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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> |
| $4.2.6$ | | $4.2.6$ |
| A piece of iron weighs 9.8 N in water. Determine its volume. The density of iron is 7.8 $\cdot$ 10$^3$ m$^3$. | | 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> | | </p> |
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| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| Let's consider the following figure | | Let's consider the following figure |
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| <img src="draw.png" | | <img src="draw.png" |
| loading="lazy" alt="4.2.6" width="300" /> | | loading="lazy" alt="4.2.6" width="300" /> |
| <figcaption> | | <figcaption> |
| Force analysis | | Force analysis |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| The normal force $N$ is what the equipment measures as apparent weight. | | The normal force $N$ is what the equipment measures as apparent weight. |
| From Newton Second Law | | From Newton Second Law |
| $$N = mg-F_A$$ | | $$N = mg-F_A$$ |
| $$N = \rho~g~V-\rho_w~g~V$$ | | $$N = \rho~g~V-\rho_w~g~V$$ |
| $$N = (\rho-\rho_w)~g~V$$ | | $$N = (\rho-\rho_w)~g~V$$ |
| and taking $\rho_w = 1000$ kg/m$^3$ | | and taking $\rho_w = 1000$ kg/m$^3$ |
| $$\boxed{V = \frac{N}{(\rho-\rho_w)~g}=147 \rm{cm}^3}$$ | | $$\boxed{V = \frac{N}{(\rho-\rho_w)~g}=147 \rm{cm}^3}$$ |
| </p> | | </p> |
| <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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