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?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.5">$\leftarrow$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="statement.png"
          loading="lazy" alt="1.5.3" width="200" />
        <figcaption>
          For problem 1.5.3
        </figcaption>
      </figure>
    </center>

    <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
      $$\tan{30^\circ}=\frac{S_r}{S_w}$$
      and this relation is valid for velocities too because the motion is uniform (at constant speed)
      $$\tan{30^\circ}=\frac{v}{v_w}=\frac{\sqrt{3}}{3}$$
      So, separating $v_w$
      $$\boxed{v_w=v\sqrt{3}}$$
    </center>

    <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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