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+ <header style="text-align:center;">
<h2>Solutions of Savchenko Physics Textbook</h2>
<p class="author">
Aliaksandr Melnichenka <br/>
October 2023
</p>
</header>
− <main>
− <article>
− <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
−
− <h4>Statement</h4>
− <p>
− $1.5.3$
− 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?
− </p>
− <center>
− <figure>
− <img src="statement.png"
− loading="lazy" alt="1.5.3" width="200" />
− <figcaption>
− For problem 1.5.3
− </figcaption>
− </figure>
− </center>
− <h4>Solution</h4>
− <p class="TxtSolutions">
− Firstly, we suppose there is no any friction. For a better understanding of the problem, consider the following figure
− </p>
+ <h3 id="back-link"><a href="../">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+
+ <p>
+ $1.5.3$
+ 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?
+ </p>
<center>
<figure>
− <img src="1.5.3.png"
+ <img src="statement.png"
loading="lazy" alt="1.5.3" width="200" />
<figcaption>
− Motion of wedge and rod
+ For problem 1.5.3
</figcaption>
</figure>
</center>
− <p class="TxtSolutions">
+
+ <h3>Solution</h3>
+
+ <p>
+ Firstly, we suppose there is no any friction. For a better understanding of the problem, consider the following figure
+ </p>
+
+ <center><figure><img
+ src="1.5.3.png" loading="lazy" alt="1.5.3" width="200" />
+ <figcaption>
+ Motion of wedge and rod
+ </figcaption>
+ </figure></center>
+
+ <p>
According to figure
− </p>
− <center>
− $\tan{30^\circ}=\frac{S_r}{S_w}$
− </center>
− <p class="TxtSolutions">
+ $$\tan{30^\circ}=\frac{S_r}{S_w}$$
and this relation is valid for velocities too because the motion is uniform (at constant speed)
− </p>
− <center>
− $\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$
+ $$\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$$
+ So, separating $v_w$
+ $$\boxed{v_w=v\sqrt{3}}$$
</center>
− So, separating $v_w$
− <center>
− $\boxed{v_w=v\sqrt{3}}$
− </center>
− <p class="TxtSolutions" 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>
Physics Department (FCNE)<br>
Universidad de Oriente, Cuba<br>
</p>
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