Work, energy and impulse

Work is done when a force moves its point of application: work equals force times the distance moved in the direction of the force, measured in joules (newton-metres). Energy is the capacity to do work. A moving body has kinetic energy, half its mass times speed squared; a raised body has potential energy, its weight times its height; a stretched spring or a bent beam stores strain energy.

The work-energy principle says the work done by all forces on a body equals its change in kinetic energy. It is often faster than Newton's law because it skips acceleration and time. If only gravity and elastic forces act, mechanical energy is conserved, so a falling hammer turns potential energy into kinetic energy; friction, plastic deformation and impact convert some of it into heat and sound, which is why real systems need an efficiency factor.

Impulse is force multiplied by the time over which it acts, and it equals the change in momentum, mass times velocity. Momentum methods suit short, violent events where forces are large and hard to measure: a vehicle striking a crash barrier, a ship berthing against a fender, or a pile hammer blow. Spreading the same momentum change over a longer time lowers the peak force, which is the principle behind every energy-absorbing barrier, fender and cushion.

Power is the rate of doing work, in watts. It sizes pumps, hoists, conveyors and compactors. In civil practice energy ideas appear in pile driving formulas, rockfall barrier ratings in kilojoules, fender selection by berthing energy, and the energy methods of structural analysis that find deflections from stored strain energy.