Work and Energy

• Work done by a constant force = force × distance moved in its direction.
• KE = ½mv²; gravitational PE = mgh.
• Work–energy principle: work done by driving forces − work against resistances = change in mechanical energy.
• Power P = Fv (driving force × speed).

The three quantities

Work done against gravity raising a mass m through height h is mgh; work done against friction F over distance s is Fs.

Balancing the books

Write: initial KE + initial PE + work done by driving force = final KE + final PE + work done against resistances.

P = Fv

At maximum (terminal) speed the driving force equals the resistance. At other speeds use F − R = ma with F = P/v.