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| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> |
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| <p class="author"> | | <p class="author"> |
| Solutions of Savchenko Problems in Physics <br> | | Solutions of Savchenko Problems in Physics <br> |
| <i><b>knowledge must be free</b></i> | | <i><b>knowledge must be free</b></i> |
| </p> | | </p> |
| </header> | | </header> |
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| <h3 id="back-link"><a href="../../#2.8">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#2.8">$\leftarrow$Back</a></h3> |
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| <h3> Statement </h3> | | <h3> Statement </h3> |
| | | |
| <p> | | <p> |
| $2.8.4$ | | $2.8.4$ |
| Through three holes made in a desktop pass threads united by a common knot. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction. | | Through three holes made in a desktop pass threads united by a common knot. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction. |
| </p> | | </p> |
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| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" alt="2.8.4" width="200" /> | | loading="lazy" alt="2.8.4" width="200" /> |
| <figcaption> | | <figcaption> |
| For problem 2.8.4 | | For problem 2.8.4 |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
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| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$ and be directed in opposed sense for maintain the equilibrium. So, consider for example the angle $\gamma$ | | Tension in each thread is the same ($T=mg$). Moreover, note that the absolute value of the sum of two any tensions must be equal to the third one which is also $T$ and be directed in opposed sense for maintain the equilibrium. So, consider for example the angle $\gamma$ |
| </p> | | </p> |
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| <img src="draw.png" | | <img src="draw.png" |
| loading="lazy" alt="2.8.4" width="300" /> | | loading="lazy" alt="2.8.4" width="300" /> |
| <figcaption> | | <figcaption> |
| Top view | | Top view |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| $$T_R = T = 2T\cos{\frac{\gamma}{2}}$$ | | $$T_R = T = 2T\cos{\frac{\gamma}{2}}$$ |
| Hence | | Hence |
