ENERGY
¶¶ Introduction to Energy
It is often said that a person A is more energetic than a person B. The meaning of this statement is that a person A can do more work than the person B. Similarly, a person after doing a lot
of work gets tired and after that he is not able to do much work. It is clear that a person doing work expends something. This ‘something’ is known as the energy of the person. The energy spent by a person is equal to the work done by him. Human beings and animals get energy by eating food.
It may be noted that anything which is capable of doing work has energy. For example, the steam pushes up the lid placed on the boiling water container. It means, the steam has the ability or capacity to do work. The work done by the steam on the lid is equal to the energy of the steam.
If a person can do a lot of work we say that he has a lot of energy or he is very energetic. In physics also, anything which is able to do work is said to possess energy. Thus, energy is the ability to do work or the capacity to do work.
¶¶ Units of energy
Unit of energy is same as that of the unit of work as work is a form of energy.
So, S.I. unit of energy is Joule (J).
When we say that energy of a body is 1 joule, it means, this body has the capacity to do 1 J work.
¶¶ Commercial unit of Energy :
The commercial unit (or trade unit) of energy is kilowatt-hour which is written in short form as kWh. Kilowatt-hour is usually used as a commercial unit of electrical energy.
One kilowatt-hour is the amount of electrical energy consumed when an electrical appliance having a power rating of 1 kilowatt is used for 1 hour. Since a kilowatt means 1000 watts, so we can also say that one kilowatt-hour is the amount of electrical energy consumed when an electrical appliance of 1000 watts is used for 1 hour.
1 kilowatt-hour is the amount of energy consumed at the rate of 1 kilowatt for 1 hour. That is, 1 kilowatt-hour = 1 kilowatt for 1 hour
or 1 kilowatt-hour =1000 watts for 1 hour
Note:
Watt or kilowatt is the unit of electrical power but kilowatt-hour is the unit of electrical energy.
Energy is a scalar quantity.
Dimensional formula of energy = \(
ML^2 T^{ - 2}
\)
KINDS OF ENERGY
In actual practice there are many kinds of energy, such as mechanical energy; heat energy; light energy; sound energy, electrical energy; nuclear energy; chemical energy, etc. Let us discuss about mechanical energy.
¶¶ Mechanical energy (M.E) :
The sum of kinetic energy (K.E) and potential energy (P.E) of a body is known as mechanical energy. \(\therefore\)M.E = K.E + P.E
¶¶ Kinetic energy:-
The kinetic energy of an object is a measure of the work an object can do by the virtue of its motion.Therefore kinetic energy is defined as ”the energy possessed by a body by virtue of its motion”.
Kinetic energy of a body of mass m moving with velocity v is expressed as K.E= \(
\frac{1}
{2}mv^2
\) Since mass and square of velocity are always positive K.E. never be negative.
Examples:
1.A vehicle in motion.
2.Water flowing along a river.
3.A bullet fired from a gun.
4.A running athlet have kinetic energy.
¶¶ Potential Energy:-
The energy possessed by a body by virtue of its state or position is known as potential energy.
Expression: P.E.=mgh
Examples:
1.Water on hill top and stretched or compressed spring possess potential energy.
2.stone at a certain height.
3.The spring wound in a watch possesses potential energy
4.An arrow in a bowl possesses potential energy.
¶¶ Gravitational potential energy :-
The Potential energy due to height above the earth’s surface is called gravitational potential energy.
In general, if the potential energy at the ground is taken as zero, the potential energy of an object at a height h above the ground is given by
U = mgh
The energy results from the force of attraction mg between the earth and the object.From newton’s third law, both earth and the object attract each other.
Hence, strictly speaking energy ‘mgh’ is not the potential energy of the object alone it is the potential energy of object-earth system.
¶¶ Heat Energy:-
Heat is the energy that is transferred between a system and its environment because of a temperature difference that exists between them.
Heat is an Internal energy that consists of the kinetic and potential energies associated with the random motion of the atoms, molecules and other micro scopic bodies within object.
¶¶ Sound Energy:-
Sound is a form of energy, that is produced by a body when it is in the state of vibration. It propagates in the form of Longitudinal waves through Elastic media and causes sensation of
hearing.
¶¶ Light Energy:-
\(\to\)Light is a form of energy, which causes sensation of vision.
\(\to\) Light travels from one place to another place in the form of Electromagnetic waves.
\(\to\)E.M wave can transport energy and deliver it to a body on which it falls.
¶¶ Elastic potential energy :-
When a spring is streched or compressed from its natural length, its get extra energy. It can return to its natural length by performing some work.
The extra energy stored in a streched or compressed spring is called elastic potential energy.
A streched rubber band also has potential energy, where as rubber band at its natural length lying on a table has no elastic potential energy.
* Other forms of energy :-
Besides mechanical energy, energy can exist in several other forms.
Charged particles and electric currents can produce electrical energy and magnetic energy.Electric batteries,cooking gas,petrol etc., have chemical energy stored in them.Even matter itself is a concentrated form of energy and can be converted into other forms of energy such as kinetic energy and heat energy.
¶¶ Electrical energy :Energy is associated with electric current is called electrical energy The flow of electrical current causes bulbs to glow, fans to rotate and bells to ring.
Relation between kinetic energy and momentum
Let us consider a body of mass ‘m’ having a velocity ‘v’ , then
momentum of the body P = mass × velocity P = m × v
\(
v\,\, = \,\,\frac{P}
{m}
\) --------- (1)
From definition, kinetic energy (K.E) of the body
K.E = \(
\frac{1}
{2}\,\,mv^2
\) --------- (2)
Now putting the value of (1) in (2) we have
\(
K.E\,\, = \,\,\frac{1}
{2}\,\,m\,\,\left( {\frac{P}
{m}} \right)^2
\)
K.E. = \(
\frac{1}
{2}\,m\,\,\frac{{P^2 }}
{{m^2 }}\,\, = \,\,\frac{1}
{2}\,\,\frac{{P^2 }}
{m}\,\, = \,\,\frac{{P^2 }}
{{2m}}
\) ----- (3)
Thus we can write P2 = 2m × K.E \(
\Rightarrow \,\,P\,\, = \,\,\sqrt {2m\,\, \times \,\,K.E}
\)
Thus momentum = \(
\sqrt {2\,\, \times \,\,mass\,\, \times \,\,\text{kinetic energy}}
\)
Note :
1. For same momentum \(
K.E\,\, \propto \,\,\frac{1}
{m}
\) Kinetic energy varies inversely as the mass.
2. If two bodies have same momentum, ratio of their kinetic energy is \(
\frac{{K.E_1 }}
{{K.E_2 }}\,\, = \,\,\frac{{m_2 }}
{{m_1 }}
\) \(
\left[ {E\,\, \propto \,\,\frac{1}
{m}} \right]
\)
3. If two bodies have same kinetic energy, ratio of their momenta is \(
\frac{{P_1 }}
{{P_2 }}\,\, = \,\,\sqrt {\frac{{m_1 }}
{{m_2 }}}
\)
4. If the momentum of a body is increased to x times, its kinetic energy increases to x2 times.
5. If the kinetic energy of a body is increased to x times, its momentum increases to \(
\sqrt x
\) times.