# Calculate the total kinetic energy, in Btu, of an object with a mass of 10 lbm when its velocity is 50 ft/s.

The aim of this article is to find the Kinetic Energy of an object in motion in $BTU$.

Kinetic Energy is defined as the energy that an object carries while in motion. All moving objects possess kinetic energy. When a net force $F$ is applied to an object, this force transfers energy, and resultantly work $W$ is done. This energy called Kinetic Energy K.E. changes the state of the object and causes it to move at a certain speed. This Kinetic Energy K.E. is calculated as follows:

$Work\ Done\ W\ =\ F\ \times\ d$

Where:

$F\ =$ Net Force Applied to the Object

$d\ =$ Distance traveled by the Object

Since:

$F\ =\ m\ \times\ a$

So:

$W\ =\ (m\ \times\ a)\ \times\ d$

As per the Equation of Motion:

$2\ a\ d\ =\ {v_f}^2\ -\ {v_i}^2$

And:

$a\ =\ \frac{{v_f}^2\ -\ {v_i}^2}{2d}$

Substituting in the equation for work done, we get:

$W\ =\ m\ \times\ d\ \times\ \left(\frac{{v_f}^2\ -\ {v_i}^2}{2d}\right)$

$W=\frac{1}{2}\ m\times({v_f}^2\ -\ {v_i}^2)$

If the object is initially at rest, then $v_i=0$. So, simplifying the equation, we get:

$K.E.\ \ =\ \frac{1}{2}\ m\ {\ v}^2$

Where:

$m$ is the mass of the object, and $v$ is the velocity of the object.

The SI Unit for Kinetic Energy K.E. is Joules $J$ or $BTU$ (British Thermal Unit).

Given that:

Mass of the Object $m\ =\ 10\ lbm$

Velocity of the Object $v\ =\ 50\ \dfrac{ft}{s}$

We need to find the Kinetic Energy K.E. which is calculated as follows:

$K.E.\ \ =\ \frac{1}{2}\ m{\ v}^2$

Substituting the given values in the above equation, we get:

$K.E.\ \ =\ \frac{1}{2}\ (10\ lbm){\ (50\ \frac{ft}{s})}^2$

$K.E.\ \ =\ 12500\ lbm \frac{{\rm ft}^2}{s^2}$

We need to calculate the Kinetic Energy K.E. in $BTU$ – British Thermal Unit.

As we know:

$1\ BTU\ =\ 25037\ lbm \frac{{\rm ft}^2}{s^2}$

$1\ lbm \frac{{\rm ft}^2}{s^2}\ =\ \frac{1}{25037}\ BTU$

Hence:

$K.E.\ \ =\ 12500\ \times\ \frac{1}{25037}\ BTU$

$K.E.\ \ =\ 0.499\ BTU$

## Numerical Result

The Kinetic Energy of the Object in BTU is as follows:

$K.E.\ \ =\ 0.499\ BTU$

## Example

If an object having a mass of $200kg$ is moving at the speed of $15\dfrac{m}{s}$, calculate its Kinetic Energy in Joules.

Solution

Given that:

Mass of the Object $m\ =\ 200\ kg$

Velocity of the Object $v\ =\ 15\ \dfrac{m}{s}$

We need to find the Kinetic Energy K.E. which is calculated as follows:

$K.E.\ \ =\ \frac{1}{2}\ m{\ v}^2$

Substituting the given values in the above equation, we get:

$K.E.\ \ =\ \frac{1}{2}\ (200\ kg){\ (15\ \frac{m}{s})}^2$

$K.E.\ \ =\ 22500\ kg\ \frac{m^2}{s^2}$

As we know:

The SI unit of Kinetic Energy is Joule $J$ which is expressed as follows:

$1\ Joule\ J\ =\ 1\ kg\ \frac{m^2}{s^2}$

Hence:

$K.E.\ \ =\ 22500\ J$

$K.E.\ \ =\ 22500\ \frac{J}{1000}$

$K.E.\ \ =\ 22.5\ KJ$