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Energy, Work, and Power

ENERGY
  • Energy is the amount of work done and it is measured in Joules (J)
  • An object may have energy due to its motion or its position.
  • The Law of Conservation of Energy states that the total energy of an isolated system cannot change – it is conserved over time.
  • An example of conservation of energy: A book on a shelf has GPE. If it falls off the shelf, it will have K.E
  • Energy can be neither created nor destroyed, but can change form.
  • Energy can be stored.

Deriving Kinetic Energy

  • W = Fs and F = ma
  • ∴ W = ma • s
  • v2 = u2 + 2as ⇒ as = 1/2 (v2 – u2)
  • ∴ W = m • 1/2 (v2 – u2); the initial velocity, u = 0
  • ∴ W = 1/2 mv2
  • Kinetic Energy (K.E.) = 1/2 × Mass × Velocity2 = 1/2 mv2
Gravitational Potential Energy (GPE)
  • Gravitational Potential Energy arises in a system of masses where there are attractive gravitational forces between them.
  • The GPE of an object is the energy it possesses by virtue of its position in a gravitational field.
  • Elastic Potential Energy arises in a system of atoms where there are either attractive or repulsive short-range inter-atomic forces between them.
  • Electric Potential Energy arises in a system of charges where there are either attractive or repulsive electric forces between them.

Deriving Gravitational Potential Energy

  • W = Fs and F = mg
  • ∴ W = mg • s
  • s in the direction of the force = h above ground
  • ∴ W = mgh
  • Gravitational Potential Energy (GPE) = Mass × Gravity × Heightmgh
Internal Energy
  • Internal energy is the sum of K.E. of the molecules due to its random motion and the P.E. of the molecules due to the inter-molecular forces.
  • Gases: K.E. >  P.E.
    • Molecules are far apart and in continuous motion; K.E.
    • Weak inter-molecular forces are so very little; P.E.
  • Liquids: K.E. ≈ P.E.
    • Molecules are able to slide past each other; K.E.
    • Inter-molecular forces is present; P.E.
  • Solids: K.E. < P.E.
    • Molecules can only vibrate; K.E. is very little
    • Strong inter-molecular forces; P.E. is high
Energy Resources
  • Renewable sources are not exhaustible.
  • Non-renewable sources of energy are exhaustible.

  • The sun is the source of energy for all our energy resources, except geothermal, nuclear, and tidal.
  • In the sun, energy is created through a process called nuclear fusion; hydrogen nuclei are pushed together to form helium.
    WORK
    • Work is done whenever a force makes something move.
    • The unit of work is the Joule (J).
    • 1 Joule of work = The force 1 Newton moves an object by 1 meter.
    • Work done by a force is the product of the force and the displacement in the direction of the force.
      • W = Fs
      • Work done (J) = Force (N) × Distance (m)
    • Work done by an expanding gas is the product of the force and the change in the volume of the gas.
      • W = p • δV
      • Condition for the formula:
        • The temperature of the gas is constant
        • The change in the distance of the piston, δx, is very small, therefore, it is assumed that p remains constant.
    POWER
    • Power is the rate of work done (work done per unit of time).
    • The unit of power is Watts (W)
    • 1 W = 1 J/s
    • Power = Work Done (J)/Time Taken (s)
    • Deriving it to form P = Fv
      • P = W/t and W = Fs
      • ∴ Fs/t = F(s/t) and v = s/t
      • ∴ P = Fv
    • Efficiency is how much useful work is done with the energy supplied; it is the ratio of (useful) output energy of a machine to the input energy.
    • Efficiency = Useful Energy Output/Total Energy Input × 100%
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