Physics & Mechanics

Potential Energy Calculator

Calculate the gravitational potential energy of an object based on its mass, height, and the acceleration due to gravity.

kg
m
m/s²
Potential Energy
490.333

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Stored Gravitational Energy

Gravitational Potential Energy is the energy an object possesses due to its position in a gravitational field. Think of it as "stored" energy—energy that has the potential to do work if the object is released.

For example, raising a heavy book from the floor to a high shelf requires work against gravity. That work is not lost; it is stored as potential energy. If the book falls, that potential energy is rapidly converted back into kinetic energy.

Practical Applications

Potential energy is a fundamental concept in engineering and physics, heavily utilized in:

  • Hydroelectric Dams: Water stored at a high elevation possesses massive potential energy. When released, it falls, converting to kinetic energy which spins turbines to generate electricity.
  • Roller Coasters: A roller coaster relies almost entirely on the potential energy gained from the initial chain lift hill to power it through the rest of the track.
  • Pile Drivers: Heavy weights are lifted high into the air and dropped, using their stored potential energy to drive massive posts into the ground.

The Formula

U=mgh\begin{aligned} U = m \cdot g \cdot h \end{aligned}

Where:
U=
Potential Energy (Joules, J)
m=
Mass of the object (kg)
g=
Acceleration due to gravity (9.81 m/s² on Earth)
h=
Height above the reference point (meters)

Example Calculation

Imagine a $50 , ext{kg}$ boulder sitting on the edge of a cliff $100 , ext{meters}$ high. (Assume Earth's gravity, $9.81 , ext{m/s}^2$).

  1. Multiply mass by gravity: $50 cdot 9.81 = 490.5 , ext{Newtons}$ (This is the boulder's weight).
  2. Multiply by height: $490.5 cdot 100 = 49,050 , ext{Joules}$.

The boulder has $49,050 , ext{J}$ of stored gravitational potential energy relative to the bottom of the cliff.

Frequently Asked Questions

Height is always measured relative to a chosen reference point, usually the ground, sea level, or the lowest point the object can fall to. At the reference point, potential energy is considered zero. It is a relative measurement.

In a closed system without friction or air resistance, total mechanical energy is conserved. As an object falls, it loses potential energy and gains an exactly equal amount of kinetic energy.

Yes, but the formula $U = mgh$ is an approximation that only works near the Earth's surface where gravity is roughly constant. In deep space, you must use the universal law of gravitation, where potential energy is calculated relative to infinity.