SCIENCE: FORCE, MOTION, AND ENERGY

MODULE 4. Conservation of Mechanical Energy

STUDENT-TEACHER: DIANA ROSE S. DE
Quarter 4 – Module 4 | A.Y. 2023 – 2024 GUZMAN
COOPERATING TEACHER: MA’AM HAZEL
MAY N. ALIGA
considered as stored energy having the
Work potential to do mechanical work.
When a force acts upon an object to cause a
displacement of the object, it is said that work The various forms of potential energy are
was done upon the object. There are three key gravitational, chemical, elastic, electrical,
ingredients to workforce, displacement, and and nuclear. Chemical, electrical and
cause. In order for a force to qualify as having nuclear energies in general exhibit
done work on an object, there must be a characteristics that are electromagnetic in
displacement and the force must cause the nature though they also have potential
displacement. energy.
Joule Equation for Potential energy
The joule is equal to the energy transferred to (or PEgrav = mgh
work done on) an object when a force of one Where;
newton acts on that object in the direction of the PEgrav = gravitational potential energy
force's motion through a distance of one meter (1 m = mass of an object
newton meter or N x m). It is named after the g = acceleration due to gravity
English physicist James Prescott Joule. h = height or elevation difference
To illustrate, PEelas = ½ kx2
A force of 20 Newton’s pushing an object 5 Where;
meters in the direction of the force does 100 PEelas = elastic potential energy
joules (or Nm) of work. k = spring constant
x = compression or extension length
This can be expressed by the equation:
W=Fxd ”Types of Potential Energy”
or for a Force acting Upwards on an object that is A. Gravitational energy- objects due to its
displaced to the right or to the left, position in gravitational field.
Examples:
W = F x d x cos θ
 A roller coaster at the top of a hill. When
where “theta” (θ) is the angle between the force
roller coaster at the highest point of the hill,
and the displacement.
it has maximum amount of gravitational
potential energy. As it down the hill, this
An example is that of a waiter carrying a tray full
potential energy is converted into kinetic
of meals across the room at a constant speed.
energy, making roller coaster move faster.
Work is not done because the force supplied is
 A book on a shelf has gravitational potential
upward but the displacement of the tray is
energy because it has potential to fall to the
horizontal. As such, the angle (θ) between the
ground due to gravity.”
force and displacement is 90 degrees. Since
cosine 90 degrees is O, then regardless of the
B. Chemical energy- released or absorbed
magnitude of force and displacement, work would
during chemical reactions.
be zero.
Example: When gasoline burn in a car
A vertical force can never cause a horizontal
engine, the chemical potential energy
displacement; thus, a vertical force does not do
stored in gasoline molecules is converted
work on a horizontally displaced object. JOULE is
into kinetic energy to power the vehicle.”
the unit of work and 1 joule is equal to 1 Newton-
meter. (1 J = 1 N x m)
C. Elastic energy- it stored within objects
elasticity and is released when objects
Energy
elasticity and is released when the object
Energy is the name of the game. Everything returns to its original shape.
exists or ceases to exist because of its presence For example: Stretch rubber band: when
or absence. It is stored in different forms and can you stretch it you’re storing elastic potential
transfer or transform. It can be transferred energy, and when you released it, the
without being transformed. It can also be energy is converted to kinetic energy.
transformed without being transferred. It can also
be transformed during transfers. D. Electrical energy- associate with the
position of charged particles within an
Mechanical Energy electrical field. It depends on amount of
The sum of potential and kinetic energy in a charge and position relative to each other
system due to its motion or position. Examples:
 Cell phone is charged, it stores electrical
“Types of Mechanical energy” potential energy, which can released
1. Potential Energy- Energy in matter due to when the cell phone is discharged.
arrangements of its parts, composition,  When you power a light bulb, electrical
location, and structure. It is commonly energy flows through the wires and
 converted into light and heat energy, conservative force, as it reduces mechanical
illuminating the room.” energy. Non-conservative forces can also
increase the total mechanical energy, making
E. Nuclear energy- energy stored in nucleus of them non-conservative.
atom dues to strong nuclear force.
An example of this energy is when uranium-
235 nucleus undergoes fission, it releases a Activities showing conservation of
large amount of energy in the form of kinetic Mechanical Energy
energy of fission fragments and emitted
neutrons.

2. Kinetic Energy - Energy in moving matter

and wave. Some forms of kinetic energy are
motion, radiant, sound, and thermal waves.

Equation for Potential energy

KE = ½ mv2
Where;
KE = kinetic energy
m = mass of an object
v = velocity of an object As the bob swings from point a to point c (on a
frictionless surface), it is accompanied by an
“Types of Kinetic Energy” increase in speed. As the bob loses height and
A. Motion (Translational kinetic energy)- Potential Energy (PE), it gains speed and
energy object possesses due to its motion Kinetic Energy (KE), yet the total of the two
from one place to another. forms of mechanical energy is conserved.
Example: A moving car in highway. It possesses
kinetic energy due to its motion. This energy
associated with its speed and mass.

B. Radiant energy- energy carried by

electromagnetic radiation.
Example: Sunlight carrying energy from the Sun
to the Earth.”

C. Sound energy- energy associated with

movement of particles in a medium as a result
of sound waves propagating through it.
Example: Movement of water molecules
transmitting sound underwater, such as in the
ocean. Another example is vibrations of a drum
or guitar string.

D. Thermal waves energy- do not possess KE

themselves; rather, they describe the
propagation of kinetic energy within
substance due to the random motion of its
particles.
Examples:
 The heat energy from stove is transferred to
water molecules, increasing their kinetic
energy and causing temperature of water to
rise.
 Feeling warmth from sunlight: when sunlight
hits an object its energy absorbed, increasing
the kinetic energy of objects molecules which
we perceive as warmth.
Conversation of Mechanical energy

The conservation of mechanical energy is a

principle states that the total mechanical energy
in a system remains constant as long as
conservative forces are acting. Conservative
forces do not change the total mechanical
energy, and can be seen in a round trip.

Gravity, for example, is conservative force, as it

maintains the same kinetic energy throughout the
path. Kinetic energy, on the other hand, is a non-