide with
friction.
– What happens to the ME as he slides down?
• Answer: It is not conserved but, instead, becomes
less and less.
– What happens to the “lost” energy?
5.3 The Conservation of Mechanical Energy
E f  Ei
ME i  ME f
mghf  mv  mghi  mv
1
2
2
f
1
2
2
i
5.3 The Conservation of Mechanical Energy
5.3 The Conservation of Mechanical Energy
Example 8 A Daredevil Motorcyclist
A motorcyclist is trying to leap across the canyon by driving
horizontally off a cliff 38.0 m/s. Ignoring air resistance, find
the speed with which the cycle strikes the ground on the other
side.
5.3 The Conservation of Mechanical Energy
E f  Ei
mghf  mv  mghi  mv
1
2
2
f
1
2
ghf  12 v2f  ghi  12 vi2
2
i
5.3 The Conservation of Mechanical Energy
ghf  12 v2f  ghi  12 vi2
v f  2 g hi  h f   vi2


v f  2 9.8 m s 35.0m   38.0 m s   46.2 m s
2
2
5.3 The Conservation of Mechanical Energy
Question #23
A bird is flying with a speed of 18.0 m/s
over water when it accidentally drops a
2.00 kg fish. Assuming the altitude of the
bird is 5.40m, and disregarding friction,
what is the speed of the fish when it hits
the water?
20.7 m/s
5.3 The Conservation of Mechanical Energy
Question #24
An Olympic high jumper leaps over a
horizontal bar. The jumper’s center of
mass is raised 0.25m during the jump.
Calculate the minimum speed with which
the athlete must leave the ground to
perform this feat?
2.2 m/s
5.3 The Conservation of Mechanical Energy
Question #25
A pendulum 2.0 m long is released from
rest when the support string is t an angle
of 25.0° with the vertical. What is the
speed of the bob at the bottom of the
swing?
1.9 m/s
5.3 The Conservation of Mechanical Energy
Question #26
A 755 N diver drops from a board 10.0 m
above the water’s surface. Find the diver’s
speed 5.00m above the water’s surface.
9.9 m/s
Find the diver’s speed just before striking
the water.
14.0 m/s