The main objective of this question is to find the **total potential energy** for an **object** in **British thermal unit Btu**.

This question uses the concept of **Potential energy**. Potential energy is indeed the** power** that an **object can store** due to its **position** in **relation** to other things, **internal tensions**,** electric charge**, or even other circumstances. **Mathematically,** Potential energy is **represented** as:

**U = mgh**

**Where** $ m $ is the** mass**, **height** is $ h $, and $ g $ is** gravitational field**.

## Expert Answer

We are **given**:

- Mass = $ 100 lbm $.
- g = $ 31.7 \frac{ft}{s^2} $.
- h = $ 20 ft $.

We have to **find the total potential energy** of an **object** in **British thermal unit Btu**.

We **know** that:

\[PE \space = \space mgh\]

By** putting** the values, we get:

\[= \space 100 \times \space 31.7 \space \times 20 \space \times \frac{1}{25037}Btu \]

\[= \space 2000 \times \space 31.7 \space \times \frac{1}{25037}Btu \]

\[= \space 63400 \times \frac{1}{25037}Btu \]

By **solving**, we get:

\[=2.5322 \space Btu \]

The **total potential energy** is $ 2.5322 Btu $ .

## Numerical Answer

The **total potential energy** of an** object** in **British thermal unit** is $ 2.5322 Btu $.

## Example

What is the total potential energy of an object in British thermal unit when the mass of object is $ 100 lbm $, gravitational field is $ 31.7 \frac{ft}{s^2}$ and object height is $ 40 ft $ and $ 60 ft $ ?

We are **given**:

- Mass = $ 100 lbm $.
- g = $ 31.7 \frac{ft}{s^2} $.
- h = $ 40 ft $.

We have to find the **total potential energy** of an **object** in **British thermal unit** Btu.

We **know** that:

\[PE \space = \space mgh\]

By **putting** the values, we get:

\[= \space 100 \times \space 31.7 \space \times 40 \space \times \frac{1}{25037}Btu \]

\[= \space 4000 \times \space 31.7 \space \times \frac{1}{25037}Btu \]

\[= \space 126800 \times \frac{1}{25037}Btu \]

By **solving**, we get:

\[= \space 5.06450 \space Btu \]

The **total potential energy** is $ 5.06450 Btu $ .

And when the **object height** is $60 ft $ , the **total potential energy** of an **object** is **calculated** below.

We are **given**:

- Mass = $ 100 lbm $.
- g = $ 31.7 \frac{ft}{s^2} $.
- h = $ 60 ft $.

We have to find the** total potential energy** of an** object** in British thermal unit Btu.

We **know** that:

\[PE \space = \space mgh\]

By **putting** the values, we get:

\[= \space 100 \times \space 31.7 \space \times 60 \space \times \frac{1}{25037}Btu \]

\[= \space 6000 \times \space 31.7 \space \times \frac{1}{25037}Btu \]

\[= \space 190200 \times \frac{1}{25037}Btu \]

By **solving**, we get:

\[= \space 7.5967\space Btu \]

The **total potential energy** is $ 7.5967 Btu $ .

Hence, the **total potential** **energy** for an** object** is $ 5.06450 Btu $ when the **object height** is $ 40 ft $. The **total potential energy** for an **object** is $ 7.5967 Btu $ when the **object height** is $ 60ft $.