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<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
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+
+ <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>
− $\varphi=\omega t \;(1)$
+ <figure>
+ <img src="statement.png"
+ loading="lazy" alt="5.2.9" width="200" />
+ <figcaption>
+ For problem 5.2.9
+ </figcaption>
+ </figure>
</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 $v$
+
+ <h3>Solution</h3>
+ <p>
+ When first atom of the beam arrives to surface after a time $t$, the cylinder has sweep the angle $\varphi$. So
+ $$\varphi=\omega t \;(1)$$
+ The atoms are displaced from center to surface during same time $t$, considering constant velocity $v$
+ $$R=vt \;(2)$$
+ Dividing $(2)$ by $(1)$ and separating $v$
+ $$\boxed{v = \frac{\omega R}{\varphi}=300 \;{\rm{m/s}}}$$
</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>
+ <p 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>
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