Added Luis's English solution of 5.2.9

Luisito правка от
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+ <title>Savchenko Solutions</title>
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+ <meta property="og:title" content="Savchenko Solutions"/>
+ <meta name="description"
+ content="A website with solutions to physics problems from Savenko Textbook" />
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+
+<body id="top">
+ <header>
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <main>
+ <article>
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h4>Statement</h4>
+ <p>
+ $5.2.9$
+ A molecular projector creates a ribbon-shaped narrow beam of silver's atoms that arrive to internal surface of a cylinder of radius $R = 30$ cm and form a spot. The device rotates with angular velocity $\omega = 100\pi$ s$^{-1}$. Find the beam's velocity, if the spot deviates an angle $\varphi=0.314$ rad respect to initial position.
+ </p>
+ <center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" alt="5.2.9" width="200" />
+ <figcaption>
+ For problem 5.2.9
+ </figcaption>
+ </figure>
+ </center>
+ <h4>Solution</h4>
+ <p class="TxtSolutions">
+ When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
+ </p>
+ <center>
+ $\varphi=\omega t \;(1)$
+ </center>
+ The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
+ <center>
+ $R=vt \;(2)$
+ </center>
+ <p class="TxtSolutions">
+ Dividing $(2)$ by $(1)$ and separating $v$
+ </p>
+ <center>
+ $\boxed{v = \frac{\omega R}{\varphi}=300 \;{\rm{m/s}}}$
+ </center>
+ <p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">
+ BSc. Luis Daniel Fernández Quintana<br>
+ Physics Department (FCNE)<br>
+ Universidad de Oriente, Cuba<br>
+ </p>
+ </article>
+ </main>
+
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