Energy, Work, and Momentum
Energy, Work, and Momentum
This domain tests conservation laws: work and the work-energy theorem, kinetic and potential energy, power, impulse and momentum, collisions, and center of mass. Many exam items ask which quantity is conserved under stated conditions.
Core rules and concepts
- Work done by a constant force is W = Fd cosθ; only the force component along displacement does work. The normal force on a level surface does no work on a horizontally moving object.
- Work-energy theorem: W_net = ΔK. Mechanical energy is conserved when only conservative forces do work.
- Power is work per time, P = W/t = Fv cosθ.
- Impulse J = FΔt = Δp. Momentum is conserved when the net external force on the system is zero.
- Elastic collisions conserve kinetic energy and momentum; perfectly inelastic collisions conserve momentum but lose maximum kinetic energy to internal energy.
Worked example
A 0.50 kg cart moving at 4.0 m/s collides and sticks to a stationary 1.5 kg cart. Total momentum before: (0.50)(4.0) = 2.0 kg·m/s. After sticking, total mass 2.0 kg, so v = 2.0/2.0 = 1.0 m/s. Kinetic energy before: 4.0 J; after: 1.0 J. The 3.0 J loss becomes thermal and deformation energy.
Traps that cost marks
Assuming kinetic energy is always conserved; forgetting that momentum is a vector; treating friction as conservative; and confusing power with energy. In incline problems, gravitational potential energy depends on vertical height, not distance along the ramp.