Work, energy and power

Objective. Connect force, displacement and kinetic energy.

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Learn: the key idea

Work done by a force is the product of force and displacement in the direction of motion, W = Fd, and this work changes the kinetic energy of an object according to the work-energy theorem: work done equals the change in kinetic energy, ½mv² − ½mu². Power is the rate of doing work, P = W/t, or equivalently P = Fv for a force acting on an object moving at velocity v. For example, a car engine delivering constant power of 20kW at a speed of 10m/s exerts a driving force of 20000/10 = 2000N.

Worked example

A car of mass 1000kg accelerates from rest to 20 m/s. Find the work done by the driving force, assuming no resistance, and the power required if this takes 10 seconds at constant power.

1 $Work done equals the change in kinetic energy: W = ½mv² - ½mu²$
2 $Substitute: W = ½(1000)(20²) - 0 = ½(1000)(400) = 200000 J$
3 $Power = work done / time taken$
4 $P = 200000/10 = 20000 W$

Answer: Work = 200000 J, Power = 20000 W

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Common mistake. Students use W=Fd even when the force and displacement are not in the same direction, forgetting to resolve the force along the direction of motion first. Always use the component of force parallel to the displacement.

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