Potential Energy
(Gravitational Potential Energy)

Calculator and formulas to calculate potential energy

Potential Energy Calculator

Gravitational Potential Energy Calculation

Calculates the energy of an object due to its height in the gravitational field. Formula: E = m · g · h

m/s²
Result
Example 1: Calculate Potential Energy
Problem:

A book with a mass of 500 g is placed on a shelf at a height of 2 meters. What is the potential energy? (g = 9.81 m/s²)

Given:
  • Mass: m = 500 g = 0.5 kg
  • Height: h = 2 m
  • Gravitational acceleration: g = 9.81 m/s²
  • Find: Potential Energy E
Solution:
\[E = m \cdot g \cdot h\]
\[E = 0.5 \text{ kg} \cdot 9.81 \text{ m/s}^2 \cdot 2 \text{ m}\]
\[E = 9.81 \text{ J}\]

Example Calculations

Example 2: Calculate Mass
Problem:

An object at 5 meters height has a potential energy of 245.25 J. What is the mass of the object?

Given:
  • Potential Energy: E = 245.25 J
  • Height: h = 5 m
  • Gravitational acceleration: g = 9.81 m/s²
  • Find: Mass m
Solution:
\[m = \frac{E}{g \cdot h}\]
\[m = \frac{245.25}{9.81 \cdot 5}\]
\[m = \frac{245.25}{49.05} = 5 \text{ kg}\]
Mass = 5000 g

Example 3: Calculate Height
Problem:

A ball with a mass of 2 kg has a potential energy of 19.62 J. At what height is the ball located?

Given:
  • Potential Energy: E = 19.62 J
  • Mass: m = 2 kg = 2000 g
  • Gravitational acceleration: g = 9.81 m/s²
  • Find: Height h

Solution:
\[h = \frac{E}{m \cdot g}\]
\[h = \frac{19.62}{2 \cdot 9.81}\]
\[h = \frac{19.62}{19.62} = 1 \text{ m}\]
The ball is located at a height of 1 meter.


Formulas of Potential Energy

Potential energy (gravitational potential energy) is the energy that an object possesses due to its position in a force field (usually the gravitational field). It is one of the most fundamental concepts in mechanics and energy conservation.

Calculate Potential Energy

The fundamental formula for gravitational potential energy.

\[E = m \cdot g \cdot h\]
E = Potential Energy [J]
m = Mass [kg]
g = Gravitational acceleration [m/s²]
h = Height [m]
Calculate Mass

Rearranged formula to solve for mass.

\[m = \frac{E}{g \cdot h}\]
When E, g, and h are known.
Calculate Height

Rearranged formula to solve for height.

\[h = \frac{E}{m \cdot g}\]
When E, m, and g are known.
Calculate Gravitational Acceleration

Rearranged formula to solve for gravitational acceleration.

\[g = \frac{E}{m \cdot h}\]
When E, m, and h are known.
Important Values and Constants
Gravitational Acceleration (g):
≈ 9.81 m/s² (standard value)
≈ 9.807 m/s² (exact)
≈ 10 m/s² (simplified)
Energy Units:
1 J = 1 N·m = 1 kg·m²/s²
1 kJ = 1000 J
1 Wh = 3600 J

Detailed Description of Potential Energy


Physical Principles

Potential energy (gravitational potential energy) is the energy that an object possesses due to its position in Earth's gravitational field. It is often denoted as Epot or U.

Unlike kinetic energy (energy of motion), which depends on velocity, potential energy depends only on height. It represents the capacity of an object to perform work due to its position.

Core Idea: The higher an object is raised, the more work is done, and the more potential energy the object stores.

Linear Relationship

Potential energy is directly proportional to height. This means: If the height is doubled, the potential energy is also doubled.

Applications

Hydroelectric Power

Dams harness the potential energy of water at height. Falling water converts gravitational potential energy into kinetic energy and drives turbines.

Civil Engineering

Potential energy is important in calculating structures and loads. Objects at height can release significant energy if structural failure occurs.

Lifting and Hoisting

In lifts, cranes, and elevators, work is done to store potential energy. This energy can later be used to move the object.

Energy Recovery

Regenerative braking systems in electric vehicles use potential energy when descending to generate electricity and charge batteries.

Conversion to Other Forms of Energy
Potential → Kinetic Energy

Example: A falling apple
As the apple falls, Epot is converted to Ekin. Upon impact, the remaining energy is released as heat and sound.

Kinetic → Potential Energy

Example: A thrown ball
As the ball rises, Ekin is converted to Epot. At the highest point, Ekin = 0 and Epot is maximum.

The Law of Energy Conservation

The Law of Energy Conservation states that the total energy in a closed system remains constant. Energy cannot be created or destroyed, only transformed from one form to another.

\[E_{total} = E_{pot} + E_{kin} = \text{constant}\]

Pendulum Example: At the highest point, the pendulum has maximum Epot and minimum Ekin. At the lowest point, it's the opposite. The sum remains constant (ignoring friction).

Practical Example: Dam

A dam stores water at great heights. This water possesses enormous potential energy. When water flows through turbines, this potential energy is converted into kinetic energy (flow) and then into electrical energy.

Calculation: 1 million tons of water (109 kg) at 100 m height

\[E = m \cdot g \cdot h = 10^9 \text{ kg} \cdot 9.81 \text{ m/s}^2 \cdot 100 \text{ m}\] \[E = 9.81 \times 10^{11} \text{ J} \approx 272 \text{ MWh}\]

Practical Significance: This enormous energy amount can power thousands of households!


Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?

More physics functions

Centrifugal Force • Efficiency • Inclined plan • kW - hp converter • PS - hp converter • Power Force Displacement and Time • Pressure, Force and Area • Torque • Weight Force • Work, Force and Displacement • Work Power and Time • Energy Density • Kinetic Energy • Specific Energy • Acceleration by Distance • Acceleration by Time • Angular Velocity • Circular Motion • Rotational Speed • Speed, Distance and Time • Free-Fall • Temperature in Atmosphere • Mach Number • Speed of sound • Sound Pressure • Belt Length • Gear Ratio • Angle of refraction