E1.5 Work, Energy and Power (Kinetic Energy):

Energy is a central concept in Physics. It can be defined as the capacity for doing work. But, it is important to understand that just because energy exists, not necessarily available to do work.

Energy can not be create or destroyed, but it can change from one form to another form.

There are many types of energy such as: Mechanical energy, chemical energy, light energy, thermal energy, electrical energy etc. Mechanical energy further divided into two parts called: Kinetic Energy and Potential Energy. Here, we mainly focused on these two energy.

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Kinetic Energy: 

Kinetic energy is the energy of motion. It is a capacity of doing work due to its motion. There are many forms of kinetic energy - vibrational (energy due to vibrational motion), rotational (energy due to motion in circle) and translation (energy due to motion in straight line). Here, we will focus upon translation kinetic energy to keep matters simple.

In classical mechanics, the kinetic energy of an (translation) object has depends upon mass (m) and velocity (v) of an object. i.e.

$K.E. = \frac{1}{2}mv^2$

In relativistic mechanics, this is a good approximation only when $v$ is much less than the speed of light.

The amount of kinetic energy an object has depends on the mass and speed of the object.

All moving object have the kinetic energy. The faster object has more speed and has more kinetic energy. 

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» Calculation of Kinetic Energy:

Consider a body of mass $m$ lying on a horizontal surface. After applying a force $F$, the body travel a distance $d$ with a moving velocity $v$.

As we know from the definition of work:

W = force * distance = $F * d$ .......... (i)

From the Newton's law of motion:

$F = ma$ .......... (ii)

And from the Kinematics, we know the formula:

$v^2 = u^2 + 2ad$ .......... (iii)

If the initial velocity of a body is at rest, so the initial velocity is zero ($u = 0$), then equation (iii) becomes,

$ad = \frac{v^2}{2}$ .......... (iv)

From equation (i), (ii) and (iii), we have

$W = F * d = ma *d $

 $= m * ad = m * \frac{v^2}{2}$

Thus, 

∴ $W = K.E. = \frac{1}{2}mv^2$ .......... (v)

Where, m - mass and v = velocity of  a body.

This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means, for a two fold increase in speed, the kinetic energy will increase by the factor four and so on.

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