Work and mechanical energy

For a constant force parallel to displacement, work is W= Fs. A force opposing displacement does negative work; a perpendicular force does zero work. More generally W= Fs cosθ, where θ is the angle between force and displacement. Work transfers energy, with joules equivalent to newton-metres. Net work on a particle equals its change in kinetic energy.

Kinetic energy is Ek= ½mv2, so it depends on speed squared and is never negative. Near Earth, a gravitational potential-energy change is ΔEp= mgΔh with approximately constant g. Choose a reference height, but remember that physical transfers depend on height differences. Distinguish the work of one force from the net work of all forces.

Watch out: Kinetic energy is proportional to speed squared, so doubling speed multiplies it by four at fixed mass.