Energy

Energy is a fundamental concept that describes the ability of a system to do work
or produce a change. It is a scalar quantity, meaning it has magnitude but no direction.

Energy cannot be created or destroyed, only transformed from one form to another.
Because energy can be found in many things, there are various types of energy. All
energy is either kinetic or potential.
Unit of Energy
The SI unit of energy is Joules (J), named in honour of James Prescott Joule.
James Prescott Joule made significant contributions to the study

of energy in physics, particularly in the field of thermodynamics. His
work helped establish the concept of energy conservation and the
relationship between mechanical work and heat.
His work contributed to the realization that energy is a
fundamental concept in physics and that it can be changed from one form
to another, such as mechanical energy to thermal energy.
The joule is widely used in scientific and engineering fields to
measure various forms of energy.
Kinetic energy is defined as the energy related to an object's motion. Kinetic

energy is present in any object that moves, whether vertically or horizontally.
Forms of Kinetic Energy
 Vibrational - the energy due to vibrational motion
 Rotational - the energy due to rotational motion
 Translational - the energy due to motion from one location to another
Kinetic energy focuses with translational. The kinetic energy of an object depends on
its mass (m) and velocity (v). The formula for kinetic energy is
1
KE=( )m v 2
2
where m = mass of the object (kg)
v = velocity of the object (m/s 2)
This equation reveals that the kinetic energy of an object is directly proportional
to the square of its velocity. That means that for a twofold increase in velocity, the kinetic
energy will increase by a factor of four. For a threefold increase in velocity, the kinetic
energy will increase by a factor of nine. And for a fourfold increase in velocity, the
kinetic energy will increase by a factor of sixteen. The kinetic energy is dependent upon
the square of the. As it is often said, an equation is not merely a recipe for algebraic
problem solving, but also a guide to thinking about the relationship between quantities.
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Kinetic energy is a scalar quantity; Mass is a scalar quantity and the velocity
which is a vector is squared which makes it a scalar quantity as well. Therefore, Kinetic
Energy is a scalar.
Potential Energy is the stored energy associated with the position or
configuration of an object in a force field.
Forms of Potential Energy
 Gravitational Potential Energy
 Elastic Potential Energy
Gravitational Potential Energy is the energy an
object possesses due to its position above the ground.
The gravitational potential energy of the massive ball
of a demolition machine is dependent on two variables - the mass of the ball and the
height to which it is raised. There is a direct relation between gravitational potential
energy and the mass of an object. More massive objects have greater gravitational
potential energy. There is also a direct relation between gravitational potential energy and
the height of an object. The higher that an object is elevated, the greater the gravitational
potential energy. These relationships are expressed by the following equation:
PE grav =mgh
where m = mass of the object
g = acceleration due to gravity (9.8 N/kg)
h = height above a reference point.
Since the gravitational potential energy of an object is directly proportional to its

height above the zero position, a doubling of the height will result in a doubling of the
gravitational potential energy. A tripling of the height will result in a tripling of the
gravitational potential energy. Therefore, an object possesses gravitational potential
energy if it is positioned at a height above (or below) the zero height.
Elastic Potential Energy is the energy stored in an elastic material, such as a
stretched or compressed spring. Elastic potential energy can be stored in rubber bands,
bungee chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of
elastic potential energy depends on the spring constant and the amount of deformation -
the more stretch, the more stored energy.
Springs are a special instance of a device that can store elastic potential energy
due to either compression or stretching. A force is required to compress a spring; the
more compression there is, the more force that is required
to compress it further. For certain springs, the amount of
force is directly proportional to the amount of stretch or
compression (x); the constant of proportionality is known
as the spring constant (k).
F spring =k • x
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Such springs are said to follow Hooke's Law. If a spring is not stretched or
compressed, then there is no elastic potential energy stored in it. The spring is said to be
at its equilibrium position. The equilibrium position is the position that the spring
naturally assumes when there is no force applied to it. In terms of potential energy, the
equilibrium position could be called the zero-potential energy position. There is a special
equation for springs that relates the amount of elastic potential energy to the amount of
stretch (or compression) and the spring constant. The equation is
PE spring = 0.5 • k • x 2
where k = spring constant

x = amount of compression (relative to equilibrium position)
An object possesses elastic potential energy if it is at a position on an elastic

medium other than the equilibrium position.
Two Spherical Masses
Now, the final formula for potential energy we will discuss is for a system of two
spherical masses, such as planets, stars, and the moon. The potential energy formula
corresponding to this type of system is
−G m1 m2
PE=
r
where G = gravitational constant

m = mass
The negative sign here indicates the bound state of a mass once it approaches a large
body. This means that the mass is stuck until enough energy is provided for it to become
unbound.
Mechanical Energy
Mechanical energy enables that

object to apply a force to another
object in order to cause it to be
displaced.
Total Mechanical Energy
the mechanical energy of an object can be the result of its motion (i.e.,
kinetic energy) and/or the result of its stored energy of position (i.e., potential energy).
The total amount of mechanical energy is merely the sum of the potential energy and the
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kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated
TME).
TME=PE+ KE
there are two forms of potential energy discussed in our course -
gravitational potential energy and elastic potential energy. Given this fact, the above
equation can be rewritten:
TME=PEgrav PEspring + KE
Law of Conservation
The law of conservation of energy states that the total amount of energy in an
isolated system remains constant over time. In other words, energy cannot be created or
destroyed; it can only be converted from one form to another.
According to the law of conservation of energy, the total energy of a closed
system, which is not influenced by external forces, remains constant. This principle is
derived from the application of the first law of thermodynamics, also known as the law of
energy conservation. This energy can be expressed as:
∆ E=E final−Einitial =0
where ΔE = change in energy

E finall = final energy state of the system
Einitial = initial energy state
This equation implies that the total energy before a process or event is equal to the
total energy after the process or event.
The law of conservation of energy applies to all types of energy, including kinetic
energy, potential energy, thermal energy, chemical energy, and nuclear energy. It allows
scientists to analyze and understand the energy transformations and interactions occurring
in various physical systems.
It's important to note that while energy is conserved, it can be transferred from
one object or system to another. For example, when a moving object collides with a
stationary object, the kinetic energy of the first object can be transferred to the second
object, causing it to move. Similarly, energy can be converted between different forms,
such as the conversion of electrical energy into light energy in a light bulb.
Work Energy theorem
work-energy theorem is relates the work done on an object to the change in its
kinetic energy. It states that the net work done on an object is equal to the change in its
kinetic energy. The work-energy theorem can be expressed as:
W net =∆ KE
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where W net = net work done on the object
ΔKE = change in kinetic energy.
The net work done on an object is the sum of the work done by all the forces
acting on it. If multiple forces are acting on the object, the net work is given by:
W net = ΣW i
where ΣW i = sum of the work done by each individual force.

The work done by a force is defined as the product of the force applied on an
object and the displacement of the object in the direction of the force. Mathematically, it
is given by:
W =F · d · cos( θ)
where W = work done
F = magnitude of the force
d = displacement of the object
θ = angle between the force and the direction of displacement
The work-energy theorem states that this net work done on an object is equal to
the change in its kinetic energy. If the net work done on an object is positive, it means
that energy is being transferred to the object, increasing its kinetic energy. On the other
hand, if the net work done is negative, energy is being taken away from the object,
decreasing its kinetic energy.
https://byjus.com/physics/work-energy-power/
https://www.physicsclassroom.com/class/energy/Lesson-1/Mechanical-Energy
https://www.studysmarter.co.uk/explanations/physics/work-energy-and-power/
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Energy is a fundamental concept that describes the ability of a system to do work

or produce a change. It is a scalar quantity, meaning it has magnitude but no direction.

James Prescott Joule made significant contributions to the study

Kinetic energy is defined as the energy related to an object's motion. Kinetic

Since the gravitational potential energy of an object is directly proportional to its

where k = spring constant

An object possesses elastic potential energy if it is at a position on an elastic

Two Spherical Masses

where G = gravitational constant

Mechanical energy enables that

Total Mechanical Energy

where ΔE = change in energy

where ΣW i = sum of the work done by each individual force.

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