Translated 2.1.1-2.1.7
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| + | <meta name="description" content="The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer."> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer."> | ||
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| + | <title>The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer.</title> | ||
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| + | <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="../../#2.1">$\leftarrow$Back</a></h3> | ||
| + | |||
| + | <h3> Statement </h3> | ||
| + | <p> | ||
| + | $2.1.2.$ The puck, which was sliding on the ice, stopped after a time $t = 5$ s after hitting the stick at a distance $l = 20$ m from the place of impact. The mass of the washer is $m = 100$ g. Determine the friction force acting on the washer. | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | <p>According to Newton's second law | ||
| + | $$ m\vec{a} = m\vec{g} + \vec{N} + \vec{F_{fr}} $$ | ||
| + | In projection onto the direction of movement | ||
| + | $$ ma = F_{fr}\;(1) $$ | ||
| + | To find the friction force, we need to determine the acceleration of the body. We will suggest one of the methods. The distance traveled by the body before stopping is equal to | ||
| + | $$ l = v_{av}t = \frac{v_0 + 0}{2}t = \frac{v_0}{2}t $$ | ||
| + | Acceleration of the body | ||
| + | $$ 0 = v_0 - at\Rightarrow v_0 = at $$ | ||
| + | Then | ||
| + | $$ l = \frac{at}{2}t = \frac{at^2}{2}\Rightarrow a = \frac{2l}{t^2} $$ | ||
| + | Making a substitution in (1) | ||
| + | $$ F_{fr} = \frac{2ml}{t^2} $$ | ||
| + | Calculations | ||
| + | $$ F_{fr} = \frac{2 \cdot 0,1 kg \cdot 20 m}{(5 с)^2} = 0.16 \text{ N} $$ | ||
| + | It is interesting that acceleration can be obtained even more sifrly by using the “method by contradiction” in solving the problem, if from the stopping point, accelerate the puck back to the stick, then | ||
| + | $$ l = \frac{at^2}{2}\text{, and }a = \frac{2l}{t^2} $$ | ||
| + | </p> | ||
| + | |||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$\fbox{$F_{fr} = \frac{2ml}{t^2}$; $F_{fr} = 0.16 \text{ N}$}$$ | ||
| + | </p> | ||
| + | |||
| + | |||
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| + | <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> | ||
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| @@ -0,0 +1,91 @@ | |||
| <!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 puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer."> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer."> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer."> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>The puck, which was sliding on the ice, stopped after a time t = 5 s after hitting the stick at a distance l = 20 m from the place of impact. The mass of the washer is m = 100 g. Determine the friction force acting on the washer.</title> | |||
| <link rel="stylesheet" href="https://savchenkosolutions.com/css/css-latex/style.css"> | |||
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| }, | |||
| 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="../../#2.1">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $2.1.2.$ The puck, which was sliding on the ice, stopped after a time $t = 5$ s after hitting the stick at a distance $l = 20$ m from the place of impact. The mass of the washer is $m = 100$ g. Determine the friction force acting on the washer. | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| <p>According to Newton's second law | |||
| $$ m\vec{a} = m\vec{g} + \vec{N} + \vec{F_{fr}} $$ | |||
| In projection onto the direction of movement | |||
| $$ ma = F_{fr}\;(1) $$ | |||
| To find the friction force, we need to determine the acceleration of the body. We will suggest one of the methods. The distance traveled by the body before stopping is equal to | |||
| $$ l = v_{av}t = \frac{v_0 + 0}{2}t = \frac{v_0}{2}t $$ | |||
| Acceleration of the body | |||
| $$ 0 = v_0 - at\Rightarrow v_0 = at $$ | |||
| Then | |||
| $$ l = \frac{at}{2}t = \frac{at^2}{2}\Rightarrow a = \frac{2l}{t^2} $$ | |||
| Making a substitution in (1) | |||
| $$ F_{fr} = \frac{2ml}{t^2} $$ | |||
| Calculations | |||
| $$ F_{fr} = \frac{2 \cdot 0,1 kg \cdot 20 m}{(5 с)^2} = 0.16 \text{ N} $$ | |||
| It is interesting that acceleration can be obtained even more sifrly by using the “method by contradiction” in solving the problem, if from the stopping point, accelerate the puck back to the stick, then | |||
| $$ l = \frac{at^2}{2}\text{, and }a = \frac{2l}{t^2} $$ | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$\fbox{$F_{fr} = \frac{2ml}{t^2}$; $F_{fr} = 0.16 \text{ N}$}$$ | |||
| </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> | |||