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			<h2>Solutions of Savchenko Problems in Physics</h2>
			<p class="author">
			Aliaksandr Melnichenka <br/>
			October 2023
			</p>
			</header>

			<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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	</head>		</head>
	<body style="">		<body style="">
	<header style="text-align:center;">		<header style="text-align:center;">
	<h2>Solutions of Savchenko Problems in Physics</h2>		<h2>Solutions of Savchenko Problems in Physics</h2>
	<p class="author">		<p class="author">
	Aliaksandr Melnichenka <br/>		Aliaksandr Melnichenka <br/>
	October 2023		October 2023
	</p>		</p>
	</header>		</header>

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

	<h3> Statement </h3>		<h3> Statement </h3>

	<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>

	<h3>Solution</h3>		<h3>Solution</h3>
	<p>		<p>
	Let's consider the following figure		Let's consider the following figure
	</p>		</p>
	<center>		<center>
	<figure>		<figure>
	<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>
	</p>		</p>



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