minor changes

Luisito правка от 20 июн. 2024 г., 03:10

правка #1460 предыдущая #1446 GitHub 6db7754 ← раньше позже →

en/2.8.4.md +2 −2


			<!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>

		@@ -34,7 +34,7 @@
			<h4>Statement</h4>
			<p>
			$2.8.4$
		−	Through three holes made in a desktop pass threads united by a common ~~nudo~~. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction.
		+	Through three holes made in a desktop pass threads united by a common knot. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction.
			</p>
			<center>
			<figure>
			<img src="statement.png"
			loading="lazy" alt="2.8.4" width="300" />
			<figcaption>
			For problem 2.8.4
			</figcaption>
			</figure>
		@@ -47,7 +47,7 @@
			</center>
			<h4>Solution</h4>
			<p class="TxtSolutions">
		−	Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$, for maintain the equilibrium. So, consider for example the angle $\gamma$
		+	Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$ and be directed in opposed sense for maintain the equilibrium. So, consider for example the angle $\gamma$
			</p>
			<center>
			<figure>
			<img src="draw.png"
			loading="lazy" alt="2.8.4" width="300" />
			<figcaption>
			Top view
			</figcaption>
			</figure>
			</center>
			<center>
			$T_R = T = 2T\cos{\frac{\gamma}{2}}$
			</center>
			<p class="TxtSolutions">
			Hence
			</p>
			<center>
			$\cos{\frac{\gamma}{2}} = 0.5$
			</center>
			<center>
			$\gamma = \frac{2\pi}{3} = 120^\circ$
			</center>
			<p class="TxtSolutions">
			But, since the above condition of the sum of two any tensions always is true, the three angles must be equal.
			</p>
			<center>
			$\boxed{\alpha=\beta=\gamma=120^\circ}$
			</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>
		ещё строк без изменений 63


	<!DOCTYPE html>		<!DOCTYPE html>
	<html lang="en">		<html lang="en">

	<head>		<head>
	<meta charset="UTF-8" />		<meta charset="UTF-8" />
	<meta name="viewport" content="width=device-width, initial-scale=1.0" />		<meta name="viewport" content="width=device-width, initial-scale=1.0" />
	<meta http-equiv="content-language" content="en">		<meta http-equiv="content-language" content="en">
	<script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script>		<script async src="https://www.googletagmanager.com/gtag/js?id=G-DDMB38YMLD"></script>

	<title>Savchenko Solutions</title>		<title>Savchenko Solutions</title>
	<meta property="og:image" content="img/logo.png">		<meta property="og:image" content="img/logo.png">
	<meta property="og:title" content="Savchenko Solutions"/>		<meta property="og:title" content="Savchenko Solutions"/>
	<meta name="description"		<meta name="description"
	content="A website with solutions to physics problems from Savenko Textbook" />		content="A website with solutions to physics problems from Savenko Textbook" />
	<meta name="keywords" content="physics, olympiads, ipho, savchenko" />		<meta name="keywords" content="physics, olympiads, ipho, savchenko" />
	<link rel="stylesheet" href="https://savchenko-physics.github.io/css/css-latex/style.css" />		<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">		<link rel="icon" type="image/x-icon" href="https://savchenko-physics.github.io/img/favicon.ico">
	</head>		</head>

	<body id="top">		<body id="top">
	<header>		<header>
	<h2>Solutions of Savchenko Physics Textbook</h2>		<h2>Solutions of Savchenko Physics Textbook</h2>
	<p class="author">		<p class="author">
	Aliaksandr Melnichenka <br/>		Aliaksandr Melnichenka <br/>
	October 2023		October 2023
	</p>		</p>
	</header>		</header>

	<main>		<main>
	<article>		<article>
	<h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>		<h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>

	@@ -34,7 +34,7 @@
	<h4>Statement</h4>		<h4>Statement</h4>
	<p>		<p>
	$2.8.4$		$2.8.4$
	Through three holes made in a desktop pass threads united by a common ~~nudo~~. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction.		Through three holes made in a desktop pass threads united by a common knot. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction.
	</p>		</p>
	<center>		<center>
	<figure>		<figure>
	<img src="statement.png"		<img src="statement.png"
	loading="lazy" alt="2.8.4" width="300" />		loading="lazy" alt="2.8.4" width="300" />
	<figcaption>		<figcaption>
	For problem 2.8.4		For problem 2.8.4
	</figcaption>		</figcaption>
	</figure>		</figure>
	@@ -47,7 +47,7 @@
	</center>		</center>
	<h4>Solution</h4>		<h4>Solution</h4>
	<p class="TxtSolutions">		<p class="TxtSolutions">
	Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$, for maintain the equilibrium. So, consider for example the angle $\gamma$		Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$ and be directed in opposed sense for maintain the equilibrium. So, consider for example the angle $\gamma$
	</p>		</p>
	<center>		<center>
	<figure>		<figure>
	<img src="draw.png"		<img src="draw.png"
	loading="lazy" alt="2.8.4" width="300" />		loading="lazy" alt="2.8.4" width="300" />
	<figcaption>		<figcaption>
	Top view		Top view
	</figcaption>		</figcaption>
	</figure>		</figure>
	</center>		</center>
	<center>		<center>
	$T_R = T = 2T\cos{\frac{\gamma}{2}}$		$T_R = T = 2T\cos{\frac{\gamma}{2}}$
	</center>		</center>
	<p class="TxtSolutions">		<p class="TxtSolutions">
	Hence		Hence
	</p>		</p>
	<center>		<center>
	$\cos{\frac{\gamma}{2}} = 0.5$		$\cos{\frac{\gamma}{2}} = 0.5$
	</center>		</center>
	<center>		<center>
	$\gamma = \frac{2\pi}{3} = 120^\circ$		$\gamma = \frac{2\pi}{3} = 120^\circ$
	</center>		</center>
	<p class="TxtSolutions">		<p class="TxtSolutions">
	But, since the above condition of the sum of two any tensions always is true, the three angles must be equal.		But, since the above condition of the sum of two any tensions always is true, the three angles must be equal.
	</p>		</p>
	<center>		<center>
	$\boxed{\alpha=\beta=\gamma=120^\circ}$		$\boxed{\alpha=\beta=\gamma=120^\circ}$
	</center>		</center>
	<p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">		<p class="TxtSolutions" style="text-align: right; font-style: italic; font-size: 14;">
	BSc. Luis Daniel Fernández Quintana<br>		BSc. Luis Daniel Fernández Quintana<br>
	Physics Department (FCNE)<br>		Physics Department (FCNE)<br>
	Universidad de Oriente, Cuba<br>		Universidad de Oriente, Cuba<br>
	</p>		</p>
	</article>		</article>
	</main>		</main>

	<script>		<script>
	MathJax = {		MathJax = {
	tex: {		tex: {
	inlineMath: [['$', '$'],],		inlineMath: [['$', '$'],],
	},		},
	}		}
	const typeFaceToggle = document.getElementById('typeface-toggle')		const typeFaceToggle = document.getElementById('typeface-toggle')
	const typeface = document.getElementById('typeface')		const typeface = document.getElementById('typeface')
	typeFaceToggle.addEventListener('click', () => {		typeFaceToggle.addEventListener('click', () => {
	document.body.classList.toggle('libertinus')		document.body.classList.toggle('libertinus')
	typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern'		typeface.textContent = document.body.classList.contains('libertinus') ? 'Libertinus' : 'Latin Modern'
	})		})

	const darkModeToggle = document.getElementById('dark-mode-toggle')		const darkModeToggle = document.getElementById('dark-mode-toggle')
	darkModeToggle.addEventListener('click', () => {		darkModeToggle.addEventListener('click', () => {
	document.body.classList.toggle('latex-dark')		document.body.classList.toggle('latex-dark')
	})		})
	</script>		</script>
	<script>		<script>
	window.dataLayer = window.dataLayer \|\| [];		window.dataLayer = window.dataLayer \|\| [];
	function gtag(){dataLayer.push(arguments);}		function gtag(){dataLayer.push(arguments);}
	gtag('js', new Date());		gtag('js', new Date());

	gtag('config', 'G-DDMB38YMLD');		gtag('config', 'G-DDMB38YMLD');
	</script>		</script>
	<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>		<script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>

	</body>		</body>

	</html>		</html>
	ещё строк без изменений 63