Calculate the total potential energy, in Btu, of an object that is 20 ft below a datum level at a location where g=31.7 ft/s^2 and which has mass of 100lbm.

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:

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

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

We know that:

$$PE=mgh$$

By putting the values, we get:

$$=100\times 31.7\times 20\times \frac{1}{25037}Btu$$

$$=2000\times 31.7\times \frac{1}{25037}Btu$$

$$=63400\times \frac{1}{25037}Btu$$

By solving, we get:

$$=2.5322Btu$$

The total potential energy is  $2.5322Btu$ .

Numerical Answer

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

Example

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

We are given:

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

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

We know that:

$$PE=mgh$$

By putting the values, we get:

$$=100\times 31.7\times 40\times \frac{1}{25037}Btu$$

$$=4000\times 31.7\times \frac{1}{25037}Btu$$

$$=126800\times \frac{1}{25037}Btu$$

By solving, we get:

$$=5.06450Btu$$

The total potential energy is $5.06450Btu$ .

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

We are given:

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

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

We know that:

$$PE=mgh$$

By putting the values, we get:

$$=100\times 31.7\times 60\times \frac{1}{25037}Btu$$

$$=6000\times 31.7\times \frac{1}{25037}Btu$$

$$=190200\times \frac{1}{25037}Btu$$

By solving, we get:

$$=7.5967Btu$$

The total potential energy is  $7.5967Btu$ .

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

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