A.3.5—Work-energy change

Work–energy theorem

The net work done by the resultant force on a system equals its change in kinetic energy:

$$W_{net}=\Delta E_k$$

Use force–distance area

For a variable resultant force, the signed area under the force–distance graph gives the work and therefore the kinetic-energy change.

Include all resultant forces

Friction, applied forces and gravity may each do work. Add their signed contributions before relating the result to the final kinetic energy.

Worked example from local Question Bank row 31356

A constant net force of $100\,\mathrm{N}$ moves an object from rest through $2.0\,\mathrm{m}$ until its speed is $10\,\mathrm{m\,s^{-1}}$.

$$W_{net}=Fs=(100)(2.0)=200\,\mathrm{J}$$
$$200=\Delta E_k=\frac12m(10)^2-0$$
$$m=4.0\,\mathrm{kg}$$

The positive net work is exactly the object's kinetic-energy gain.

Common trap

Do not use the work of one force as the net work unless all other force contributions are zero or already included.