Gravitational Potential Energy (GPE)

Gravitational potential energy is the energy an object has because it is in a gravitational field. Lifting a book onto a shelf stores energy; the higher it is, the more energy it has and the more it can do if it falls.

Key ideas

• Energy store: GPE is an energy store that increases when you lift an object and decreases when it falls.
• What it depends on: mass of the object, height change, and gravitational field strength.
• Symbols and units: mass m (kg), gravitational field strength g (N/kg), height change Δh (m), energy in joules (J).
• Near Earth’s surface, g ≈ 9.8 N/kg (often rounded to 10 N/kg in simple calculations). It is also the acceleration of free fall.

Equation

Change in gravitational potential energy is given by:

$$\Delta E_p = m g\,\Delta h$$

Use Δh = final height − initial height. Lifting up gives positive Δh (energy gained). Falling down gives negative Δh (energy lost).

Energy transfers

• When you lift an object, mechanical work done on it increases its GPE.
• When it falls, GPE is mainly transferred to kinetic energy (and to the surroundings as heat and sound if there is air resistance or impact).

Real-world links

• Roller coasters: high points store GPE that becomes kinetic energy on the way down.
• Hydroelectric dams: water held high stores GPE; as it falls, it turns turbines to generate electricity.

Common misconceptions

• Path does not matter: lifting straight up or along a ramp to the same height gives the same change in GPE (it depends only on Δh).
• Reference level: GPE is measured from a chosen zero level (often the ground). Only changes in GPE have physical meaning.
• Mass vs weight: mass is in kg; weight is a force W = mg in newtons. Do not mix them.