In this article, we shall study the concept of energy, types of mechanical energies, and the law of conservation of energy

Energy:

Different types of energy are mechanical energy, sound energy, heat energy, light energy, chemical energy, electrical energy, atomic energy, nuclear energy. Mechanical energy is further classified into kinetic energy and potential energy.

Kinetic Energy:

The energy possessed by the body on account of its motion is called kinetic energy. e.g Energy possessed by flowing water and wind, moving bicycle

Consider a body of mass ‘m’ lying on the smooth horizontal surface, is acted upon by a constant force of magnitude ‘F’ which displaces it through a distance ‘s’ in its own direction. Then the work done by the force is given by

W  =  F .  s     ……….. (1)

By Newton’s second law of motion

F  =  m . a     ……….. (2)

Where ‘a’ is the magnitude of the acceleration in the body.

From equations  (1) and (2)

∴  W  =  m a s  …………… (3)

By equation of motion we have

v² = u²   +  2as

Where u  = magnitude of the initial velocity. In this case u = 0

v =  magnitude of final velocity after covering the distance ‘s’

∴  v² =  2 a s

∴ as =  v²/2

Substituting in equation (3) we get

∴  W  =  mv²/2

∴  W  =  ½mv²

This work is stored as kinetic energy in the body. Thus the kinetic energy of the body is given by

K.E. = ½mv²

This is an expression of the kinetic energy of a body.

Potential Energy:

The energy possessed by a body or a system on account of its position and configuration is called potential energy. e.g. energy possessed by water stored in a dam, in wound spring of a watch

Suppose that body of mass ‘m’ be raised to some height say ‘h’ against the gravitational force which is equal to the weight of the body ‘mg’. Where ‘g’ is an acceleration due to gravity.

As the applied force and the displacement of the body are in the same direction.

Work = Force × Displacement

W = mg × h

∴  W = mgh

This work is stored as the potential energy in the body.

∴  P.E. = mgh

This is an expression for the gravitational potential energy of a body, raised to some height above the earth’s surface.

Units and Dimensions of Energy and that of Work are the Same:

The capacity of a body to do work is called energy. Hence energy is measured in terms of work. Therefore, the units and dimensions of energy and that of work are the same.

kilowatt-hour:

a kilowatt-hour is a unit of measuring energy. This unit is a general unit of energy consumption bills (Electricity bills)

Now Work = Power x time

Hence, 1 kilowatt hour= 1 kilowatt × 1 hour

If the power of 1 kilowatt is used for 1 hour, the work done or energy consumed is said to be 1 kilowatt hour.

1 kWh   = 1kW x 1 hour

= 1000 W x 60 x 60 sec

= 1000 J/s x 3600 s

= 3600000 J

= 3.6 x 10⁶ J

Kinetic Energy is Always Positive:

The kinetic energy of a body is given by the expression. K.E. = ½mv²

The right-hand side contains the term mass ‘m’ which is always positive and a term square of velocity which is also positive. Thus the right-hand side of the expression is always positive. Thus kinetic energy is always positive.

Principle of Conservation of Energy:

The energy cannot be created nor it can be destroyed but can be converted from one form to another. Thus the total energy of the isolated system remains the same.

Energy can be converted from one form to another Examples

• In an electrical bulb, electrical energy is converted into light energy and heat energy.
• When the hammer strikes the nail mechanical energy gets converted into sound energy and heat energy.

Working of Hydroelectric Power Station :

The principle of conservation of energy can be explained by the example of a hydroelectric power station.

Water is stored in the artificial reservoirs created in the mountains by constructing a dam across the river. Thus the kinetic energy of flowing water is converted into potential energy of stored water. This stored water is brought downhill i.e. at the foot of the mountain through pipes. This water is then directed on blades of the wheel of the turbine. Thus the kinetic energy of water is used to rotate the coil in the turbine. Due to rotation of the coil in the magnetic field the kinetic energy gets converted into electrical energy. This energy can further be converted into different forms of energy like sound, heat, light, magnetism, etc.

Principle of Conservation of Mass:

The mass cannot be created nor it can be destroyed but can be converted from one form to another. Thus the total mass of isolated system remains the same.

Einstein’s Mass-Energy Relation:

According to Albert Einstein, the mass and energy are interconvertible and the equivalence between them is given by the relation

E  =  m c²

Where   E = amount of energy

M = Mass

c = speed of light in vacuum

This relation is known as Einstein’s mass-energy relation.

Thus mass and energy are not two different physical quantity or the mass is a form energy.

Examples of Mass-Energy Interconversion:

Phenomenon of pair production :

In the phenomenon of pair production, the energy of gamma rays photons is converted under proper conditions, into a positron-electron pair. Thus here energy gets converted into mass.

Phenomenon of pair annihilation:

In the phenomenon of pair annihilation, a positron and electron under proper conditions combine to form the gamma-ray photon. Thus the particles (mass) are converted into energy.

Note:

Positrons and electrons both are similar particles having the same mass only difference is their charges. Positrons are positively charged while electrons are negatively charged.

Modified Law of Conservation of Mass and Energy:

The total amount of mass and energy in the universe is always constant.

Einstein’s Formula for the Variation of Mass with Velocity:

When the velocity of light is comparable with that of light, then, the mass of the particle in motion is given by

Where m_o = mass of a body at rest.

m = mass of a body when moving with a velocity ‘ v ’

c = velocity of light in vacuum.

This relation is known as Einstein’s formula for the variation of mass with velocity. This relation shows that the mass of a body increases with the increase in its velocity.

Science > Physics > Work, Power, and Energy > Conservation of Energy

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