<p>The following example illustrates the use of the law of conservation of mechanical energy.</p>
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<h2>Example: Using the Law of Conservation of Mechanical Energy</h2>
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<h3>Question</h3>
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<p>During a flood a tree trunk of mass $\text{100}$ $\text{kg}$ falls down a waterfall. The waterfall is $\text{5}$ $\text{m}$ high.</p>
<img alt="c070ce0e7348c3633c3d4f1e1bb082e0.png" src="https://data.ulearngo.com/assets/c710d40e-00f3-48d7-8438-d5e88a719c2c"/>
<p>If air resistance is ignored, calculate:</p>
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<p>the potential energy of the tree trunk at the top of the waterfall.</p>
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<p>the kinetic energy of the tree trunk at the bottom of the waterfall.</p>
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<p>the magnitude of the velocity of the tree trunk at the bottom of the waterfall.</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 tree trunk $m = \text{100}\text{ kg}$</p>
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<p>The height of the waterfall $h = \text{5}\text{ m}$.</p>
<p>These are all in SI units so we do not have to convert.</p>
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<h3>Step 2: Analyse the question to determine what is being asked</h3>
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<p>Potential energy at the top</p>
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<p>Kinetic energy at the bottom</p>
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<p>Velocity at the bottom</p>
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<h3>Step 3: Calculate the potential energy at the top of the waterfall.</h3>

\begin{align*} {E}_{P} &amp; = mgh \\ &amp; = \left(\text{100}\text{ kg}\right)\left(\text{9.8}\text{ m·s$^{-2}$}\right)\left(\text{5}\text{ m}\right) \\ &amp; = \text{4 900}\text{ J} \end{align*}</div>
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<h3>Step 4: Calculate the kinetic energy at the bottom of the waterfall.</h3>
<p>The total mechanical energy must be conserved.</p>

\[{E}_{K1} + {E}_{P1} = {E}_{K2} + {E}_{P2}\]

<p>Since the trunk's velocity is zero at the top of the waterfall, ${E}_{K1}=0$.</p>
<p>At the bottom of the waterfall, $h = \text{0}\text{ m}$, so ${E}_{P2}=0$.</p>
<p>Therefore ${E}_{P1} = {E}_{K2}$ or in words:</p>
<p>The kinetic energy of the tree trunk at the bottom of the waterfall is equal to the potential energy it had at the top of the waterfall. Therefore ${E}_{K} = \text{4 900}\text{ J}$</p>
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<h3>Step 5: Calculate the velocity at the bottom of the waterfall.</h3>
<p>To calculate the velocity of the tree trunk we need to use the equation for kinetic energy.</p>

\begin{align*} {E}_{K} &amp; = \frac{1}{2}m{v}^{2} \\ \text{4 900} &amp; = \frac{1}{2}\left(\text{100}\text{ kg}\right)\left({v}^{2}\right) \\ 98 &amp; = {v}^{2} \\ v &amp; = \text{9.899...}\text{ m·s$^{-1}$} \\ v &amp; = \text{9.90}\text{ m·s$^{-1}$} \end{align*}</div>
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Conservation of Energy Example

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.


Conservation of Energy Example

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