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| <h2>Solutions of Savchenko Problems in Physics</h2> | | <h2>Solutions of Savchenko Problems in Physics</h2> |
| <p class="author"> | | <p class="author"> |
| Aliaksandr Melnichenka <br/> | | Aliaksandr Melnichenka <br/> |
| October 2023 | | October 2023 |
| </p> | | </p> |
| </header> | | </header> |
| | | |
| <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3> |
| <img src="https://savchenkosolutions.com/2/2.1.19/statement.png" | | <img src="https://savchenkosolutions.com/2/2.1.19/statement.png" |
| loading="lazy" width="140" /> | | loading="lazy" width="140" /> |
| <figcaption> | | <figcaption> |
| For problem $2.1.19$ | | For problem $2.1.19$ |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <p> | | <p> |
| Let's do a visual experiment, put a pen on a piece of paper and slowly move it to the side | | Let's do a visual experiment, put a pen on a piece of paper and slowly move it to the side |
| </p> | | </p> |
| <br> | | <br> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.19/demo.gif" | | <img src="https://savchenkosolutions.com/2/2.1.19/demo.gif" |
| loading="lazy" width="350" /> | | loading="lazy" width="350" /> |
| <figcaption> | | <figcaption> |
| Demonstration of a pen falling | | Demonstration of a pen falling |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| At some point, the pen will go in the opposite direction and slip out from under your hand | | At some point, the pen will go in the opposite direction and slip out from under your hand |
| </p> | | </p> |
| <br> | | <br> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.19/draw.png" | | <img src="https://savchenkosolutions.com/2/2.1.19/draw.png" |
| loading="lazy" width="250" /> | | loading="lazy" width="250" /> |
| <figcaption> | | <figcaption> |
| The pen is in a critical condition | | The pen is in a critical condition |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| Using a special program, we will determine the angle of the pen at this moment | | Using a special program, we will determine the angle of the pen at this moment |
| </p> | | </p> |
| <br> | | <br> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.19/angle.jpg" | | <img src="https://savchenkosolutions.com/2/2.1.19/angle.jpg" |
| loading="lazy" width="450" /> | | loading="lazy" width="450" /> |
| <figcaption> | | <figcaption> |
| Measuring the critical angle | | Measuring the critical angle |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| It worked | | It worked |
| $$ \boxed{\alpha = 7^{\circ}} $$ | | $$ \boxed{\alpha = 7^{\circ}} $$ |
| Let's display the forces acting on the handle | | Let's display the forces acting on the handle |
| </p> | | </p> |
| <br> | | <br> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="https://savchenkosolutions.com/2/2.1.19/draw1.png" | | <img src="https://savchenkosolutions.com/2/2.1.19/draw1.png" |
| loading="lazy" width="180" /> | | loading="lazy" width="180" /> |
| <figcaption> | | <figcaption> |
| Forces acting on the handle | | Forces acting on the handle |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| Since the friction force is the force of static friction | | Since the friction force is the force of static friction |
| $$ F_{тр} = \mu N $$ | | $$ F_{тр} = \mu N $$ |
| Let us write down the equilibrium condition at the critical moment | | Let us write down the equilibrium condition at the critical moment |
| $$ \left\{\begin{matrix} | | $$ \left\{\begin{matrix} |
| \mu N = F \sin \alpha\\ | | \mu N = F \sin \alpha\\ |
| N = F \cos \alpha | | N = F \cos \alpha |
| \end{matrix}\right. $$ | | \end{matrix}\right. $$ |
| Where | | Where |
| $$ \boxed{\mu = \tan \alpha} $$ | | $$ \boxed{\mu = \tan \alpha} $$ |
| We substitute experimental data | | We substitute experimental data |
| $$ \mu = \tan 7^{\circ} = 0.12 $$ | | $$ \mu = \tan 7^{\circ} = 0.12 $$ |
| </p> | | </p> |
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