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| <h2>Solutions of Savchenko Physics Textbook</h2> | | <h2>Solutions of Savchenko Physics Textbook</h2> |
| <p class="author"> | | <p class="author"> |
| Aliaksandr Melnichenka <br/> | | Aliaksandr Melnichenka <br/> |
| October 2023 | | October 2023 |
| <p> | | <p> |
| $1.5.3$ | | $1.5.3$ |
| A wedge has a slope's angle of 30$^\circ$. A vertical rod goes down with velocity $v$ and pushes the wedge. What velocity will develope the wedge? | | A wedge has a slope's angle of 30$^\circ$. A vertical rod goes down with velocity $v$ and pushes the wedge. What velocity will develope the wedge? |
| </p> | | </p> |
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| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" alt="1.5.3" width="200" /> | | loading="lazy" alt="1.5.3" width="200" /> |
| <figcaption> | | <figcaption> |
| For problem 1.5.3 | | For problem 1.5.3 |
| </figcaption> | | </figcaption> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
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| <p> | | <p> |
| Firstly, we suppose there is no any friction. For a better understanding of the problem, consider the following figure | | Firstly, we suppose there is no any friction. For a better understanding of the problem, consider the following figure |
| </p> | | </p> |
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| src="1.5.3.png" loading="lazy" alt="1.5.3" width="200" /> | | src="1.5.3.png" loading="lazy" alt="1.5.3" width="200" /> |
| <figcaption> | | <figcaption> |
| Motion of wedge and rod | | Motion of wedge and rod |
| </figcaption> | | </figcaption> |
| </figure></center> | | </figure></center> |
| | | |
| <p> | | <p> |
| According to figure | | According to figure |
| $$\tan{30^\circ}=\frac{S_r}{S_w}$$ | | $$\tan{30^\circ}=\frac{S_r}{S_w}$$ |
| and this relation is valid for velocities too because the motion is uniform (at constant speed) | | and this relation is valid for velocities too because the motion is uniform (at constant speed) |
| $$\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$$ | | $$\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$$ |
| So, separating $v_w$ | | So, separating $v_w$ |
| $$\boxed{v_w=v\sqrt{3}}$$ | | $$\boxed{v_w=v\sqrt{3}}$$ |
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| <p style="text-align: right; font-style: italic; font-size: 14;"> | | <p style="text-align: right; font-style: italic; font-size: 14;"> |
| BSc. Luis Daniel Fernández Quintana<br> | | BSc. Luis Daniel Fernández Quintana<br> |
| Physics Department (FCNE)<br> | | Physics Department (FCNE)<br> |
| Universidad de Oriente, Cuba<br> | | Universidad de Oriente, Cuba<br> |
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