Translated 2.1.34-2.1.47

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+ <meta name="description" content="Which washer, rotating around its axis or not rotating, will go the longest way to stop on a rough horizontal surface? The initial velocity of the puck centers is the same.">
+ <meta name="author" content="Aliaksandr Melnichenka">
+ <meta name="date" content="2023-10" scheme="YYYY-MM">
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+ <span><img src = "../../img/book.png"><span><span>Savchenko Solutions</span>
+ </div>
+ <p class="author">
+ Solutions of Savchenko Problems in Physics <br>
+ <i><b>knowledge must be free</b></i>
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../../#2.1">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $2.1.41.$ Which washer, rotating around its axis or not rotating, will go the longest way to stop on a rough horizontal surface? The initial velocity of the puck centers is the same.
+</p>
+<center>
+ <figure>
+ <img src="https://savchenkosolutions.com/2/2.1.41/statement.png"
+ loading="lazy" width="250" />
+ <figcaption>
+ For problem $2.1.41$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <center>
+<figure>
+<img src="https://savchenkosolutions.com/2/2.1.41/sol.png"
+loading="lazy" width="350" />
+<figcaption>
+Motion of a rotating puck
+</figcaption>
+</figure>
+</center>
+
+<p>
+1. A reciprocating puck has only the kinetic energy of reciprocating motion
+$$ K_1=\frac{mv^2}{2} $$
+the flat motion of the puck, which is a superposition of translational and rotational motion, is characterized by two components of kinetic energy: translational and rotational:
+$$ K_2=\frac{mv^2}{2}+J_z\frac{\omega ^2}{2} $$
+
+$$ K_2=\frac{mv^2}{2}+\frac{mr^2}{2}\cdot\frac{\omega ^2}{2} $$
+
+$$ K_2=\frac{m}{2}(v^2+\frac{r^2 \omega ^2}{2}) $$
+
+$$ K_2=\frac{3}{4}mv^2 $$
+
+$$ K_2>K_1 $$
+2. The initial kinetic energy of the washers in both cases will be spent on work against the friction force.
+$$ A_{тр} = µmg\Delta x $$
+3. According to the theorem on the change in kinetic energy:
+$$ \frac{K_2}{K_1}=\frac{\Delta x_2}{\Delta x_1}=1.5 $$
+</p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ Rotating
+ </p>
+
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