Calculate work done by a force, relate net work to change in kinetic energy via the work-energy theorem, and define power as the rate of doing work.

What this dot point is asking

You need to calculate work done by a force (including when the force is at an angle to the motion), use the work-energy theorem to connect net work and change in kinetic energy, and define and calculate power.

Work done by a force

Work is done only when a force has a component along the displacement.

The $\cos\theta$ factor is important:

• Force along the motion ($\theta = 0$): $W = Fs$ (maximum positive work).
• Force perpendicular to the motion ($\theta = 90°$): $W = 0$. A centripetal force, or the normal force on a sliding box, does no work.
• Force opposing the motion ($\theta = 180°$): $W = -Fs$ (negative work, removes energy - e.g. friction).

The work-energy theorem

The total (net) work done on an object equals its change in kinetic energy.

Kinetic energy itself is $E_k = \tfrac{1}{2}mv^2$. The theorem follows directly from $F=ma$ combined with $v^2 = u^2 + 2as$.

Power

Power is how quickly work is done - the rate of energy transfer.

A more powerful engine does the same work in less time, or more work in the same time. At a steady speed against a constant resistive force, the driving power equals $Fv$.

Gravitational potential energy

Lifting a mass through a height $h$ stores gravitational potential energy $E_p = mgh$. The work you do against gravity equals the energy stored. In energy problems, total mechanical energy ($E_k + E_p$) is conserved when only gravity does work; friction or drag does negative work and converts mechanical energy to heat.