Things in nature prefer to be in the lowest energy condition possible. Throwing a ball in the air causes it to fall back down because it has less energy on the surface! This is essential to understand. What causes this to happen? Enter the universe of potential! (Introduction to potential energy)

**Caranx Melampygus** , To know Potential energy, we must first recognize potential; therefore, what is your potential? In simpler terms, your potential may be thought of as your internal ability. The amount of energy a body has inside is defined by its potential energy. We can’t measure its exact value; therefore, we calculate its true value by assuming that everyone’s potential energy at infinity is zero.

Every object has a certain amount of energy. Even the smallest atom has a lot of energy. This energy exists as a result of its location within a force field or potential field. This article explains how to compute the energy released by potential fields of this type.

## Introduction to potential energy

“The amount of work done on a body by conservative forces (forces that do not depend on the trajectory of the body) to bring it from a reference point to a particle point in space is called potential energy.”

OR

“The energy that an object has as a result of its position in a force field or the energy that a system has as a result of the configuration of its elements is known as potential energy.”

**SI unit**

The Joule is the SI unit for gravitational potential energy. Over a one-meter distance, the amount of work done by a force of one newton (N) is represented as one joule.

### Formula of potential energy

The following is the formula for calculating potential energy:

P.E = mgh

Where m is the mass of the body, g represents the gravitational acceleration and h is the change in position or height of the body. The term P.E stands for potential energy.

The above formula can also be used to get a body’s mass, gravitational acceleration, and height.

- Mass = m = P.E/gh
- Gravitational acceleration = g = P.E/mh
- Height of body = h = P.E/mg

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**Explanation**

Begin with the most basic example: weights in a gravitational field. Make things even easier by presuming you’re close enough to the Earth’s surface to pretend the field is constant.

Consider a weight on a rope that can be raised and lowered in a straight, vertical line. Set the zero for (potential) energy at the floor, and observe that the amount of work required to elevate that weight of mass m is mgh, where h is the height and g is the acceleration due to gravity.

However, you can have the dropping weight do work as well, and that work will also turn out to be mgh when you reduce it by a certain amount.

**Derivation**

We know from physics that the quantity of work done by a body equals the potential energy stored in the body. It can be expressed as follows:

Work done = P.E = Fh

Or

P.E = Fh

Now as newton’s second law states that force is equal to the product of mass and acceleration so

P.E = mah

Since we are talking about the gravitational field so acceleration can be replaced by gravitational acceleration g.

**P.E = mgh**

The above relation shows that potential energy is directly proportional to mass, height, and gravitational acceleration.

## How to calculate the problems of potential energy?

**Example 1:**

Evaluate the potential energy if an 800g ball is dragged up a 0.2m-high slope and its mass is 0.8kg.

**Solution **

**Step I:** write given terms along with their units.

Gravitational acceleration = g =10ms^{-2}

Mass = m = 800g = 0.8kg

Height = h = 0.2m

P.E =?

**Step II:** Write general formula P.E

P.E = mgh

**Step III:** Put the given data values

P.E = (0.8kg) (10ms^{-2}) (0.2)

P.E = 1.6J

Hence P.E of ball is **1.6J.**

To improve accuracy in the given problem, use the potential energy calculator by following the steps given below.

**Step 1: **Select the missing term, you want to calculate.

**Step 2: **Input the values of requires input fields and press the calculate button.

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**Example 2:**

The weight of a box is 5.8kg. The box is raised from the floor of the garage and placed on a shelf. How tall is the shelf if the box gains 145J of Potential Energy?

**Solution **

**Step I:** write given terms along with their units.

Mass = m = 5.8kg

Gravitational acceleration = g =10ms^{-2}

Height = h =?

P.E = 145j

**Step II:** Write general formula for height

h = P.E/mg

**Step III:** Put the given data values

h = 145j / (5.8kg) (10ms^{-2})

h = 2.5m

Hence the height of shelf is **2.5m.**

**Example 3:**

A man scales a 3.6m high wall and gains 2268J of potential energy. What is the man’s mass?

**Solution**

**Step I:** write given terms along with their units.

Height = h = 3.6m

P.E = 2268j

Gravitational acceleration = g =10ms^{-2}

Mass = m =?

**Step II:** Write the general formula for height

m = P.E/gh

**Step III:** Put the given data values

m = 2268j / (10ms^{-2}) (3.8m)

m = 63kg

Hence the weight of a man is **63kg.**

## Summary

Energy is sometimes defined as the ability to do an effort, that is, to push anything against a force. We’re upon the marginally stronger ground now that we have potential energy.

When a body can do work, physicists refer to it as having potential energy, because work and energy are synonymous in classical physics. (Introduction to potential energy)

Daily life potential energy problems can be solved by applying the general equation of potential energy, which allows us to comprehend how much ability an object has to do work.

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