Calculate mechanical work by multiplying the force by the displacement in the force's direction. Calculate power by dividing work by time, or by multiplying force by velocity for instantaneous power.
The Reasoning and Mechanism
Work occurs only when a force causes displacement. Both force and displacement are vectors, so the angle between them must be considered:
| Quantity | Formula | Meaning |
|---|---|---|
| Work | Energy transferred by a force through a displacement, measured in joules | |
| Average power | Rate of work over a time interval, measured in watts | |
| Instantaneous power | Power at a particular moment |
The cosine term selects the component of force parallel to movement. Positive work transfers energy to the athlete or object, while negative work removes energy, such as during braking.
If force and displacement are in the same direction, and , so . If they are perpendicular, no mechanical work is done by that force.
For example, a sprinter applies an average horizontal propulsive force of through a displacement of :
If this takes , average power is:
For an angled pulling force of acting through at , the parallel component is , so the work done is .
When analysing vertical movement, gravitational work may be negative during ascent and positive during descent. Use net force only when calculating net work; otherwise identify the work done by each individual force.
This links to Newton's second law in subtopic B.2.1 because an unknown net force can be found using . The work-energy theorem states that net work equals the change in kinetic energy: .
Exam Technique
State the force being analysed, include the angle, substitute SI units, and distinguish average from instantaneous power. A common misconception is that holding a stationary weight involves mechanical work; because displacement is zero, external mechanical work on the weight is zero, although the muscles still use metabolic energy.