The potential energy of a particle depends on its position in a field of force. For a 1 kg particle, the potential energy can be calculated by multiplying the particle’s mass (1 kg) by the gravitational field strength g (9.81 m/s2 on Earth’s surface) and the particle’s height h above some reference level:

## Quick Answer

The potential energy of a 1 kg particle is given by:

PE = mgh

Where:

- m = mass of particle (1 kg)
- g = gravitational field strength (9.81 m/s2 on Earth’s surface)
- h = height of particle above reference level (in m)

## What is Potential Energy?

Potential energy is the stored energy that an object possesses because of its position or state. There are several types of potential energy:

- Gravitational potential energy – depends on height of object above a reference level
- Elastic potential energy – depends on deformation of elastic object like a spring
- Chemical potential energy – depends on composition of atoms and molecules
- Nuclear potential energy – depends on composition of nucleus

This article focuses on gravitational potential energy for a particle in a uniform gravitational field like the Earth’s surface.

## Gravitational Potential Energy

Gravitational potential energy (PE) depends on the mass of an object, gravitational field strength, and height of the object. It is defined as:

PE = mgh

Where:

- m = mass of object (in kg)
- g = gravitational field strength (9.81 m/s2 on Earth’s surface)
- h = height of object above reference level (in m)

Gravitational potential energy is the energy possessed by an object because of its vertical position in a gravitational field. As the object gains height, it has more potential energy. As it falls, this potential energy gets converted to kinetic energy.

### Reference Level

An important point is that potential energy depends on the choice of a reference level. This level is arbitrary, but usually we choose it to be y = 0 or the ground level. The potential energy is 0 at the reference level.

## Calculating Potential Energy of a 1 kg Particle

To find the gravitational potential energy of a 1 kg particle, we use the above formula:

PE = mgh

Where:

- m = 1 kg (mass of particle)
- g = 9.81 m/s2 (acceleration due to gravity on Earth’s surface)
- h = height of particle above reference level (in m)

Let’s take an example. Say the particle is at a height 10 m above the ground. Then:

PE = (1 kg)(9.81 m/s2)(10 m)

= 98.1 J

So the potential energy of a 1 kg particle at a height 10 m above ground level is 98.1 J.

### Relationship Between Height and Potential Energy

We can see that as the height increases, the potential energy also increases proportionally. This is because potential energy depends directly on the height of the object.

Doubling the height doubles the potential energy. Tripling the height triples the potential energy and so on. The relationship is linear.

We can visualize this relationship in a graph:

Height h (m) | Potential Energy PE (J) |
---|---|

5 | 49.05 |

10 | 98.1 |

15 | 147.15 |

20 | 196.2 |

The graph shows that potential energy and height have a linear relationship. As height increases uniformly, potential energy also increases linearly.

## Examples of Potential Energy Calculations

Let’s calculate the potential energy of a 1 kg particle at different heights:

### Example 1

Height (h) = 5 m

PE = (1 kg)(9.81 m/s2)(5 m)

= 49.05 J

### Example 2

Height (h) = 25 m

PE = (1 kg)(9.81 m/s2)(25 m)

= 245.25 J

### Example 3

Height (h) = 100 m

PE = (1 kg)(9.81 m/s2)(100 m)

= 981 J

This shows that as the height increases, the potential energy increases proportionally.

## Potential Energy Near Earth’s Surface

Near the surface of the Earth, the gravitational field strength g remains fairly constant at 9.81 m/s2. Therefore, we can use this simplified formula to find potential energy for small heights:

PE = mgh

Where:

- m = mass of object (in kg)
- g = 9.81 m/s2
- h = height above ground level (in m)

This formula is valid for heights up to a few hundred meters above Earth’s surface. For larger heights, the variation of g with height must be taken into account.

## Potential Energy Near Other Celestial Bodies

To calculate potential energy near other planets or celestial bodies, the appropriate value of g must be used. For example:

- On the surface of the Moon, g = 1.62 m/s2
- On the surface of Mars, g = 3.71 m/s2
- On the surface of Jupiter, g = 24.79 m/s2

So for a 1 kg object on the surface of the Moon at a height 10 m, the potential energy would be:

PE = (1 kg)(1.62 m/s2)(10 m)

= 16.2 J

## Converting Between Potential Energy and Kinetic Energy

Potential energy can be converted to kinetic energy and vice versa. Some examples:

- When an object falls, its potential energy gets converted to kinetic energy.
- When a ball is thrown upwards, its kinetic energy gets converted to potential energy.
- A pendulum converts kinetic energy to potential energy and back again in each swing.

According to the law of conservation of energy, the total mechanical energy (kinetic + potential) remains constant in the absence of non-conservative forces like friction.

For example, if 100 J of potential energy gets converted to kinetic energy, the total kinetic energy gained will be 100 J. This kinetic energy gain can result in a change in velocity using the work-energy theorem.

### Key Points

- Potential energy depends on object’s mass, gravity, and height.
- Gravitational potential energy PE = mgh, where m is mass, g is gravity, h is height.
- Higher the height, greater is the potential energy.
- Potential energy can convert to kinetic energy and vice versa.
- Total mechanical energy (PE + KE) is conserved if no non-conservative forces act.

## Conclusion

The potential energy of a 1 kg particle can be calculated using the formula PE = mgh, where m = 1 kg, g = 9.81 m/s2 on Earth’s surface, and h is the height of the particle above a reference level. The potential energy increases linearly with height. By converting between potential and kinetic energy, useful mechanical work can be done.