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 × Height = mgh

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
  • ∴ F^s/_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%