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Energy

Work is always done at the expense of energy of the agency doing work. Man, animal or machine requires energy to do work. Energy is spent when a force does the work on an object. Energy can be defined as the capacity to do work. Hence, it is measured in the same units as that of work. In other words, energy changes are involved whenever work is done. The unit of energy is the same as the unit of work, i.e., joule.

Commercial Unit of Energy

The unit joule is too small and hence is inconvenient to express large quantities of energy.
 
The most convenient unit to measure large quantities of energy such as electrical energy is kilowatt hour (kWh).

The energy used in households, industries and commercial establishments are usually expressed in kilowatt hour.
 
For example, electrical energy used during a month is expressed in terms of units. Here, one unit means 1 kilowatt hour.

1 kilowatt hour = 3.6 × 106 J (i.e., the work done at the rate of 1000 Js−1 for a period of 1 hour).

Forms of Energy

 
Description: 66314.png
 

Mechanical Energy
 
Mechanical energy is the energy associated with the motion of a body (kinetic energy) or the energy stored in the body (potential energy). Thus, we can define mechanical energy as the energy associated with a body due to its position, configuration or motion. The total mechanical energy (E) is the sum of potential energy (U) and kinetic energy (T), i.e., E = U T.
 
Potential Energy
 
The energy stored in a body by virtue of its position or configuration is called potential energy.
 
Position-dependent Potential Energy
 
Consider a brick lying on the ground near a building. As such, this brick seems to have no energy. If we can carry this brick to the top of the building, we do some amount of work against the gravitational force. In other words, we spend some amount of energy. This energy spent by us is stored in the brick in the form of potential energy. It must be kept in mind that potential energy is dormant or latent in nature, i.e., it does not show by itself unless released.
 
For example, the brick on the top of the roof does not seem to have energy. However, if we drop the brick from the roof, its potential energy is released and hence work is done.
 
Similarly, water stored in water tanks and in dams, the water carried by the clouds in the form of tiny droplets, an aeroplane or a helicopter in the sky possess potential energy due to their position, above the earth’s surface.
 
Description: 67216.png
Figure 6.4 Gravitational Potential Energy

 

Mathematical Representation for Gravitational Potential Energy
 
Consider a body of mass m, being raised vertically upward through a height h, against the force due to gravity (Figure 6.4).
 
Force applied on the body for lifting mg
Total work done in lifting the body = Force  Height
  mg × h
  mgh
  = Energy spent in lifting the body
 
 
Thus, energy spent in lifting the body is stored in the form of potential energy. Thus,
Potential energy U mgh
 
Configuration-dependent Potential Energy
 
When a spring is stretched or compressed, work is done against the elastic forces binding the atoms, in the process of deforming the original shape. The energy stored in a stretched or compressed spring is called elastic potential energy.
Other examples of potential energy possessed on account of the configuration are
  1. a stretched rubber band,
  2. a wound spring of a watch or a toy car,
  3. stretched string of a bow and catapult and
  4. compressed air in a container.
Kinetic Energy
 
Consider examples such as flowing water can turn the blades of a water mill (or turbine), a swinging bat can hit a cricket ball over the boundary, the blowing air can rotate the blades of a wind mill, etc. In all these cases, it is the motion of bodies which is responsible for doing work. Therefore, motion is responsible for the energy possessed by them. A moving vehicle, a moving cycle, flowing water, blowing wind, etc., possess energy. The energy possessed by a body by virtue of its motion is called kinetic energy.
 
Thus, the objects acquire kinetic energy due to motion.
 
Mathematical Expression for Kinetic Energy
 
Consider a body m at rest. Let a force F be applied to it causing a constant acceleration a. The body attains a final velocity v through a displacement s. Kinetic energy is measured in terms of the work done on the body.
 
Kinetic energy = Work done by the force Description: 63552.png = Fs = (ma)s  [∴ cos 0° = 1]
 
But, from the equation of motion, we have
v2 = u2 + 2as, where u and v denote the initial and final velocities, respectively. Thus,
Description: 63570.png   [ initial velocity u = 0]
 
Substituting the above expression for sa in the expression for work done, we get,
 
Kinetic energy Description: 63585.png 
 
Transformation of Energy
 
Energy can be obtained in different forms and can be transformed or converted from one form to another.
 
The change of one form of energy into another form is called transformation of energy.
 
For example, when an electric current is passed through the filament of a bulb, the electrical energy is first converted into heat as the filament becomes red hot and then as temperature increases it emits light.
 
Transformation of Energy
 
From
To
Example
PE
KE
Water let out through gates from a dam
KE
PE
Water flowing in a river stored in a dam
Electricity
Heat
Bulb
Heat
Electricity
Thermal power plants
Mechanical
Heat
Rubbing parts of a machines
Heat
Mechanical
Steam engine
Electricity
Mechanical
Motor
Mechanical
Electricity
Generator
Chemical
Electricity
Cell
Electricity
Chemical
Electrolysis, storage batteries
Electricity
Light
Bulb
Light
Electricity
Solar cells
Electricity
Sound
Electric bell, speaker, thunder
Sound
Electricity
Mike or microphone
Nuclear
Light, heat and electricity
Nuclear reactor, nuclear bomb
Infrared radiations
Heat
Solar heater, solar cooker
Heat
Light
Bulb, carbon are lamp in a projector, lightning


The Law of Conservation of Energy
 
According to the law of conservation of energy, energy can be transformed from one form to another form, but the total amount of all the energy remains the same. In other words, energy can neither be created nor destroyed but can only be transformed from one form to another.

 

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