Translated 3.1.1-3.1.17
en/3.1.11.md
+96 −0
| @@ -0,0 +1,96 @@ | |||
| + | <!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="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | ||
| + | <meta name="description" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | ||
| + | <meta property="og:image" content="img/logo.png"> | ||
| + | <meta property="og:description" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | ||
| + | <meta name="yandex-verification" content="6cfda41f74038368"> | ||
| + | <title>Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?</title> | ||
| + | <link rel="stylesheet" href="https://savchenkosolutions.com/css/css-latex/style.css"> | ||
| + | <link rel="icon" href="https://savchenkosolutions.com/img/logo.png" type="image/png"> | ||
| + | <script src="https://savchenkosolutions.com/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;"> | ||
| + | <div id = "logo"> | ||
| + | <span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span> | ||
| + | </div> | ||
| + | <p class="author"> | ||
| + | Solutions of Savchenko Problems in Physics <br> | ||
| + | <i><b>knowledge must be free</b></i> | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <h3 id="back-link"><a href="../../#3.1">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $3.1.11.$ Two springs of stiffness $k$ connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance $x$ to the equilibrium position? | ||
| + | </p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/3/3.1.11/statement.png" | ||
| + | loading="lazy" width="130" /> | ||
| + | <figcaption> | ||
| + | For problem $3.1.11$ | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | <p> | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | Each spring will have an elastic force when stretched | ||
| + | $$ F_y=k\Delta l=kx\cos\alpha $$ | ||
| + | Condition of equality of forces | ||
| + | $$ mg=2F_y\cos\alpha=2kx\cos^2\alpha $$ | ||
| + | Where, weight of cargo | ||
| + | $$ \boxed{m=\frac{2kx\cos^2\alpha}{g}} $$ | ||
| + | </p> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$m=\frac{2kx\cos^2\alpha}{g}$$ | ||
| + | </p> | ||
| + | <p style="text-align: right; font-style: italic; font-size: 14;"> | ||
| + | Dzikan Mikita<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> alex@savchenkosolutions.com <br></small> | ||
| + | </p> | ||
| + | </footer> | ||
| + | </body> | ||
| + | |||
| + | </html> | ||
| @@ -0,0 +1,96 @@ | |||
| <!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="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda"> | |||
| <meta name="description" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?"> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>Two springs of stiffness k connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance x to the equilibrium position?</title> | |||
| <link rel="stylesheet" href="https://savchenkosolutions.com/css/css-latex/style.css"> | |||
| <link rel="icon" href="https://savchenkosolutions.com/img/logo.png" type="image/png"> | |||
| <script src="https://savchenkosolutions.com/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;"> | |||
| <div id = "logo"> | |||
| <span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span> | |||
| </div> | |||
| <p class="author"> | |||
| Solutions of Savchenko Problems in Physics <br> | |||
| <i><b>knowledge must be free</b></i> | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../../#3.1">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $3.1.11.$ Two springs of stiffness $k$ connected as shown in the figure are not deformed. What mass should the load be suspended from the point where the springs are connected so that it falls a small distance $x$ to the equilibrium position? | |||
| </p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/3/3.1.11/statement.png" | |||
| loading="lazy" width="130" /> | |||
| <figcaption> | |||
| For problem $3.1.11$ | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p> | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| Each spring will have an elastic force when stretched | |||
| $$ F_y=k\Delta l=kx\cos\alpha $$ | |||
| Condition of equality of forces | |||
| $$ mg=2F_y\cos\alpha=2kx\cos^2\alpha $$ | |||
| Where, weight of cargo | |||
| $$ \boxed{m=\frac{2kx\cos^2\alpha}{g}} $$ | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$m=\frac{2kx\cos^2\alpha}{g}$$ | |||
| </p> | |||
| <p style="text-align: right; font-style: italic; font-size: 14;"> | |||
| Dzikan Mikita<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> alex@savchenkosolutions.com <br></small> | |||
| </p> | |||
| </footer> | |||
| </body> | |||
| </html> | |||