WORK AND ENERGY.

Work Done

Work done on an object is defined as the product of the magnitude of the force acting on the body and the displacement in the direction of the force. W = F.s

If a force acting on a body causes no displacement, the work done is 0. For example, pushing a wall.

Energy is defined as the ability to do work. Its unit is same as that of work.
SI unit of energy or work = Joule (Nm) or $K g m^{2} s^{- 2}$ .
Energy has different forms: Light, heat, chemical, electrical or mechanical.
Mechanical energy is the sum of:
(i) Kinetic energy (K.E)
(ii) Potential energy (P.E)

Objects in motion possess energy and can do work. This energy is called Kinetic Energy.
F = ma.
Also W = F.s
From 2nd equation of motion

v^{2} - u^{2} = 2 a s,

we get s =

\frac{v^{2} - u^{2}}{2 a}

Substituting in equation for work done by a moving body,
we get W

= m . a \times \frac{v^{2} - u^{2}}{2 a}

Or,

K . E = \frac{1}{2} m v^{2}

(taking initial velocity

u = 0

)
When two identical bodies are in motion, the body with a higher velocity has more K.E.

The work-energy theorem states that the net work done by a moving body can be calculated by finding the change in KE.
$W_{n e t} = K E_{f i n a l} - K E_{i n i t i a l}$
$W_{n e t} = \frac{1}{2} m [v^{2} - u^{2}]$

Energy can get stored in an object when work is done on it. For example, stretching a rubber string.
The energy that is possessed by a body by virtue of its configuration or change in position is known as Potential Energy.

When an object is raised to a certain height, work is done against gravity to change its position. This energy is stored as Potential Energy.
W = F.s
F = ma
In the case of increasing the height, F = mg
$∴$ W (P.E) = mgh
$Δ P E = m g (h_{f i n a l} - h_{i n i t i a l})$

Law of conservation of energy states that energy can neither be created nor destroyed, but can be transferred from one form to another. The total energy before and after the transformation remains constant.
Total energy = KE + PE
For example, consider a ball falling freely from a height. At height h, it has only PE = mgh. By the time it is about to hit the ground it has a velocity and therefore has $K E = \frac{1}{2} m v^{2}$ . Therefore, energy gets transferred from $P E$ to $K E,$ while the total energy remains same.

The rate of doing work or the rate of transfer of energy is called power.
$P = \frac{W}{t}$
SI unit is Watt $(J s^{- 1})$ .
Average power $= \frac{T o t a l e n e r g y c o n s u m e d}{T o t a l t i m e t a k e n}$
The commercial unit of power is kWh i.e. energy used in 1 hour at 1000 Joules/second.
$1 k W h = 3.6 \times 10^{6} J$