Added Luis's English solution of 5.2.9
en/5.2.9.md
+102 −0
| @@ -0,0 +1,102 @@ | |||
| + | |||
| + | <!DOCTYPE html> | ||
| + | <html lang="en"> | ||
| + | |||
| + | <head> | ||
| + | <meta charset="UTF-8" /> | ||
| + | <meta name="viewport" content="width=device-width, initial-scale=1.0" /> | ||
| + | <meta http-equiv="content-language" content="en"> | ||
| + | <script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script> | ||
| + | |||
| + | <title>Savchenko Solutions</title> | ||
| + | <meta property="og:image" content="img/logo.png"> | ||
| + | <meta property="og:title" content="Savchenko Solutions"/> | ||
| + | <meta name="description" | ||
| + | content="A website with solutions to physics problems from Savenko Textbook" /> | ||
| + | <meta name="keywords" content="physics, olympiads, ipho, savchenko" /> | ||
| + | <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css" /> | ||
| + | <link rel="icon" type="image/x-icon" href="https://savchenko-physics.github.io/img/favicon.ico"> | ||
| + | </head> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | <script> | ||
| + | MathJax = { | ||
| + | tex: { | ||
| + | inlineMath: [['$', '$'],], | ||
| + | }, | ||
| + | } | ||
| + | const typeFaceToggle = document.getElementById('typeface-toggle') | ||
| + | const typeface = document.getElementById('typeface') | ||
| + | typeFaceToggle.addEventListener('click', () => { | ||
| + | document.body.classList.toggle('libertinus') | ||
| + | typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern' | ||
| + | }) | ||
| + | |||
| + | const darkModeToggle = document.getElementById('dark-mode-toggle') | ||
| + | darkModeToggle.addEventListener('click', () => { | ||
| + | document.body.classList.toggle('latex-dark') | ||
| + | }) | ||
| + | </script> | ||
| + | <script> | ||
| + | window.dataLayer = window.dataLayer || []; | ||
| + | function gtag(){dataLayer.push(arguments);} | ||
| + | gtag('js', new Date()); | ||
| + | |||
| + | gtag('config', 'G-DDMB38YMLD'); | ||
| + | </script> | ||
| + | <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> | ||
| + | |||
| + | </body> | ||
| + | |||
| + | </html> | ||
| @@ -0,0 +1,102 @@ | |||
| <!DOCTYPE html> | |||
| <html lang="en"> | |||
| <head> | |||
| <meta charset="UTF-8" /> | |||
| <meta name="viewport" content="width=device-width, initial-scale=1.0" /> | |||
| <meta http-equiv="content-language" content="en"> | |||
| <script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script> | |||
| <title>Savchenko Solutions</title> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:title" content="Savchenko Solutions"/> | |||
| <meta name="description" | |||
| content="A website with solutions to physics problems from Savenko Textbook" /> | |||
| <meta name="keywords" content="physics, olympiads, ipho, savchenko" /> | |||
| <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css" /> | |||
| <link rel="icon" type="image/x-icon" href="https://savchenko-physics.github.io/img/favicon.ico"> | |||
| </head> | |||
| <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> | |||
| <script> | |||
| MathJax = { | |||
| tex: { | |||
| inlineMath: [['$', '$'],], | |||
| }, | |||
| } | |||
| const typeFaceToggle = document.getElementById('typeface-toggle') | |||
| const typeface = document.getElementById('typeface') | |||
| typeFaceToggle.addEventListener('click', () => { | |||
| document.body.classList.toggle('libertinus') | |||
| typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern' | |||
| }) | |||
| const darkModeToggle = document.getElementById('dark-mode-toggle') | |||
| darkModeToggle.addEventListener('click', () => { | |||
| document.body.classList.toggle('latex-dark') | |||
| }) | |||
| </script> | |||
| <script> | |||
| window.dataLayer = window.dataLayer || []; | |||
| function gtag(){dataLayer.push(arguments);} | |||
| gtag('js', new Date()); | |||
| gtag('config', 'G-DDMB38YMLD'); | |||
| </script> | |||
| <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> | |||
| </body> | |||
| </html> | |||