$\leftarrow$Back

  <h4>Statement</h4>
  <p>
    $2.8.4$
    Through three holes made in a desktop pass threads united by a common nudo. At the free ending of each thread is hanged equal loads. Determine the angles between threads. There is no friction.  
  </p>
  <center>
    <figure>
      <img src="statement.png"
        loading="lazy" alt="2.8.4" width="300" />
      <figcaption>
        For problem 2.8.4
      </figcaption>
    </figure>
  </center>
  <h4>Solution</h4>
  <p class="TxtSolutions">
    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 $T$, for maintain the equilibrium. So, consider for example the angle $\gamma$
  </p>
  <center>
    <figure>
      <img src="draw.png"
        loading="lazy" alt="2.8.4" width="300" />
      <figcaption>
        Top view
      </figcaption>
    </figure>
  </center>
  <center>
    $T_R = T = 2T\cos{\frac{\gamma}{2}}$
  </center>
   <p class="TxtSolutions">
    Hence
   </p>
    <center>
      $\cos{\frac{\gamma}{2}} = 0.5$
    </center>
    <center>
      $\gamma = \frac{2\pi}{3} = 120^\circ$
    </center>
    <p class="TxtSolutions">
      But, since the above condition of the sum of two any tensions always is true, the three angles must be equal.
    </p>
    <center>
        $\boxed{\alpha=\beta=\gamma=120^\circ}$
    </center>
    <p class="TxtSolutions" 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>
</article>