A piece of iron weighs 9.8 N in water. Determine its volume. The density of iron is 7.8 \cdot 10^3 m^3.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#4.2">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>

    <p>
      $4.2.6$
      A piece of iron weighs 9.8 N in water. Determine its volume. The density of iron is 7.8 $\cdot$ 10$^3$ m$^3$.      
    </p>

    <h3>Solution</h3>
    <p>
      Let's consider the following figure
    </p>
    <center>
        <figure>
          <img src="draw.png"
            loading="lazy" alt="4.2.6" width="300" />
          <figcaption>
            Force analysis
          </figcaption>
        </figure>
      </center>
    <p>
      The normal force $N$ is what the equipment measures as apparent weight. 
      From Newton Second Law
      $$N = mg-F_A$$
      $$N = \rho\~g\~V-\rho_w\~g\~V$$
      $$N = (\rho-\rho_w)\~g\~V$$
      and taking $\rho_w = 1000$ kg/m$^3$
      $$\boxed{V = \frac{N}{(\rho-\rho_w)\~g}=147 \rm{cm}^3}$$
    </p>
    <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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