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en/2.1.29.md
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| + | <meta name="description" content="A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?"> | ||
| + | <meta name="author" content="Aliaksandr Melnichenka"> | ||
| + | <meta name="date" content="2023-10" scheme="YYYY-MM"> | ||
| + | <meta property="og:title" content="A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?"> | ||
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| + | <title>A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?</title> | ||
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| + | </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> | ||
| + | $2.1.29.$ A car with a powerful engine, starting from a place, gains a speed of $72$ $\frac{km}{h}$ in $5$ seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed? | ||
| + | </p> | ||
| + | |||
| + | <h3>Solution</h3> | ||
| + | <p> | ||
| + | a<center> | ||
| + | <figure> | ||
| + | <img src="https://savchenkosolutions.com/2/2.1.29/sol.jpg" | ||
| + | loading="lazy" width="350" /> | ||
| + | <figcaption> | ||
| + | Forces acting on the car | ||
| + | </figcaption> | ||
| + | </figure> | ||
| + | </center> | ||
| + | |||
| + | <p> | ||
| + | Finding the deceleration value | ||
| + | $$ a = -\frac{\Delta v}{\Delta t} = -4 \,\frac{m}{s} $$ | ||
| + | |||
| + | $$ \Delta t = \frac{\Delta v}{a} $$ | ||
| + | 2. The kinematic equations of motion in this case are represented as follows: | ||
| + | $$ \boxed{x=v_0t-\frac{v \Delta t^2}{2}=\frac{v_0^2}{2a}=50 \,m} $$ | ||
| + | Let's find the coefficient of friction $\mu $: | ||
| + | $$ ma = \mu mg $$ | ||
| + | |||
| + | $$ \boxed{\mu = \frac{a}{g} = 0.4} $$ | ||
| + | </p> | ||
| + | </p> | ||
| + | |||
| + | <h4>Answer</h4> | ||
| + | <p> | ||
| + | $$\mu ≈ 0.4\text{; }l ≈ 50 \text{ m}$$ | ||
| + | </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> | ||
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| + | </footer> | ||
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| + | </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="A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?"> | |||
| <meta name="author" content="Aliaksandr Melnichenka"> | |||
| <meta name="date" content="2023-10" scheme="YYYY-MM"> | |||
| <meta property="og:title" content="A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?"> | |||
| <meta property="og:image" content="img/logo.png"> | |||
| <meta property="og:description" content="A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?"> | |||
| <meta name="yandex-verification" content="6cfda41f74038368"> | |||
| <title>A car with a powerful engine, starting from a place, gains a speed of 72 \frac{km}{h} in 5 seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed?</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"> | |||
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| <script async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.7/MathJax.js?config=TeX-MML-AM_CHTML"></script> | |||
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| MathJax.Hub.Config({ | |||
| extensions: ['tex2jax.js'], | |||
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| tex2jax: { | |||
| inlineMath: [['$', '$'], ['$', '$']], | |||
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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="../../#2.1">$\leftarrow$Back</a></h3> | |||
| <h3> Statement </h3> | |||
| <p> | |||
| $2.1.29.$ A car with a powerful engine, starting from a place, gains a speed of $72$ $\frac{km}{h}$ in $5$ seconds. Find the coefficient of friction between the wheels and the road. What is the shortest braking distance of a car that has reached this speed? | |||
| </p> | |||
| <h3>Solution</h3> | |||
| <p> | |||
| a<center> | |||
| <figure> | |||
| <img src="https://savchenkosolutions.com/2/2.1.29/sol.jpg" | |||
| loading="lazy" width="350" /> | |||
| <figcaption> | |||
| Forces acting on the car | |||
| </figcaption> | |||
| </figure> | |||
| </center> | |||
| <p> | |||
| Finding the deceleration value | |||
| $$ a = -\frac{\Delta v}{\Delta t} = -4 \,\frac{m}{s} $$ | |||
| $$ \Delta t = \frac{\Delta v}{a} $$ | |||
| 2. The kinematic equations of motion in this case are represented as follows: | |||
| $$ \boxed{x=v_0t-\frac{v \Delta t^2}{2}=\frac{v_0^2}{2a}=50 \,m} $$ | |||
| Let's find the coefficient of friction $\mu $: | |||
| $$ ma = \mu mg $$ | |||
| $$ \boxed{\mu = \frac{a}{g} = 0.4} $$ | |||
| </p> | |||
| </p> | |||
| <h4>Answer</h4> | |||
| <p> | |||
| $$\mu ≈ 0.4\text{; }l ≈ 50 \text{ m}$$ | |||
| </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> | |||