Kinetic and gravitational potential energy · GCSE Physics

Kinetic energy

A moving object has energy in its kinetic store: Eₖ = ½ m v², where m is mass in kg and v is speed in m/s.
Doubling the mass doubles the kinetic energy; doubling the speed makes it four times bigger, because speed is squared.
To find speed from kinetic energy: v = √(2Eₖ ÷ m).

Lifting an object increases the energy in its gravitational potential store: Eₚ = m g h.
g is the gravitational field strength (9.8 N/kg on Earth) and h is the change in height in metres. AQA papers use 9.8 N/kg; Edexcel and OCR papers use 10 N/kg.
To find height: h = Eₚ ÷ (m g).

A stretched or compressed spring stores elastic potential energy: Eₑ = ½ k e².
k is the spring constant in N/m and e is the extension in metres. This works as long as the spring is not stretched past its limit of proportionality.

When an object falls, energy is transferred from its gravitational potential store to its kinetic store.
If air resistance is ignored, the energy lost from the gravitational store equals the energy gained in the kinetic store: m g h = ½ m v².
In real life some energy is dissipated to the surroundings by air resistance, so the object is slightly slower.

Write down the equation, substitute the values in SI units (kg, m, m/s), then calculate.
Convert grams to kilograms (÷ 1000) and centimetres to metres (÷ 100) first.
Give the unit, joules (J), with your answer.

Kinetic energy: The energy an object has because it is moving: Eₖ = ½mv².
Gravitational potential energy: Energy gained when an object is raised: Eₚ = mgh.
Elastic potential energy: Energy stored in a stretched or compressed object: Eₑ = ½ke².
Gravitational field strength: The force of gravity on each kilogram of mass; 9.8 N/kg on Earth.
Spring constant: A measure of how stiff a spring is, in N/m.
Extension: How much longer a spring gets when it is stretched, in metres.
Joule: The unit of energy (J).