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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 =  $ 100 lbm $.
  2. g = $ 31.7 \frac{ft}{s^2} $.
  3. 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:

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

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

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