Learning outcomes
- Describe energy stores and transfer pathways.
- Apply conservation of energy.
- Calculate work, kinetic energy and gravitational potential-energy change.
- Recognise dissipated energy and avoid “energy lost” language.
11.1 Energy stores and pathways
Energy can be stored kinetically, gravitationally, chemically, elastically, nuclearly, electrostatically and internally (thermally). Energy is transferred between stores by mechanical work, electrical work, heating and waves including light and sound.
Describe an event by identifying the initial store, transfer pathway and final stores. In a battery-powered toy car, energy begins in a chemical store, is transferred electrically to the motor, then mechanically to the car’s kinetic store, while some increases internal stores and is carried away by sound.
11.2 Conservation and dissipation
The total energy of a closed system is conserved. Energy is never created or destroyed. In real processes, some energy becomes spread into the internal energy of surroundings and is less useful. This is called dissipation, not disappearance.
When an object falls, gravitational potential energy decreases. If air resistance is negligible, kinetic energy increases by the same amount. With air resistance, some energy is transferred to internal energy of the air and object, so the kinetic gain is smaller.
11.3 Work
Work is energy transferred by a force moving through a distance in the force direction: W = Fd. One joule is the work done by a force of 1 N moving its point of application 1 m in the force direction.
If force is perpendicular to motion, no work is done by that force. The normal contact force on a horizontally moving box does no work because there is no vertical displacement, although friction can do negative work by removing kinetic energy.
11.4 Kinetic energy
Kinetic energy is Eₖ = ½mv². Doubling mass doubles kinetic energy at the same speed; doubling speed multiplies kinetic energy by four. This square relationship explains why high-speed collisions and braking require much more energy transfer.
Use kilograms and metres per second. Do not substitute velocity with a negative sign and report negative kinetic energy; kinetic energy is a scalar and depends on v².
11.5 Gravitational potential energy
Near Earth’s surface, change in gravitational potential energy is ΔEₚ = mgΔh. The height change is vertical, not the distance travelled along a slope. Raising an object transfers energy to its gravitational store; lowering it decreases that store.
If the object starts and ends at the same height, the net GPE change is zero, regardless of the path. Work done against friction along a longer path can still make the total input energy larger.
Worked examples
Work doneA 35 N force moves a box 4.0 m in the force direction. W = 35×4.0 = 140 J.
Kinetic energyA 1200 kg car travels at 15 m s⁻¹. Eₖ = ½×1200×15² = 135 000 J.
GPE changeA 3.0 kg bag is lifted vertically 2.5 m. ΔEₚ = 3.0×9.8×2.5 = 73.5 J.
Energy balanceA 2.0 kg object falls 5.0 m. GPE decrease ≈ 98 J. If kinetic energy increases by 80 J, about 18 J has been dissipated to internal energy and sound.
Practical focus
InvestigationInvestigate GPE to KE transfer using a trolley descending a ramp. Measure vertical height rather than ramp length. Estimate final KE from speed and compare with mgh, then explain the difference using friction, wheel rotation and measurement uncertainty.
Examination guidance
- Say energy is transferred or dissipated, not “used up”.
- For GPE, use vertical height change.
- In KE calculations, square the speed before multiplying.
Check your understanding
- What is one joule?
- If speed triples, by what factor does KE change?
- A box moves horizontally while its weight acts vertically. Does weight do work?
Answers
- Energy transferred when a force of 1 N moves 1 m in its direction.
- Nine.
- No, because displacement is perpendicular to weight.
