Kinetic, elastic and gravitational energy explained

Principles of energy • Energy stores and changes

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A polystyrene ball of mass 0.0005 kg launched by a spring: how to combine elastic and gravitational calculations?

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Calculate elastic energy from the spring then set E_e = E_p at the highest point (0.5ke^2 = mgh) to find maximum height, using consistent units

Key concepts

What you'll likely be quizzed about

Kinetic energy (Ek)

Kinetic energy is the energy held by an object because of its motion. The kinetic energy equation is E_k = 0.5 × m × v^2 where m is mass in kilograms and v is speed in metres per second. Doubling mass doubles kinetic energy; doubling speed increases kinetic energy by a factor of four because speed is squared. Kinetic energy calculations use the SI unit joule (J). Practical calculations link kinetic energy change to work done by forces, for example when brakes convert kinetic energy to thermal energy in stopping a car .

Elastic potential energy (Ee)

Elastic potential energy is the energy stored in an elastic object when it is stretched or compressed, provided the deformation stays within the elastic limit. The equation on the physics equation sheet is E_e = 0.5 × k × e^2 where k is the spring constant (N/m) and e is extension (m). Energy stored is proportional to the square of extension, so small increases in extension produce larger increases in stored energy. If deformation passes the limit of proportionality, the formula no longer applies and permanent deformation occurs .

Gravitational potential energy (Ep)

Gravitational potential energy is the energy associated with an object’s position in a gravitational field. The equation is E_p = m × g × h where m is mass (kg), g is gravitational field strength (N/kg, typically 9.8 N/kg near Earth's surface) and h is height above a chosen reference point (m). Raising an object against gravity requires work; the work done equals the increase in gravitational potential energy. The equation applies for uniform g and for height changes small enough that g is effectively constant .

Key notes

Important points to keep in mind

Use SI units: mass in kg, distance in m, speed in m/s, g ≈ 9.8 N/kg unless instructed otherwise.

Square the speed in the kinetic energy equation; small changes in speed strongly affect Ek.

E_e = 0.5ke^2 applies only within the elastic (proportional) limit of the spring.

Choose a clear reference level for height when using E_p = mgh; negative heights give negative Ep relative to that reference.

When energy transfers occur, check for losses to thermal energy or sound; mechanical energy is conserved only if losses are negligible.

Convert units before substituting into equations (g, m, v and e must be in SI units).

For combined problems, use energy conservation: initial total energy = final total energy (account for all relevant stores).