Gravitational Potential Energy Formula

The Formula

PE = mgh (mass times gravity times height)

When to use: The higher you lift something, the more energy it stores (ready to fall).

Quick Example

A roller coaster at the top of a hill has maximum gravitational PE.

Notation

U_g or PE_g is gravitational potential energy in joules (J), m is the object's mass in kg, g \approx 9.8 m/s² is gravitational acceleration near Earth, h is height in metres, G is the gravitational constant, and M is Earth's mass.

What This Formula Means

Energy stored in an object due to its height above a reference point in a gravitational field: PE = mgh.

The higher you lift something, the more energy it stores (ready to fall).

Formal View

Near Earth's surface, gravitational PE is U_g = mgh, where h is the height above the reference level. For large distances, the exact form is U_g = -\frac{GmM}{r}, where r is the distance from the centre of the Earth and the reference is at infinity.

Worked Examples

Example 1

easy
What is the gravitational potential energy of a 4 \text{ kg} book on a shelf 2.5 \text{ m} above the floor? Use g = 9.8 \text{ m/s}^2.

Solution

  1. 1
    Use the gravitational potential energy formula: PE = mgh.
  2. 2
    Substitute the values: PE = 4 \times 9.8 \times 2.5.
  3. 3
    PE = 98 \text{ J}

Answer

PE = 98 \text{ J}
Gravitational potential energy depends on mass, gravitational acceleration, and height above a reference point. It represents stored energy due to an object's position in a gravitational field.

Example 2

medium
A 50 \text{ kg} person climbs a 15 \text{ m} ladder. How much gravitational PE do they gain? Use g = 9.8 \text{ m/s}^2.

Common Mistakes

  • Changing the reference height partway through a problem — once you choose where h = 0, you must keep it consistent for all calculations.
  • Using the formula PE = mgh at very large distances from Earth where g is no longer constant — for orbital distances, use PE = -GmM/r instead.
  • Confusing height h with total distance traveled — h is the vertical height difference, not the path length along a ramp or slope.

Why This Formula Matters

Gravitational PE is the energy source for hydroelectric dams, falling objects, and roller coasters. It is central to understanding projectile motion, orbital mechanics, and energy conservation in any system involving height changes.

Frequently Asked Questions

What is the Gravitational Potential Energy formula?

Energy stored in an object due to its height above a reference point in a gravitational field: PE = mgh.

How do you use the Gravitational Potential Energy formula?

The higher you lift something, the more energy it stores (ready to fall).

What do the symbols mean in the Gravitational Potential Energy formula?

U_g or PE_g is gravitational potential energy in joules (J), m is the object's mass in kg, g \approx 9.8 m/s² is gravitational acceleration near Earth, h is height in metres, G is the gravitational constant, and M is Earth's mass.

Why is the Gravitational Potential Energy formula important in Physics?

Gravitational PE is the energy source for hydroelectric dams, falling objects, and roller coasters. It is central to understanding projectile motion, orbital mechanics, and energy conservation in any system involving height changes.

What do students get wrong about Gravitational Potential Energy?

The formula mgh only works near Earth's surface where g is constant.

What should I learn before the Gravitational Potential Energy formula?

Before studying the Gravitational Potential Energy formula, you should understand: potential energy, gravity.

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