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<h2 class="title">Kinetic Energy</h2>
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<h3>Definition: Kinetic Energy</h3>
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<p>Kinetic energy is the energy an object has due to its motion.</p>
<p>Quantity: Kinetic energy ${E}_{K}$         Unit name: Joule         Unit symbol: J</p>
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<p>Kinetic energy is the energy an object has because of its motion. This means that any moving object has kinetic energy. Kinetic energy is defined as:</p>

\[{E}_{K} = \frac{1}{2}m{v}^{2}\]

<p>where ${E}_{K}$ is the kinetic energy (measured in joules, $\text{J}$)</p>
<p>$m =$ mass of the the object (measured in $\text{kg}$)</p>
<p>$v =$ velocity of the object (measured in $\text{m·s$^{-1}$}$).</p>
<p>Therefore the kinetic energy ${E}_{K}$ depends on the mass and velocity of an object. The faster it moves, and the more massive it is, the more kinetic energy it has. A truck of $\text{2 000}$ $\text{kg}$, moving at $\text{100}$ $\text{km·h$^{-1}$}$ will have more kinetic energy than a car of $\text{500}$ $\text{kg}$, also moving at $\text{100}$ $\text{km·h$^{-1}$}$.</p>
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<h3>Tip:</h3>
<p>You may sometimes see kinetic energy written as KE. This is simply another way to write kinetic energy. We will not use this form in this tutorial, but you may see it written like this in other places.</p>
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<p>Consider the $\text{1}$ $\text{kg}$ suitcase on the cupboard that was discussed earlier. When it is on the top of the cupboard, it will not have any kinetic energy because it is not moving:</p>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{1}\text{ kg}\right){\left(\text{0}\text{ m·s$^{-1}$}\right)}^{2} = \text{0}\text{ J} \end{align*}

<p>When the suitcase falls, its velocity increases (falls faster), until it reaches the ground with a maximum velocity. As its velocity velocity increases, it will gain kinetic energy. Its kinetic energy will increase until it is a maximum when the suitcase reaches the ground. If it has a velocity of $\text{6.26}$ $\text{m·s$^{-1}$}$ when it reaches the ground, its kinetic energy will be:</p>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{1}\text{ kg}\right){\left(\text{6.26}\text{ m·s$^{-1}$}\right)}^{2} = \text{19.6}\text{ J} \end{align*}<img alt="30d0ab1f59dafe8ed1ffab8935b105aa.png" src="https://data.ulearngo.com/assets/39038d8f-df14-4af0-b4fd-1471df259775"/>
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<h2>Example: Calculation of Kinetic Energy</h2>
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<h3>Question</h3>
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<p>A $\text{1}$ $\text{kg}$ brick falls off a $\text{4}$ $\text{m}$ high roof. It reaches the ground with a velocity of $\text{8.85}$ $\text{m·s$^{-1}$}$. What is the kinetic energy of the brick when it starts to fall and when it reaches the ground?</p>
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<h3>Step 1: Analyse the question to determine what information is provided</h3>
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<p>The mass of the brick $m = \text{1}\text{ kg}$</p>
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<p>The velocity of the brick at the bottom $v = \text{8.85}\text{ m·s$^{-1}$}$</p>
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<p>These are both in the correct units so we do not have to worry about unit conversions.</p>
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<h3>Step 2: Analyse the question to determine what is being asked</h3>
<p>We are asked to find the kinetic energy of the brick at the top and the bottom. From the definition we know that to work out ${E}_{K}$, we need to know the mass and velocity of the object and we are given both of these values.</p>
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<h3>Step 3: Calculate the kinetic energy at the top</h3>
<p>Since the brick is not moving at the top, its kinetic energy is zero.</p>
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<h3>Step 4: Substitute and calculate the kinetic energy</h3>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{1}\text{ kg}\right){\left(\text{8.85}\text{ m·s$^{-1}$}\right)}^{2} = \text{39.2}\text{ J} \end{align*}</div>
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<h2>Example: Kinetic Energy of Two Moving Objects</h2>
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<h3>Question</h3>
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<p>A herder is herding his sheep into the kraal. A mother sheep and its lamb are both running at $\text{2.7}$ $\text{m·s$^{-1}$}$ towards the kraal. The sheep has a mass of $\text{80}$ $\text{kg}$ and the lamb has a mass of $\text{25}$ $\text{kg}$. Calculate the kinetic energy for each of the sheep and the lamb.</p>
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<h3>Step 1: Analyse the question to determine what information is provided</h3>
<ul>
<li>
<p>the mass of the mother sheep is $\text{80}$ $\text{kg}$</p>
</li>
<li>
<p>the mass of the lamb is $\text{25}$ $\text{kg}$</p>
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<li>
<p>both the sheep and the lamb have a velocities of $\text{2.7}$ $\text{m·s$^{-1}$}$</p>
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<h3>Step 2: Analyse the question to determine what is being asked</h3>
<p>We need to find the kinetic energy of the sheep and the kinetic energy of its lamb</p>
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<h3>Step 3: Use the definition to calculate the sheep's kinetic energy</h3>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{8}\text{ kg}\right){\left(\text{2.7}\text{ m·s$^{-1}$}\right)}^{2} = \text{291.6}\text{ J} \end{align*}</div>
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<h3>Step 4: Use the definition to calculate the lamb's kinetic energy</h3>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ &amp; = \frac{1}{2}\left(\text{25}\text{ kg}\right){\left(\text{2.7}\text{ m·s$^{-1}$}\right)}^{2} = \text{91.13}\text{ J} \end{align*}

<p>Note: Even though the sheep and the lamb are running at the same velocity, due to their different masses, they have different amounts of kinetic energy. The sheep has more than the lamb because it has a higher mass.</p>
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</section>
<section></section>
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Kinetic Energy

Physics is a science discipline concerned with the nature and properties of matter and energy. Physics topics include mechanics, heat, light and radiation, sound, electricity, magnetism, the structure of atoms, and so on.

Physics

Explore the concepts of mechanical energy, potential and kinetic energy, work, power, and conservation of energy through examples like pendulum, roller coaster, and inclined plane.


Kinetic Energy

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