Work, Energy and Power – STD09

  1. 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 – 103 J
    • 1MJ = 1 mega joule = 106 J
  2. Power (P)
    • Rate of doing work is called power.
    • Power = work / time
    • P = w/t
    • Unit of power = watt
    • 1 watt = 1 Js-1
    • 1 kW = 1000 W
    • 1 MW = 106 W
  3. 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 106 J
  4. Different forms of energy
    • Kinetic energy
    • Potential energy
    • Wind energy
    • Solar energy
    • chemical energy
    • light energy
    • heat energy
  5. Law of conservation of energy
    • Energy can neither be created nor be destroyed.
    • It can only be changed from one form to another.
  6. System and surrounding
    • System – portion of the Universe under observation
    • Surrounding – the remaining portion of the Universe.
    • Wall (boundary) – distinguishes system from the surrounding.
  7. 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
  8. 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
  9. Kinetic energy
    •  KE = 1/2 mv2
    • 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 = kgm2s-2 = J
  10. 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 = kgm2s-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,

v2 = u2 + 2as …………. (4)

(v2 – u2)/2 = as ………… (5)

Substituting the value of as in eqn. 3

W = m . (v2 – u2)/2

when initial velocity, u = 0

W = mv2/2

KE = (1/2) mv2


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 . mv2

According fundamental laws of motion, v2 = u2 + 2as

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

v2 = 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 . mv2

s = x, a = g, u = 0

According fundamental laws of motion, v2 = u2 + 2as

v2 = 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.