# Energy

**Energy** is something that is found all over the physical and life sciences. **Thermal Energy** is what you experience when you burn your hand on the stove (again). **Chemical Energy** is what causes that (safely contained) explosion in chemistry class. In this section, we will focus solely on **mechanical energy**, or energy due to the movement (or potential movement) of an object.

## Types of Mechanical Energy

### Kinetic

**Kinetic energy** is the amount of energy an object has due to its movement (**velocity**).

##### [![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/MGlimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/MGlimage.png)Example

<p class="callout info">Mr. Box, who has a mass of **10 kilograms (kg)**, is sliding on a patch of ice at **2 meters per second (m/s)** of velocity. How much **kinetic energy** would he have?</p>

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/l6yimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/l6yimage.png)

<p class="callout success">Mr. Box would have **20 Joules** of **Kinetic Energy**.</p>

### Potential

**Potential energy** is the energy of an object or system due to its position relative to other objects.

#### Gravitational

**Gravitational potential energy** is calculated using an object's position within a gravitational field. Typically, this is considered to be the **height** (**h**) above the surface of the earth, which provides a constant **gravitational acceleration** (**g**) of around 9.8 meters per second squared.

##### [![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/8nhimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/8nhimage.png)Example

<p class="callout info">Mr. Box, who has a **mass** of **10 kg**, is lifted **5 meters** into the air above the surface of the Earth, which provides a **gravitational acceleration** of **9.8 meters per second** **squared**. How much **gravitational potential energy** would Mr. Box have?</p>

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/QCFimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/QCFimage.png)

<p class="callout success">Mr. Box would have **490 Joules** of **gravitational potential energy**.</p>

#### Elastic Potential

Although similar to gravitational potential energy, **elastic potential energy** instead deals with the energy provided by a spring (or elastic) rather than gravity. A spring's constant (**k**), also known as "stiffness", is determined by its **shape** and **material**.

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/VIwimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/VIwimage.png)

##### Example

<p class="callout info">Mr. Box (**mass** of **10 kg**) is pressed against a spring with a spring constant of **1 N/m** for **10 centimeters** (or **0.1 meters**). How much **elastic potential energy** does Mr. Box now have?</p>

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/sZ3image.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/sZ3image.png)

<p class="callout success">Mr. Box would have an **elastic potential energy** of **0.005 Joules**.</p>

## Conservation of Energy

The conservation of energy is a fundamental principle of physics, which states:

> The **total energy** of an isolated system is **constant** despite internal changes.

What this means within the context of our work in mechanical engineering is that the **type** **of energy** a system experiences may change, but the total amount of energy in that system will not.

For example:

<p class="callout info">In a previous question, we lifted Mr. Box (mass of **10 kg**) to a height of **5 meters,** which gave him a gravitational potential energy of **490 Joules**. Dropping him from that height would begin to **convert** the **potential energy** into **kinetic energy**. When Mr. Box gets back to the ground (height of **0 meters**) his potential energy will have been entirely converted to kinetic energy.</p>

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/zD6image.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/zD6image.png)

<p class="callout info">How much **velocity** is he moving with when he hits the ground (**GPE = 0 J, KE = 490 J**)?</p>

[![image.png](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/scaled-1680-/PGAimage.png)](https://bookstack.thebetalab.org/uploads/images/gallery/2026-06/PGAimage.png)