SL and HL: Work is a mechanism for energy transfer. When a force acts through a displacement, the work done by that force equals the energy transferred to or from the system.
For a constant force, work is calculated using
where is the force, is the displacement, and is the angle between the force and displacement. Work and energy are both measured in (J), where .
The angle determines how much of the force transfers energy:
| Direction of force | Work and energy transfer |
|---|---|
| Force parallel to displacement, | Positive work: energy is transferred to the system. |
| Force opposite to displacement, | Negative work: energy is transferred from the system. |
| Force perpendicular to displacement, | Zero work because . |
For example, a horizontal force of moves a box in the same direction:
Therefore, the force transfers of energy to the box. If this is the resultant force, the work-energy theorem states that the net work equals the change in kinetic energy:
Work can also transfer energy between stores. Lifting an object transfers energy to its gravitational potential energy, while compressing a spring transfers energy to its elastic potential energy.
A common misconception is that a force always does work. It does not: a centripetal force is perpendicular to instantaneous displacement, so it changes the direction of velocity but transfers no energy and does no work.
For a Calculate question, show the equation, substitution, angle and answer. For an Explain question, link force, displacement and energy transfer explicitly; do not merely state that “energy is used.” This is syllabus topic A.3, Work, energy and power, for both SL and HL.
