Added en 2.8.37 7.1.12

astrosander edited
View solution History
revision #2524 GitHub 21fdd30 newer →
en/2.8.37.md +110 −0
@@ -0,0 +1,110 @@
+<!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">
+ <meta name="keywords" content="solutions, savchenko, physics problems, olympiad physics, physics book">
+ <meta name="description" content="A website with solutions to physics problems from Savchenko Textbook">
+ <meta property="og:title" content="Savchenko Solutions">
+ <meta property="og:image" content="img/logo.png">
+ <meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
+ <meta name="yandex-verification" content="6cfda41f74038368">
+ <title>Savchenko Solutions</title>
+ <link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css">
+ <link rel="icon" href="https://savchenko-physics.github.io/img/logo.png" type="image/png">
+ <script src="https://savchenko-physics.github.io/js/jquery-1.10.1.min.js"></script>
+ <script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script>
+ <script type="text/x-mathjax-config">
+ MathJax.Hub.Config({
+ extensions: ['tex2jax.js'],
+ jax: ['input/TeX', 'output/HTML-CSS'],
+ tex2jax: {
+ inlineMath: [['$', '$'], ['$', '$']],
+ processEscapes: true,
+ processClass: 'tex2jax',
+ ignoreClass: 'html'
+ },
+ showProcessingMessages: false,
+ messageStyle: 'none'
+ });
+ </script>
+</head>
+ <body style="">
+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Physics Textbook</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../#2.8">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $2.8.37^*.$ A wheel of radius $R$ can rotate freely around its axis. Drive belts moving at a speed $v$ are pressed against the side surface of the wheel at a distance $h$ from the axis of rotation. Determine the steady-state angular velocity of the wheel if its contact with the drive belt occurs only along the rim.
+
+</p>
+<center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" width="230" />
+ <figcaption>
+ For problem $2.8.37^*$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+
+</p>
+<center>
+ <figure>
+ <img src="2.8.37.jpg"
+ loading="lazy" width="300" />
+ <figcaption>
+ Geometry of the problem
+ </figcaption>
+ </figure>
+</center>
+<p>
+From the geometry of the problem
+$$\left\{\begin{matrix}
+\frac{h}{R} = \cos\alpha \\
+\frac{u}{v} = \cos\alpha
+\end{matrix}\right.$$
+Considering the relationship between velocity $u$ and angular velocity $\omega$
+$$\left\{\begin{matrix}
+\frac{h}{R} = \frac{u}{v} \\
+u=\omega R
+\end{matrix}\right.$$
+From where
+$$\boxed{\omega=\frac{hv}{R^2}}$$
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$\omega=\frac{hv}{R^2}$$
+ </p>
+ <p style="text-align: right; font-style: italic; font-size: 14;">
+ Yuldashev Ulugbek<br>
+ </p>
+
+
+ <footer class="row container">
+ <br>
+ <p>
+ <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
+ </p>
+ <p>
+ <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
+ </p>
+ </footer>
+ </body>
+
+</html>