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<section>
<h2 class="title">Mechanical Energy</h2>
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<h3>Definition: Mechanical energy</h3>
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<p>Mechanical energy is the sum of the gravitational potential energy and the kinetic energy of a system.</p>
<p>Quantity: Mechanical energy (${E}_{M}$)         Unit name: Joule         Unit symbol: $\text{J}$</p>
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<p>Mechanical energy, ${E}_{M}$, is simply the sum of gravitational potential energy (${E}_{P}$) and the kinetic energy (${E}_{K}$). Mechanical energy is defined as:</p>

\[{E}_{M}={E}_{P}+{E}_{K}\]\[{E}_{M} = mgh + \frac{1}{2}m{v}^{2}\]

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<h3>Tip:</h3>
<p>You may see mechanical energy written as $U$. We will not use this notation in this book, but you should be aware that this notation is sometimes used.</p>
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<h2>Example: Mechanical Energy</h2>
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<h3>Question</h3>
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<p>Calculate the total mechanical energy for a ball of mass $\text{0.15}$ $\text{kg}$ which has a kinetic energy of $\text{20}$ $\text{J}$ and is $\text{2}$ $\text{m}$ above the ground.</p>
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<h3>Step 1: Analyse the question to determine what information is provided</h3>
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<li>
<p>The ball has a mass $m = \text{0.15}\text{ kg}$</p>
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<li>
<p>The ball is at a height $h = \text{2}\text{ m}$</p>
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<li>
<p>The ball has a kinetic energy ${E}_{K} = \text{20}\text{ J}$</p>
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<h3>Step 2: Analyse the question to determine what is being asked</h3>
<p>We need to find the total mechanical energy of the ball</p>
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<h3>Step 3: Use the definition to calculate the total mechanical energy</h3>

\begin{align*} {E}_{M} &amp; = {E}_{P}+{E}_{K} \\ &amp; = mgh + \frac{1}{2}m{v}^{2} \\ &amp; = mgh + 20 \\ &amp; = \left(\text{0.15}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-1}$}\right)\left(\text{2}\text{ m}\right) + \text{20}\text{ J} \\ &amp; = \text{2.94}\text{ J} + \text{20}\text{ J} \\ &amp; = \text{22.94}\text{ J} \end{align*}</div>
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Mechanical 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.


Mechanical Energy

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