Week 4 - Conservation of Mechanical Energy.pptx

Conservation of
mechanical
Energy

Define potential energy and kinetic energy
Identify daily activities to demonstrate
conservation of mechanical energy.
Derive a conclusion that the total mechanical
energy in a given system is the same.
objectives:
Define the total mechanical energy

The conservation of
momentum states that the
amount of momentum
remains constant inside a
problem domain.
forces and motion (conservation of momentum)
review
Energy is not created nor
destroyed, but only
altered by the action of
forces as defined by
Newton’s Law of motion.

ELASTIC COLLISION
review
The total energy of the
system does not
change, and colliding
objects bounce off after
collision.

INELASTIC COLLISION
review
The total energy of the
system changes (e.e.,
converted to some other form
of energy). Objects that stick
together after collision is said
to be perfectly inelastic.

• Moving objects possess
momentum.
• Moving objects also have energy.
• All objects regardless of their
state of motion (at rest of in
motion) possess a certain amount
I should know that...

• Energy can be
transformed from one
form to another.
• In such transformations,
energy is said to be
conserved.

• One form of energy is mechanical
energy.
• Mechanical Energy is energy
acquired by objects upon which
work is done.

the total energy
stored before
the total energy
stored after
How can energy be transferred?
This is observed when a force
is applied to move an object
through a distance.
Mechanical Work
Energy can be transferred from one store to another in four ways:
Lifting a box
mechanical work

chemical store in
battery
kinetic store
in a toy car
It involves charges moving in
a circuit due to a potential
difference.
ELECTRICAL
Work
electrical work
Powering a toy car
with battery

It involves the transfer of
energy from a hotter object
to a colder one.
Heating
heating
boiling water
thermal store in the
surroundings
thermal store of the
water

It occurs when energy is
transferred as a wave, such
as visible light or infrared.
radiation
radiation
Warming of surrounding
thermal store
of the Sun
thermal store
of the pavement

1. Potential Energy
2. Kinetic Energy
two forms of mechanical energy

Energy possessed by
objects at rest.
POTENTIAL ENERGY
Tree types of Potential Energy:
1. Gravitational Potential Energy
2. Elastic Potential Energy
3. Chemical Potential Energy

Energy possessed by objects
because of its location or position.
gravitational POTENTIAL
ENERGY
The higher the position of an
object, the higher its GPE.

Energy stored in a stretched or
compressed elastic material such
as spring.
ELASTIC POTENTIAL
ENERGY
It is a result of applying a force
to deform an elastic object.

Energy stored in a bonds
between atoms and molecules.
chemical potential
ENERGY
The plants use energy from the
sun to convert water and carbon
dioxide to make their own food
(photosynthesis).

Battery is another example of
Chemical Potential Energy
A battery contains chemicals which
when connected to a circuit undergo a
chemical reactions that transform their
CPE into electrical energy powering our
devices.
chemical potential
ENERGY

Energy possessed by objects
by virtue of its motion.
kinetic ENERGY
The object is in motion.

the total
energy stored
before
the total
energy stored
after
The total amount of
energy in a system is:
Energy is neither created nor
destroyed. It just transfers
between different stores of
energy.
This is known as the Law of
Conservation of Energy.
What happens
to energy?

1. At what point in the
pendulum is the potential
energy maximum?
Answer: At point A
Rationale: Because of the
height

pendulum is the kinetic energy
zero?
Answer: At point A
ball is still at rest

pendulum is the potential
energy zero?
Answer: At point B
decrease in height

pendulum is the kinetic energy
maximum?
Answer: At point B
Rationale: Due to the
movement of the pendulum

5. What is the total mechanical
energy of the pendulum?
Answer:
T.E. = P.E. + K.E

Keep in Mind:
The total mechanical
energy of an object is
equal to the sum of the
potential energy and
kinetic energy if friction
is negligible.
50 J
50 J
50 J

5. What is the total mechanical
energy of the pendulum?
Answer:
T.E. = P.E. + K.E
T.E. = 50 J

6. Describe the Law of Conservation of Mechanical Energy.
Answer:
The Law of Conservation of Mechanical Energy
states that in the absence of dissipative forces (such as
friction or air resistance), the total amount of
mechanical energy in a closed system remains
constant.

6. Describe the Law of Conservation of Mechanical Energy.
Implication:
This means that potential energy can become
kinetic energy, or vice versa, but energy cannot
“disappear”.

The most common application
of gravitational potential
energy is for an object at the
Earth’s surface with a constant
gravitational acceleration of
9.8 m/s .
2

Equation:
GPE = 1/2 mgh
Where:
m - mass of the object
g - acceleration due to gravity
h - height or elevation of object

PE = mgh
Where:
g - acceleration due to gravity
h - height or elevation of object
POTENTIAL ENERGY of an
object is determined by the
equation:

KE = 1/2 mv
Where:
v - velocity of the object
kinetic ENERGY of an object is
determined by the equation:
2

Equation:
GPE = 1/2 mgh
Solution:
GPE = 1/2 mgh
GPE = 1/2 (0.1 kg)(-9.8 m/s )(10 m)
GPE = 4.9 kg. m /s or 4.9 J
sample problem
2
Consider the figure on the left. If the ball
has a mass of 0.1 kg, the gravitational
potential energy it contains is:
2 2
J =

Equation: GPE = 1/2 mgh
Solution:
GPE = 1/2 mgh
GPE = 1/2 (0.1 kg)(-9.8 m/s )(8 m)
GPE = 3.92 kg. m /s or 3.92 J
sample problem
2
Since the ball is at rest, it has no kinetic energy and
thus the total mechanical energy of the ball is also
4.9 J. If the ball moves downhill, some gravitational
potential energy gets transformed to kinetic energy.
At point B, the gravitational potential energy
decreases.
2 2
J =

Equation:
TME = PE + KE
Solution:
TME = PE + KE
4.9 J - 3.92 J = KE
0.98 J = KE
KE = 0.98 J
sample problem But since the total mechanical energy is a
constant, the kinetic energy of the ball is:
J =

“spend your energy for
something worthwhile and
valuable to man.”

Week 4 - Conservation of Mechanical Energy.pptx

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