Translated 1.5.11-1.5.20
en/1.5.20.md
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| + | <meta name="description" content="The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?"> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?"> | ||
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| + | <title>The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?</title> | ||
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| + | <body style=""> | ||
| + | <header style="text-align:center;"> | ||
| + | <h2>Solutions of Savchenko Problems in Physics</h2> | ||
| + | <p class="author"> | ||
| + | Aliaksandr Melnichenka <br/> | ||
| + | October 2023 | ||
| + | </p> | ||
| + | </header> | ||
| + | |||
| + | <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $1.5.20.$ The reel of tape is played back during time $t$ at the film drawing speed $v$. The initial radius of the reel (with film) is $R$, and the final radius (without film) is $r$. What is the thickness of the film? | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | <center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/1/1.5.20/draw.png" | ||
| + | loading="lazy" width="150" /> | ||
| + | <figcaption> | ||
| + | Film reel | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | |||
| + | <p>Film wound on a reel takes up an area</p> | ||
| + | <p> | ||
| + | $$ S = \pi (R^2 - r^2) $$ | ||
| + | </p> | ||
| + | <p>If the film is completely unwound at a speed of $v$ in time $t$, then the length of the film </p> | ||
| + | <p> | ||
| + | $$ l = vt $$ | ||
| + | </p> | ||
| + | <p>In cross-section, the film is a rectangle whose area is $S$ and length is $l$. Then the width of this rectangle (it is also the thickness of the film)</p> | ||
| + | <p> | ||
| + | $$ \fbox{$d = \frac{S}{l} = \frac{\pi (R^2 - r^2)}{vt}$} $$ | ||
| + | </p> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$d = \frac{\pi (R^2 - r^2)}{vt}$$ | ||
| + | </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 +1,95 @@ | |||
| <!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="The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?"> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?"> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?"> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>The reel of tape is played back during time t at the film drawing speed v. The initial radius of the reel (with film) is R, and the final radius (without film) is r. What is the thickness of the film?</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> | |||
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| processClass: 'tex2jax', | |||
| ignoreClass: 'html' | |||
| }, | |||
| showProcessingMessages: false, | |||
| messageStyle: 'none' | |||
| }); | |||
| </script> | |||
| </head> | |||
| <body style=""> | |||
| <header style="text-align:center;"> | |||
| <h2>Solutions of Savchenko Problems in Physics</h2> | |||
| <p class="author"> | |||
| Aliaksandr Melnichenka <br/> | |||
| October 2023 | |||
| </p> | |||
| </header> | |||
| <h3 id="back-link"><a href="../../#1.5">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $1.5.20.$ The reel of tape is played back during time $t$ at the film drawing speed $v$. The initial radius of the reel (with film) is $R$, and the final radius (without film) is $r$. What is the thickness of the film? | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| <center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/1/1.5.20/draw.png" | |||
| loading="lazy" width="150" /> | |||
| <figcaption> | |||
| Film reel | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p>Film wound on a reel takes up an area</p> | |||
| <p> | |||
| $$ S = \pi (R^2 - r^2) $$ | |||
| </p> | |||
| <p>If the film is completely unwound at a speed of $v$ in time $t$, then the length of the film </p> | |||
| <p> | |||
| $$ l = vt $$ | |||
| </p> | |||
| <p>In cross-section, the film is a rectangle whose area is $S$ and length is $l$. Then the width of this rectangle (it is also the thickness of the film)</p> | |||
| <p> | |||
| $$ \fbox{$d = \frac{S}{l} = \frac{\pi (R^2 - r^2)}{vt}$} $$ | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$d = \frac{\pi (R^2 - r^2)}{vt}$$ | |||
| </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> | |||