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+ <meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
+ <meta name="description" content="Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.">
+ <meta name="author" content="Aliaksandr Melnichenka">
+ <meta name="date" content="2023-10" scheme="YYYY-MM">
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+ <title>Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.</title>
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+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Problems in Physics</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $2.1.11.$ Find the acceleration of loads and tension forces of threads in the system shown in the figure. The block and threads are weightless, there is no friction.
+</p>
+<center>
+ <figure>
+ <img src="https://savchenkosolutions.com/2/2.1.11/statement.png"
+ loading="lazy" width="100" />
+ <figcaption>
+ For problem $2.1.11$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <center>
+<figure>
+<img src="https://savchenkosolutions.com/2/2.1.11/draw.png"
+loading="lazy" width="100" />
+<figcaption>
+Forces acting on loads
+</figcaption>
+</figure>
+</center>
+
+<p>
+Let's write Newton's second law for the vertical axis
+$$ \left\{\begin{matrix}
+ m_1a = T - m_1g\\
+ m_2a = m_2g - T
+ \end{matrix}\right. $$
+From here we express the acceleration, which will be the same for both loads due to the inelasticity of the thread.
+$$ \fbox{$a = g\frac{m_2-m_1}{m_2+m_1}$} $$
+We substitute into the system of equations and find the tension force of the thread $T$
+$$ \fbox{$T = \frac{2m_1m_2g}{m_1+m_2}$} $$
+</p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ <p>
+ $$a = g\frac{m_2-m_1}{m_2+m_1}$$
+ $$T = \frac{2m_1m_2g}{m_1+m_2}$$</p>
+ <p style="text-align: right; font-style: italic; font-size: 16;">Straton</p>
+
+
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