Work, energy, power, momentum and impulse
Work, energy, power, momentum and impulse
This domain covers scalar energy methods and vector momentum methods. Expect work-energy calculations, power, conservation of momentum, impulse and collision problems with restitution.
Core rules
- Work done by a constant force is Fd cos θ; for a variable force, work = ∫F dx. Kinetic energy = ½mv²; gravitational potential energy = mgh.
- Work-energy theorem: total work done = change in kinetic energy. Mechanical energy is conserved only when no non-conservative work is done.
- Power is work done per unit time: average P = W/t; instantaneous P = Fv.
- Impulse = ∫F dt = change in momentum. Momentum is conserved in a collision or explosion when no external resultant force acts.
- For direct collision, coefficient of restitution e = relative speed of separation / relative speed of approach, with 0 ≤ e ≤ 1. Kinetic energy is lost unless e = 1.
Worked example
A 0.2 kg ball falls 1.8 m and rebounds to 0.8 m. Impact speed = √(2 × 9.81 × 1.8) = 5.94 m s⁻¹; rebound speed = √(2 × 9.81 × 0.8) = 3.96 m s⁻¹. Thus e = 3.96/5.94 = 0.67.
Common traps
Treating momentum as a scalar and ignoring signs; assuming kinetic energy is conserved in every collision; using average power as instantaneous power; forgetting that friction does negative work; and substituting energies into the restitution formula instead of speeds.