- Work
- Work = Force x displacement
- work done by the force – displacement of body occurs in the direction of force.
- work done against the force – displacement of body against the direction of force.
- work is zero when the force acts perpendicular to the desired direction of movement
- When a work is done by a force, both force and displacement are positive , and the work done is also positive. W = F x S
- When the work is done against the force, then force has a positive sign, but displacement has a negative sign and the work done has a negative sign. W = F x (-S).
- Unit of work – Joule
- W = F x S = N x m
- 1 Nm = 1 J
- 1kJ = 1000 J – 10
^{3}J - 1MJ = 1 mega joule = 10
^{6}J

- Power (P)
- Rate of doing work is called power.
- Power = work / time
- P = w/t
- Unit of power = watt
- 1 watt = 1 J
^{s-1} - 1 kW = 1000 W
- 1 MW = 10
^{6}W

- Energy
- Capacity to do a work is called energy.
- Energy is invisible, but work is not.
- Practical unit of consumption of energy = unit
- 1 unit = 1kWh = 1000 W for one hour
- 1 unit = 1000w x 3600 s = 3600000 = 3.6 x 10
^{6}J

- Different forms of energy
- Kinetic energy
- Potential energy
- Wind energy
- Solar energy
- chemical energy
- light energy
- heat energy

- Law of conservation of energy
- Energy can neither be created nor be destroyed.
- It can only be changed from one form to another.

- System and surrounding
- System – portion of the Universe under observation
- Surrounding – the remaining portion of the Universe.
- Wall (boundary) – distinguishes system from the surrounding.

- Types of system (based on the nature of wall)
- Open system – both mass transfer and heat transfer occur between system and surrounding.
- Closed system – no mass transfer, but there is heat transfer
- Isolated system – neither mass transfer nor heat transfer, system is totally isolated from the surrounding by adiabatic wall.
- nature of adiabatic wall – does not allow heat transfer

- Mechanical energy
- The energy acquired by objects upon which work is done.
- Work done causes increase in speed – kinetic energy
- State of strain or increase in height – potential energy

- Kinetic energy
- KE = 1/2 mv
^{2} - where m = mass, v = velocity
- Energy possessed by movement of a body is called kinetic energy.
- unit of mass = kg
- unit of velocity = ms
^{-1} - unit of KE = kgm
^{2}s^{-2 }= J

- KE = 1/2 mv
- Potential energy
- PE = mgh
- where, m = mass; g = acceleration due to gravity, h = height
- Energy possessed by a body by virtue of its position
- Unit of PE = kg. ms
^{-2}. m = kgm^{2}s^{-2 }= J - value of g = 9.8 ms
^{-2}

** Derivation of kinetic energy**

Work done on an object is given by

W = F x S ………. (1)

where,

F = Force

S = Displacement

We know,

F = ma …………. (2)

Substituting the value of F in eqn. 1

W = m.as …………. (3)

According fundamental laws of motion,

v^{2} = u^{2} + 2as …………. (4)

(v^{2} – u^{2})/2 = as ………… (5)

Substituting the value of as in eqn. 3

W = m . (v^{2} – u^{2})/2

when initial velocity, u = 0

W = mv^{2}/2

KE = (1/2) mv^{2}

**Derivation of potential energy**

W = F . s

where, s = displacement = height = h

F = mg

where, g = acceleration due to gravity, g = 9.8 ms^{-2}.

W = mgh

PE = mgh

What is the PE of the body kept on the Earth?

Since h = 0,

PE = mgh = m.g. (0) = 0

PE = 0

Conservation of Mechanical Energy

- Consider a body of mass, m, freely falling from a height, h.
- The total mechanical energy is constant at each point of the journey of the falling body.
- In other words, the total mechanical energy is conserved.
- TME, Total mechanical energy = PE + KE = mgh

**At A (initial position of freely falling body
**

PE = mgh , KE = 0. since v = 0

TME = PE + KE = mgh + 0 = mgh

TME at A = mgh …………. (1)

**At C (when the body is about to reach the ground)
**

PE = mgh = m.g. (0) = 0, because, h = 0

KE = 1/2 . mv^{2}

According fundamental laws of motion, v^{2} = u^{2} + 2as

s = h, a = g, initial velocity, u = 0

v^{2} = 0 + 2gh

KE = 1/2 . m . 2gh

KE = mgh

TME at C = PE + KE = 0 + mgh = mgh

TME at C = mgh ………………….(2)

**At B (any position during the free falling)**

PE = mgh

h = h-x

PE = mg(h-x)

KE = 1/2 . mv^{2}

s = x, a = g, u = 0

According fundamental laws of motion, v^{2} = u^{2} + 2as

v^{2} = 0 + 2gx

KE = 1/2. m. 2gx = mgx

TME at B = PE + KE

TME at B = mg (h-x) + mgx = mgh – mgx + mgx

TME at B = mgh ……………….. (3)

Total mechanical energy is constant at A, B and C , that is equal to mgh. Hence the total mechanical energy is conserved.