Energy, Momentum, and Conservation Laws
What this domain tests
Energy, momentum and conservation laws: work, kinetic and gravitational potential energy, power, efficiency, momentum, impulse, collisions, and the principle that total energy and total momentum are conserved in a closed system.
Core rules
- Work W = Fs cosθ; power P = W/t = Fv; efficiency = useful output ÷ total input × 100%.
- KE = ½mv²; ΔGPE = mgΔh; elastic PE = ½kx².
- Energy is conserved but degraded to thermal energy by friction, so always account for it.
- Momentum p = mv is a vector; impulse Ft = Δp = m(v − u).
- Total momentum before an interaction equals total momentum after, in any collision or explosion.
- Elastic collisions conserve KE; inelastic collisions do not, and objects may stick together.
Worked example
A 0.02 kg bullet at 400 m s⁻¹ embeds in a 1.98 kg block at rest. Momentum before = 0.02 × 400 = 8 kg m s⁻¹. After: (0.02 + 1.98)v = 8, so v = 4 m s⁻¹. KE before = ½ × 0.02 × 400² = 1600 J; KE after = ½ × 2 × 16 = 16 J. So 1584 J became heat and deformation. The collision is inelastic: momentum is conserved, kinetic energy is not.
Traps that cost marks
- Giving momentum without direction, or adding opposing momenta as if both were positive.
- Assuming kinetic energy is conserved in every collision.
- Reporting efficiency above 100% because input and output units differ.
- Forgetting that work done against friction leaves the mechanical system as heat.
- Using total mass only after a collision, not before.