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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/2/2.1.17/statement.png" | | <img src="https://savchenkosolutions.com/2/2.1.17/statement.png" |
| loading="lazy" width="120" /> | | loading="lazy" width="120" /> |
| <figcaption> | | <figcaption> |
| For problem $2.1.17$ | | For problem $2.1.17$ |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
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| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
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| loading="lazy" width="250" /> | | loading="lazy" width="250" /> |
| <figcaption> | | <figcaption> |
| Forces acting on a magnet | | Forces acting on a magnet |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| 1. The body can be considered as free if the connections are replaced by their reactions. The friction force in this case is caused by the action of the magnetic force, i.e. | | 1. The body can be considered as free if the connections are replaced by their reactions. The friction force in this case is caused by the action of the magnetic force, i.e. |
| $$ F_{fr} = \mu F_m $$ | | $$ F_{fr} = \mu F_m $$ |
| 2. The condition of mass equilibrium, in this case, will take place when the magnitudes of gravity and friction are equal. | | 2. The condition of mass equilibrium, in this case, will take place when the magnitudes of gravity and friction are equal. |
| $$ m_0 g = \mu F_m\Rightarrow \boxed{F_m = \frac{gm_0}{\mu}} $$ | | $$ m_0 g = \mu F_m\Rightarrow \boxed{F_m = \frac{gm_0}{\mu}} $$ |
| 3. When the body starts moving at $m > m_0$, then the equation of Newton's second law becomes valid, which in projection onto the $y$ axis will be written as follows | | 3. When the body starts moving at $m > m_0$, then the equation of Newton's second law becomes valid, which in projection onto the $y$ axis will be written as follows |
| $$ mg - m_0 g = ma $$ | | $$ mg - m_0 g = ma $$ |
| | | |
| $$ \boxed{a = g \frac{m - m_0}{m}} $$ | | $$ \boxed{a = g \frac{m - m_0}{m}} $$ |
| </p> | | </p> |
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| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| $$F = m_0g/\mu ;$$ | | $$F = m_0g/\mu ;$$ |
| $$a = g(m − m_0)/m$$ | | $$a = g(m − m_0)/m$$ |
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