Work, Energy and Power - Part III

3. Transformation of energy  
Whenever energy in one form is lost, it appears in another form. The changing of one form of energy into another is called transformation of energy. For example, the chemical energy stored in petrol is converted into heat in a car engine. This heat energy is used to move mechanical parts of the car because of which the car can move. Thus chemical energy is converted into kinetic energy. In a thermal power station the coal is burned to heat water into steam. The steam turns the turbines which in turn produces electricity. Thus the chemical energy stored in coal is converted into electrical energy. The energy that we get from food finds its origin in the solar energy.

It is important to understand the concept of transformation of energy.[1] The example of an oscillating pendulum is a very good example for understanding how one type of energy changes into another type and vice versa.  

Energy changes in a simple pendulum

A simple pendulum is hung form a point O. The bob of the pendulum with mass m, is stationary at point A. It is then set into motion from one extreme position B. The bob swings from one extreme position B to another extreme position C via position A.

You can easily observe that

1. at position A : the P.E. = 0

2. at position B : the P.E. = maximum = mgh, the bob stops for a fraction of a second, hence its 
   K.E. = 0  

3. at position C : the P.E. = maximum = mgh the bob stops for a fraction of a second, hence its 
    K.E. = 0

4. at position A, notice that the velocity of the swing is high, Thus at A the K.E. = maximum.

Thus as the bob swings back and forth, the K.E. and the P.E. vary from 0 to maximum, but in the opposite direction. That is, as the K.E. changes from 0 to maximum, the P.E. changes from maximum to 0. Thus the sum of the K.E. + P.E. remains constant.

Consider another example of a ball falling from a height h under the force of gravity.  

Energy changes in a ball falling from a height

At point A, the P.E. = mgh
The ball starts from zero velocity at A, hence its K.E. = 0

When the ball reaches the ground at position C, its P.E. = 0 and its K.E. will be maximum.

At any other position B at a distance x from the ground

K.E.  = ‡ mv² = ‡ mgx  (v² = u² + 2as, putting u = 0 and a = g , s=x, we get v² =  2 gx )

P.E. = mgx

Thus the P.E. + K.E. = mg(h - x) + mgx = mgh

Thus at any time, the total energy of the falling ball is constant.

4. Definition of power and its units  
When you lift a box from the ground to the table top, you are doing work. You can lift the box slowly or fast, the work done would be the same, as the distance though which the box has moved under the force is the same. To distinguish the fast or slowness of work done, another term is used. This new term is called power. The rate of doing work is called power.

If work done W is done in time t, then Power P = W/t

The unit of power is called a Watt in the honor of  Sir James Watt. Watt is Joules/second. Usually a larger unit is used called a kilowatt.

1 kilowatt = 10³ watt

Another unit of power called a horse power (hp) is used. 1 hp = 746 watt.

The relation between power and velocity can be calculated as follows :

P =   W    =   F.s    =   F. v
         t            t

Summary
In this chapter we have seen the definition of work and energy. We saw the different types of energy and how one type of energy can be transformed into another type. We also studied the definition of power. Units of work and energy are same; they are joules in the MKS system. The unit of power is a watt or a kilowatt.

[1] In reality mass and energy are conserved. This is given by Einsteinís famous equation E = mc². But for the present syllabus we will consider only transformation of energy.

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