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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> |
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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> |
| $2.8.11.$ In a smooth fixed hemisphere, a stick of mass $m$ freely lies so that its angle with the horizon is equal to $\alpha$, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between $A$ and $B$? | | $2.8.11.$ In a smooth fixed hemisphere, a stick of mass $m$ freely lies so that its angle with the horizon is equal to $\alpha$, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between $A$ and $B$? |
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| For problem $2.8.11$ | | For problem $2.8.11$ |
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| <p> | | <p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| | | |
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| <img src="2.8.11_1.png" | | <img src="2.8.11_1.png" |
| loading="lazy" width="300" /> | | loading="lazy" width="300" /> |
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| Forces acting on the stick | | Forces acting on the stick |
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| </figure> | | </figure> |
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| <p> | | <p> |
| Equilibrium condition for vertical and horizontal axes respectively | | Equilibrium condition for vertical and horizontal axes respectively |
| $$mg = N_A \sin2\alpha +N_B\cos\alpha\quad(1)$$ | | $$mg = N_A \sin2\alpha +N_B\cos\alpha\quad(1)$$ |
| $$N_A \cos2\alpha = N_B\sin\alpha\quad(2)$$ | | $$N_A \cos2\alpha = N_B\sin\alpha\quad(2)$$ |
| Moment of forces with respect to point $A$ | | Moment of forces with respect to point $A$ |
| $$mg\cos\alpha \cdot \frac{l}{2} = N_B\cdot l_{AB}\quad(3)$$ | | $$mg\cos\alpha \cdot \frac{l}{2} = N_B\cdot l_{AB}\quad(3)$$ |
