## Potential Energy Calculator User Guide

This Potential Energy Calculator allows you to easily calculate the potential energy (PE) of an object, as well as other related properties like mass, acceleration of gravity, and height. Follow this step-by-step guide to make the most out of this handy calculator.

**Step 1: Choose the property you want to calculate**

- Locate the “I want to calculate” dropdown menu at the top of the calculator.
- Click on the dropdown menu to reveal the following options:
- Potential Energy (PE)
- Mass (m)
- Acceleration of Gravity (g)
- Height (h)

- Select the property you wish to calculate by clicking on it.

**Step 2: Input the known values**

Depending on the property you want to calculate, you’ll need to provide the values for the remaining properties:

- Mass (m): Enter the object’s mass in kilograms (kg).
- Height (h): Enter the object’s height above the reference point in meters (m).
- Acceleration of Gravity (g): By default, the calculator uses the Earth’s standard acceleration due to gravity, 9.8 m/s². If you need to use a different value, simply enter it in the provided field.

**Step 3: Calculate**

Once you have entered the required values, click on the “Calculate” button. The calculator will then perform the necessary calculations and display the result in the corresponding field. If there are any errors in the input, an error message will be displayed in the “dynErrDisp” section.

**Step 4: Reset the calculator**

To perform a new calculation or clear the input fields, click on the “Reset” button. This will revert all fields to their default values and allow you to start a new calculation.

**Example Calculation**

Let’s say you want to calculate the potential energy of an object with a mass of 5 kg, located 10 meters above the ground. Follow these steps:

- Choose “Potential Energy (PE)” from the “I want to calculate” dropdown menu.
- Enter “5” in the Mass (m) field.
- Enter “10” in the Height (h) field.
- Make sure the Acceleration of Gravity (g) field shows the default value of 9.8 m/s².
- Click the “Calculate” button.

The calculator will now display the potential energy of the object as 490 Joules (J) in the Potential Energy (PE) field.

## What is Potential Energy?

Potential energy is the energy that an object possesses due to its position or condition. It is a form of energy that can be stored within an object and can be transformed into other forms of energy. Potential energy is a scalar quantity, meaning it has only magnitude and no direction.

## The Formula for Potential Energy

The formula for potential energy is given:

**Potential Energy (PE) = mgh**

Where: **m** = mass of the object **g** = acceleration due to gravity (9.8 m/s^2 on Earth) **h** = height of the object

## Units of Potential Energy

The SI unit of potential energy is Joule (J). Other units of potential energy include calories, kilocalories, electronvolt, and British thermal unit (BTU).

## Examples of Potential Energy

Let us consider a few examples to understand potential energy better.

### Example 1:

A book is placed on a shelf that is **2 meters** above the ground. The mass of the book is **1 kg**.

Calculate the potential energy of the book.

Solution: We know that **m** = 1 kg, **g** = 9.8 m/s^2, and **h** = 2 m.

**Potential Energy (PE)** = **mgh PE** = 1 x 9.8 x 2 **PE** = 19.6 **J**

Therefore, the potential energy of the book is **19.6 Joules.**

### Example 2:

A roller coaster is at the top of a hill, **50 meters** above the ground. The mass of the roller coaster is **1000 kg**.

Calculate the potential energy of the roller coaster.

Solution: We know that **m** = 1000 kg, **g **= 9.8 m/s^2, and **h** = 50 m.

**Potential Energy (PE)** = **mgh PE** = 1000 x 9.8 x 50 **PE** = 490,000 **J**

Therefore, the potential energy of the roller coaster is **490,000 Joules.**

Potential energy is a crucial concept in classical physics. It is the energy that an object possesses due to its position or condition. The formula for potential energy is PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object. The SI unit of potential energy is Joule (J).