Updated spacing between @ latex expressions

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правка #10535 предыдущая #10073 GitHub c702ebe ← раньше позже →
en/2.1.44.md +8 −8
@@ -6,14 +6,14 @@
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta http-equiv="content-language" content="en">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
− <meta name="description" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu, angle of inclination of the plane \alpha, tg \alpha < \mu.">
+ <meta name="description" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu , angle of inclination of the plane \alpha , \tan\alpha < \mu .">
<meta name="author" content="Aliaksandr Melnichenka">
<meta name="date" content="2023-10" scheme="YYYY-MM">
− <meta property="og:title" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu, angle of inclination of the plane \alpha, tg \alpha < \mu.">
+ <meta property="og:title" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu , angle of inclination of the plane \alpha , \tan\alpha < \mu .">
<meta property="og:image" content="img/logo.png">
− <meta property="og:description" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu, angle of inclination of the plane \alpha, tg \alpha < \mu.">
+ <meta property="og:description" content="Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu , angle of inclination of the plane \alpha , \tan\alpha < \mu .">
<meta name="yandex-verification" content="6cfda41f74038368">
− <title>Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu, angle of inclination of the plane \alpha, tg \alpha < \mu.</title>
+ <title>Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity u to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction \mu , angle of inclination of the plane \alpha , \tan\alpha < \mu .</title>
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@@ -50,7 +50,7 @@
<h3> Statement </h3>
<p>
− $2.1.44^*.$ Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity $u$ to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction $\mu$, angle of inclination of the plane $\alpha$, $tg \alpha < \mu$.
+ $2.1.44^*.$ Determine the steady-state velocity of a body on an inclined plane that changes one direction of its velocity $u$ to the opposite direction with high frequency. The direction of movement of the plane is shown in the figure. Coefficient of friction $\mu$, angle of inclination of the plane $\alpha$, $\tan\alpha < \mu$.
</p>
<center>
<figure>
@@ -80,21 +80,21 @@
</p>
<p>
Since $v=\text{const}$, there is no acceleration in the direction along the speed $\vec{v}$
−$$ mg\sin\alpha = \mu mg \cos\alpha\cos\beta $$
+$$ mg\sin\alpha = \mu mg \cos\alpha\cos\beta$$
$$ \cos\beta = \frac{\tan\alpha}{\mu} $$
From geometric considerations, the moduli of the vectors $\vec{v}$ and $\vec{u}$ are related by the relation
$$ v=\frac{u}{\tan\beta} $$
$$ v=u \frac{\frac{\tan\alpha}{\mu}}{\sqrt{1-\frac{\tan^2\alpha}{\mu^2}}} $$
−$$ \boxed{v = u \frac{\tan \alpha }{\sqrt{\mu ^{2} − \tan^{2} \alpha }}} $$
+$$ \boxed{v = u \frac{\tan\alpha}{\sqrt{\mu^{2} − \tan^{2} \alpha}}} $$
</p>
</p>
<h4>Answer</h4>
<p>
− $$v = u \frac{\, \text{tg} \alpha }{\sqrt{\mu ^{2} − \text{tg}^{2} \alpha }}$$
+ $$v = u \frac{\, \text{tg} \alpha}{\sqrt{\mu^{2} − \text{tg}^{2} \alpha}}$$
</p>
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