Updated spacing between @ latex expressions

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revision #10579 parent #9819 GitHub c702ebe ← older
en/2.8.13.md +5 −5
@@ -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="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
+ <meta name="description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<meta name="author" content="Aliaksandr Melnichenka">
<meta name="date" content="2023-10" scheme="YYYY-MM">
− <meta property="og:title" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
+ <meta property="og:title" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<meta property="og:image" content="img/logo.png">
− <meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
+ <meta property="og:description" content="Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.">
<meta name="yandex-verification" content="6cfda41f74038368">
− <title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu, and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
+ <title>Rolling mill rolls have radius R. Rotating, they retract the workpiece, if its thickness is small enough. The coefficient of friction between the rolls and the workpiece is \mu , and the gap between the rolls is d_0. Find the maximum thickness of the blank. The blank is not pushed.</title>
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@@ -85,7 +85,7 @@
Considering the value of friction force $F_\text{fr} = \mu N$:
$$\mu = \tan\alpha\quad(1)$$
From the drawing
−$$\frac{d-d_0}{2} = R(1-\cos\alpha) \Rightarrow \boxed{d = d_0 + 2R(1-\cos\alpha)}\quad(2)$$
+$$\frac{d-d_0}{2} = R(1-\cos\alpha ) \Rightarrow \boxed{d = d_0 + 2R(1-\cos\alpha )}\quad(2)$$
From the expression $(1)$,
$$\cos\alpha = \frac{1}{\sqrt{1+\tan^2\alpha}}=\frac{1}{\sqrt{1+\mu^2}}\quad(3)$$
After substituting $(3)$ into $(2)$, we could obtain the maximum thickness of the blank
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