Work, Power & Energy Resources

Energy equivalence in a perfect transfer

• When a force acts through a distance, the energy that leaves one store and enters another equals the work done by that force (mechanical pathway)
• In a perfect transfer (one with no friction or air resistance), no energy is dissipated as waste, so the full amount can be equated:

energy in one store before = energy in another store after

• The phrase "ignore air resistance" or "ignore frictional effects" in an exam question is the signal that you should use this energy-equivalence shortcut

Pendulum: GPE ↔ KE swap

• A swinging pendulum bob exchanges energy back and forth between its two stores on every swing:
  • At the highest point of the swing, the bob is momentarily at rest. All its energy sits in the gravitational potential store
  • At the lowest point of the swing, the bob is at its fastest. All its energy sits in the kinetic store
• For a frictionless pendulum, the maximum GPE at the top equals the maximum KE at the bottom:

m × g × h_max = ½ × m × v_max²

• The mass cancels from both sides, leaving:

v_max = √(2 × g × h_max)

Rollercoaster: same idea on a track

• A rollercoaster carriage starting at rest at the top of a tall hill arrives at the bottom with maximum speed; all the GPE lost during the descent has been converted to KE (ignoring friction and air drag)
• The maximum speed depends only on the drop in height, not on the route the track takes between the top and bottom