Potential and Kinetic Energy Study Material

Potential and Kinetic Energy Study Material 

Introduction
Energy exists in many forms, including mechanical, chemical, electromagnetic, and nuclear,
and can be converted from one form to another
Mechanical engineering is concerned principally with two kinds of energy, potential energy and kinetic energy.
Total mechanical energy of a system is the sum of potential energy and kinetic energy in the system

Potential Energy

Thermal potential energy is potential energy at the atomic and molecular levels, where it has the potential of becoming kinetic energy or related forms of energy. Common types of thermal potential energy are chemical bonds, electrostatic or inter molecular forces, and nuclear bonds.
Two specific types of potential energy are gravitational potential energy and spring potential energy.

Gravitational potential energy

Gravitational potential energy is energy associated with an object’s height and is related to gravity and the object’s mass

FIG 1

The force exerted on a mass of m kg is mg N (where g = 9.81 m/s², the acceleration due to gravity). When the mass is lifted vertically through a height h m above some datum level, the work done is given by: force × distance =  (mg)(h) J. This work done is stored as potential energy in the mass.

Gravitational Potentia Energy = Mass ∗ Gravity ∗ Height

PE = m g h  (joules)

 Potential energy in a spring

Potential energy is a measure of stored energy. One way to store energy is in a spring. For
example, when you wind a mechanical watch, energy is stored by stretching the spring inside
the watch. This energy is then used to make the watch run. The potential energy stored in a
linear spring is calculated by the equation

Spring Potential Energy = 1/ 2 × Spring Constant × Spring Stretch²

FIG 2

Chemical potential energy

Many molecules are held together by chemical bonds that can be a thermal potential energy.
Exothermic chemical reactions, such as oxidation, convert the potential energy of the materials into thermal kinetic energy, thus increasing the resulting temperature. For example, when a piece of paper burns, the oxidation process turns the thermal potential energy into thermal kinetic energy.

FIG 3

Nuclear potential energy

Some atoms—especially at the higher end of the Periodic Table—have the potential of decaying into other particles. These radioactive nuclear reactions, give off radiation and high-speed particles that increase the thermal kinetic energy and thus the temperature of a material.

FIG 4

Intermolecular potential energy

Molecules in a liquid or solid are held together by electrostatic or intermolecular forces. Heating the substance—or transferring thermal energy—can overcome those forces, allowing the material to change its phase or state (liquid to gas or solid to liquid). and thus creating thermal kinetic energy. Intermolecular potential energy can also be considered latent potential energy.

Electrical potential energy

An object can have potential energy by virtue of its electric charge and several forces related to their presence. There are three main types of this kind of potential energy: electrostatic potential energy, electrodynamic potential energy (also sometimes called magnetic potential energy), and nuclear potential energy.

Electrostatic potential energy
In case the electric charge of an object can be assumed to be at rest, it has potential energy due to its position relative to other charged objects.
The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, in the absence of any non-electrical forces on the object. This energy is non-zero if there is another electrically charged object nearby.
The simplest example is the case of two point-like objects A₁ and A₂ with electrical charges q₁ and q₂. The work W required to move A₁ from an infinite distance to a distance d away from A₂ is given

by:

FIG 5

w = k × ( q₁ q₂ ) /r

where k is Coulomb's constant, equal to .

This equation is obtained by integrating the Coulomb force between the limits of infinity and d.
A related quantity called electric potential is equal to electric potential energy of a unit charge.

Electro dynamic potential energy
In case a charged object or its constituent charged particles are not at rest, it generates a magnetic field giving rise to yet another form of potential energy, often termed as magnetic potential energy. This kind of potential energy is a result of the phenomenon magnetism, whereby an object that is magnetic has the potential to move other similar objects. Magnetic objects are said to have some magnetic moment. Magnetic fields and their effects are best studied under electrodynamics.

Kinetic energy

Kinetic energy measures the energy of an object in motion. It is related to the speed and mass

of an object. The more massive a moving object is, the more kinetic energy it has. A moving

train has more kinetic energy than a car travelling at the same speed

FIG 6

IF  a force F acts on an object of mass m originally at rest (i.e. u = 0) and accelerates it to a velocity v in a distance s:

work done =  force ð distance 

                   =  F× s = (ma)(s)

so   Kinetic Energy =  1/2 ∗ Mass ∗ Speed²

        KE = 1/2 × m × v²  (joules )

Kinetic Energy of Rotation

The tangential velocity v of a particle of mass m moving at an angular velocity 

ω rad/s at a radius r metres (see Figure 7) is given by

FIG 7

v = ω r  rad/ s

The kinetic energy of a particle of mass m is given by: 

kinetic energy = 1/2 m v²

     KE    = 1/ 2 m× (ωr)²

            KE    = 1/2 m ω²r²  joules

                    KE    = 1/2 I ω²  where I = m r²

Conservation of energy

Energy may be converted from one form to another. The principle of conservation of energy states that the total amount of energy remains the same in such conversions, . energy cannot be created or destroyed. In mechanics, the potential energy possessed by a body is frequently converted into kinetic energy, and vice versa. 

When a mass is falling freely, its potential energy decreases as it loses height, and its kinetic energy increases as its velocity increases. Ignoring air frictional losses, at all times

potential energy+  kinetic energy = a constant

friction is present, then work is done overcoming the resistance due to friction and this is dissipated as heat. Then

initial energy =  final energy + work done overcoming frictional resistance