A2. Work, Power & Energy

A2. Work, Power & Energy

1. 1. Work

   • Work is done when the force applied on a body makes the body move. Amount of work is the product of the force applied and the displacement of the body in the direction of the force. It is a scalar quantity, with unit N.m
     • E.g. Man pushing a car, cyclist pedalling, body climbing stairs, throwing a ball
     • No work is done when a man pushes a wall, man standing with a load on the head
   • Work depends on (1) Magnitude of force applied (2) Displacement produced by the force
     • Work (W) = Force (F) x Displacement (S) in the direction (Cos θ) of the force. W = F.S Cos θ Joules
       • Product of two vectors is a scalar
       • 1 Joule is the work done when a force of 1 newton displaces a body through a distance of 1m in the direction of the force
         • 1 kJ = 10^3 J, 1 MJ = 10^6 J, 1 GJ = 10^9 J
       • 1 erg is the work done when a force of 1 dyne displaces a body through a distance of 1cm in the direction of the force
         • 1 J = 1 N x 1m = 10^5 dyne x 1m = 10^5 dyne x 10^2 cm = 10^7 dyne.cm = 10^7 erg

2. 2. Power

   • Power (P) = Work (W)/Time (t) Watt (or J/s)
     • Power depends on work done (directly proportional) & time taken (inversely proportional)
     • 1 Watt is the Power spent if 1 Joule (or 10^7 erg) of work done in 1 sec
       • 1 µW = 10^-6 W, 1 mW = 10^-3 W, 1 kW = 10^3 W, 1 MW = 10^6 W, 1 GJ = 10^9 W
         • 1 W = 1 J/s = 10^7 erg/s
           • 1 HP = 746 W; Used as a unit of power primarily in mech. engg
   • Rate of doing work or work done in unit time. It is a scalar quantity

3. 3. Energy (Work Done)

   • Capacity of a body to do work. It is a scalar quantity
   • No transfer of energy or work done if body is acted upon by a force normal to the direction of displacement. E.g. body moving in a circular path Centripetal force is normal to displacement, θ = 90 deg, so Cos θ = 0
   • Energy = Work; Unit = Joules (J), erg , Watt Hour (Wh), Calorie (Cal), Electron Volt (eV)
     • 1 Wh is the energy spent or work done by a source of 1 W power in 1 hr; 1 kWh is the energy spent by a source of 1 kW power in 1 hr
       • 1 Wh = 1 Watt x 1 hour = 1 J/s x 3600 s = 3600 J
       • 1 kWh = 1 kW x 1 hour = 1000 J/s x 3600 s = 3.6 x 10^6 J = 3.6 MJ
     • 1 Calorie is the heat energy required to raise the temp of 1g of water from 14.5 deg C to 15.5 deg C
       • 1 Cal = 4.18 J, 1 kCal = 4180 J
     • 1 eV is the energy gained by an electron when it is accelerated through a potential difference of 1 volt
       • 1 eV = charge of an electrol x 1 V = 1.6 x 10^-19 C x 1 V = 1.6 X 10^-19 J
   • W & kW are units of Power, Wh & kWh are units of work or energy
   • 3.1 Mechanical Energy
     • Potential Energy
       • Energy possessed by a body at rest due to its position or size and shape
         • E.g. Body placed at a height above ground, a bent bow, stretched rubber band
       • Gravitational Potential Energy (U)
         • Potential energy possessed by a body due to the force of attraction of earth on it (gravity or weight)
           • U = Force (mg) * Displacement (h) = mgh
           • Work is done against gravity (F = mg) in lifting the body to a height h. This energy (mgh) is stored as gravitational potential energy
       • Elastic Potential Energy
         • Potential energy possessed by a body in its deformed state dur to change in size or shape.
           • Work is done in deforming the body (changing the size or shape of the body). This is stored as elastic potential energy
       • E.g. Potential to Kinetic energy - Hammer hitting a nail,, Watch spring, Bow & Arrow, Compressed spring
     • Energy possessed by a body due to its state of rest or of motion
     • Kinetic Energy (K)
       • Energy possessed by a body due to its state of motion. It is the work that can be done by the moving body before it comes to rest
         • K = (1/2).mv^2
           • K = (1/2) mv^2 = (1/2).m.(p/m)^2 = (p^2)/2m OR p^2 = 2mK
       • Work Energy Theorem
         • Increase in Kinetic Energy of a moving body is equal to work done by a force acting in the direction of the moving body
           • Work Done (W) = Force (ma) x Displacement (S) ; v^2 - u^2 = 2aS i.e. S = (v^2 - u^2)/2a; Substituting...W = ma*(v^2-u^2)/2a = (1/2) m*v^2 - (1/2) m*u^2 = Increase in Kinetic energy
       • Translational kinetic energy
         • Due to motion of the body in a straight line path. E,.g. Car moving in a straight path, a falling body, molecule of a monoatomic gas
         • Rolling Ball, Rotating car wheel has Translational & Rotational kinetic energy
       • Rotational kinetic energy
         • Due to body rotating about an axis. E.g. Spinning top., Rotating wheel, fan
       • Vibrational kinetic energy
         • Due to a body vibrating to and fro about its mean position. E.g. guitar strings, steel strip clamped at one end and disturbed at the other end
       • Atoms of a moving polyatomic molecule rotate about a fixed axis, in a straight line (?) & also vibrate about their mean position. Hence they have translational, rotational & vibrational kinetic energy

4. Different Energy Forms

   • Wind
   • Nuclear
   • Light
   • Chemical
   • Geo Thermal
   • Electrical
   • Hydro
   • Solar
   • Heat
   • Sound
   • Magnetic
   • Mechanical
   • Energy Conversion
     • Mechanical <-> Electrical Dynamo <-> Motor
     • Electrical <-> Heat Electric heater/oven/geyser <-> thermocouple
     • Electrical <-> Sound Loudspeaker/Bell <-> Microphone
     • Electrical <-> Chemical Battery Charging <-> Drawing current from battery
     • Chemical <-> Light Candle, Kerosene Lamp <-> Photosynthesis
     • Electrical <-> Light Electric Bulb <-> Photoelectric Bulb, Solar cell
     • Heat - Mechanical Steam engine...steam to kinetic energy
     • Chemical - Heat Burning of fuel, Crackers, Candle, Match, Respiration
     • Chemical - Mechanical Automobiles burning fuel to move pistons, wheels
     • Electrical - Magnetic Electromagnet
     • Nuclear - Electrical Nuclear fission or fusion based power plant
     • Mechanical - Heat Heating of moving parts of a machine, water falling to ground
     • Energy degrades (loss) when transforming from one form to another, and is lost to the surrounding. Cannot be put to any productive use

5. Conservation of energy

   • Principle of conservation of energy states that energy can neither be created nor destroyed. It can only be transformed from one form to another
   • Potential & Kinetic energy for a body in vertical motion (gravity)
   • Potential & Kinetic energy for a simple pendulum in motion

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