Gravitational Potential Energy Calculator

What is Gravitational Potential Energy?

Gravitational potential energy is the energy possessed by an object due to its position in a gravitational field. It represents the work done against gravity to bring an object to a certain height above a reference point, typically the Earth's surface. This form of potential energy is crucial in understanding the behavior of objects in gravitational fields and plays a significant role in various physical phenomena, from the motion of planets to the design of roller coasters.

Formula

The formula for gravitational potential energy is:

\[ PE = m \times g \times h \]

Where:

• \( PE \) is the gravitational potential energy (in Joules, J)
• \( m \) is the mass of the object (in kilograms, kg)
• \( g \) is the gravitational acceleration (in meters per second squared, m/s²)
• \( h \) is the height above the reference point (in meters, m)

Calculation Steps

Let's calculate the gravitational potential energy for an object lifted above the Earth's surface:

1. Given:
   • Mass (\( m \)) = 5 kg
   • Gravitational acceleration (\( g \)) = 9.8 m/s² (approximate value on Earth's surface)
   • Height (\( h \)) = 10 m
2. Apply the gravitational potential energy formula: \[ PE = m \times g \times h \]
3. Substitute the known values: \[ PE = 5 \text{ kg} \times 9.8 \text{ m/s²} \times 10 \text{ m} \]
4. Perform the calculation: \[ PE = 490 \text{ J} \]

Example and Visual Representation

Let's visualize the gravitational potential energy of an object lifted above the Earth's surface:

This diagram illustrates:

• The Earth's surface (blue line)
• The height (\( h \)) above the surface (green dashed line)
• The object with mass (\( m \)) (yellow circle)
• The gravitational potential energy (\( PE \)) represented by the red arrow
• The gravitational field acting on the object (not shown, but implied)