Unit 5: Work, Energy and Power

• Principle of conservation of energy:

  • Energy can neither be created nor destroyed, only transferred into alternative forms of energy
  • Total energy in a closed system will always remain the same
• Definition of work done:

  • Work done is equal to the energy transferred usefully
  • It is the product of the force applied and the displacement moved in the direction of the force
• Definition of kinetic energy:

  • The energy associated with the motion of an object with mass
  • SI base unit is J and its SI base unit is kgm^2s^-2
  • Formula: Ek = 1/2 mv^2
• Definition of gravitational potential energy:

  • The energy stored by an object at a point in a gravitational field
  • Formula: GPE = mgΔh
• Definition of elastic potential energy:

  • The energy stored by an object as a result of a reversible change in an object’s shape
  • Formula: EPE = 1/2kx^2 where k is spring constant N/m and x is the extension in m
• Formula for the velocity of an object in a gravitational field:

  • All initial GPE is converted to KE as the object falls, and this KE is converted back to GPE as it rises
  • Equation: mgh = 1/2 mv^2
  • Rearranging gives v^2 = 2gh, so v = 2gh^(1/2)
  • The velocity of the object is independent of mass
• Rate of work done is equal to:

  • Power
• Definition of efficiency:

  • Efficiency (%) = (The useful output energy / total input energy) x 100 = (The useful output power / total input power) x 100
• How to maximize efficiency:

  • By minimizing energy losses into non-useful forms
  • Reduce friction, air resistance, noise generation, heat production, etc., in a system designed to do work
• Calculation of work done by an expanding gas:

  • Work done = pΔV where p is pressure (constant) and ΔV is the change in the gas’s volume
• Increasing efficiency of a system losing energy due to friction:

  • Lubricate parts of the system and reduce the number of parts that touch
• Derivation of power as the product of force and velocity:

  • Power = force x displacement / time
  • Power = force x velocity