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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 $BTU$.

The basic concept behind this article is the understanding of Kinetic Energy K.E. and its unit conversion.

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).

Expert Answer

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:

\[ K.E.\ \ =\ 22500\ J \]

\[ K.E.\ \ =\ 22500\ \frac{J}{1000} \]

\[ K.E.\ \ =\ 22.5\ KJ \]

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