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+ <meta name="description" content="A system of three identical balls connected by identical springs is suspended on a thread. The thread is burned out. Find the acceleration of the balls immediately after burning the thread.">
+ <meta name="author" content="Aliaksandr Melnichenka">
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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>
+ $2.1.14.$ A system of three identical balls connected by identical springs is suspended on a thread. The thread is burned out. Find the acceleration of the balls immediately after burning the thread.
+</p>
+<center>
+ <figure>
+ <img src="https://savchenkosolutions.com/2/2.1.14/statement.png"
+ loading="lazy" width="250" />
+ <figcaption>
+ For problem $2.1.14$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <center>
+<figure>
+<img src="https://savchenkosolutions.com/2/2.1.14/draw.png"
+loading="lazy" width="270" />
+<figcaption>
+Forces acting on the system
+</figcaption>
+</figure>
+</center>
+
+<p>
+When the oscillations have already stopped, the balls move with the same acceleration $a$.
+</p>
+<p>
+Let's write Newton's second law
+$$
+ \left\{\begin{matrix}
+ m_1a_1 = -k\Delta x \\
+ m_2a_2 = -F + k\Delta x
+ \end{matrix}\right. $$
+Socratic to $a$
+$$ \frac{m_1}{m_2} = \frac{-k\Delta x}{-F + k\Delta x} $$
+We express $\Delta x$
+$$ \boxed{\Delta x = \frac{F}{k} \frac{m_1}{m_1+m_2}} $$
+Immediately after the force ceases to act on the bodies, the elastic force $k \Delta x$ will act, which will cause acceleration
+$$
+ \left\{\begin{matrix}
+ m_1a_1 = -k\Delta x \\
+ m_2a_2 = k\Delta x
+ \end{matrix}\right. $$
+Where do we express $a_1$?
+$$ \boxed{a_1 = -\frac{F}{m_{2}+m_{1}}} $$
+And similarly $a_2$
+$$ \boxed{a_1 = \frac{Fm_{1}}{m_{2}(m_{1}+m_{2})}} $$
+<p>
+
+ </p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ <p>
+ $$x=-\frac{Fm_{1}}{k(m_{1}+m_{2})}$$
+ $$a_{1}=-\frac{F}{m_{2}+m_{1}}$$
+ $$a_{2}=\frac{Fm_{1}}{m_{2}(m_{1}+m_{2})}$$
+ </p>
+ <p style="text-align: right; font-style: italic; font-size: 16;">Straton</p>
+ </p>
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