Revision summary

Choose the quantity before calculating

Kinetic energy

E_k = 1/2 mv². Use m in kg and speed v in m/s; the result is J. Doubling speed gives four times the energy at fixed mass.

Gravitational energy change

Change = mgh. h is vertical height change, not path length. Use an approximately constant g in N/kg near Earth and a stated zero level for E_p.

Mechanical transfer

Work W (also written E) = Fd, where d is the distance moved in the constant force's direction. N x m gives J. Distinguish work W in J from weight W in N and the unit watt W. No displacement in that direction means no work by that force on that object.

Rate of transfer

Average P = E / t; E = Pt; t = E / P. Use E in J and t in s for P in W. 1 W = 1 J/s.

Useful fraction

Efficiency = useful energy output / total energy input over the same process and interval. Multiply the fraction by 100% for a percentage.

Stores and transfer pathways

Stores include kinetic, gravitational potential, chemical, elastic potential, nuclear and internal. Transfers occur mechanically, electrically, by heating or by waves. Include both electromagnetic examples such as sunlight and mechanical examples such as sound.

Name the objects and the stores that change. Gravitational energy concerns the mass-Earth interaction; internal energy concerns particles. Heat, sound and electricity should not be added as extra stores in this description.

Close the energy account

Energy cannot be created or destroyed. Initial energy + transfers in = final energy + transfers out. With no transfer across the boundary, the total for the system stays constant.

Equate a gravitational decrease with a kinetic increase only when the other changes are negligible. If friction or air resistance increases internal stores, include that amount. A body released from rest starts with zero kinetic energy; a moving starting body does not.

Power from a steady lift

Measure total lifted mass, vertical rise and elapsed time for the same steady interval. mgh/t gives average useful gravitational output power. It does not measure total electrical input power. Match height and timing marks, include the hanger and distinguish repeated random variation from an incorrect reference.

Pure: compare electricity resources

Non-renewable: fossil and nuclear fuels. Renewable: biofuel, wind, tides, hydropower, geothermal reservoirs and solar. Explain the transfer route, then compare efficiency, cost, reliability and environmental impact.

Define the input before comparing efficiencies. Include construction, operation and any storage or backup in costs. Match available output to the time of demand. Include the whole resource process in environmental comparisons; renewable does not mean constant, cost-free or impact-free.