Work, energy and power

Learning objectives

• Calculate work using a force component.
• Relate work to kinetic-energy change.
• Evaluate power and efficiency.

The big idea

Work done by a constant force is the component of force along displacement multiplied by displacement. A force perpendicular to motion does no work even when its magnitude is large.

The work–energy principle links net work to kinetic-energy change. Include gravitational and other stores when choosing a system, and include dissipative transfers when calculating efficiency.

1. The useful component of a force

A constant force does work W = Fs cos θ, where θ is between force and displacement. Carrying a bag horizontally at constant height involves an upward supporting force but no work by that vertical force on the idealised horizontal displacement. Real muscles can still consume energy, so distinguish work done on the bag from biochemical energy use inside the person.

2. Choose energy stores and boundaries

Net work changes kinetic energy. Near Earth, raising a mass changes gravitational potential energy by mgΔh. When friction matters, mechanical energy need not remain constant: include thermal transfers and identify the surroundings receiving energy. A 1 kg object losing 20 J gravitational energy might gain only 15 J kinetic energy if 5 J transfers elsewhere. Energy conservation still holds for the wider system.

3. Speed has a squared effect

Kinetic energy is ½mv², so doubling speed at fixed mass quadruples it. A heavier moving object also has greater kinetic energy at equal speed. For a fixed resisting force, the work–energy relationship then predicts a larger stopping distance at higher speed. This ideal model does not include changing braking force, reaction time or road conditions; identify those omissions before making a real-world claim.

4. Power describes the rate

Average power is transferred energy divided by elapsed time; instantaneous mechanical power is the scalar product of force and velocity. For parallel force and velocity, P = Fv. A motor lifting the same load twice as fast supplies twice the useful power, although the energy per lift stays unchanged. Efficiency compares useful output with total input as energy ratios or power ratios over compatible intervals.

A method you can reuse

1. Choose the object or system and name energy transfers.
2. Resolve a force along displacement when calculating work.
3. Use squared speed in kinetic energy.
4. Include dissipative transfers rather than deleting missing mechanical energy.
5. Use time only for power and matching quantities for efficiency.

Equations and relationships

Investigate and explain

Compare energy bar charts for the same release height with and without friction. Explain the extra thermal energy.

Use energy bars alongside motion and force information. Simulations can isolate friction or constant force, while real machines often have several changing loss mechanisms.

Open the interactive investigation

Check your understanding