Updated spacing between @ latex expressions

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revision #10561 parent #10144 GitHub c702ebe ← older
en/2.8.11.md +7 −7
@@ -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="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
+ <meta name="description" content="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha , and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
<meta name="author" content="Aliaksandr Melnichenka">
<meta name="date" content="2023-10" scheme="YYYY-MM">
− <meta property="og:title" content="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
+ <meta property="og:title" content="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha , and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
<meta property="og:image" content="img/logo.png">
− <meta property="og:description" content="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
+ <meta property="og:description" content="In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha , and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?">
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− <title>In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha, and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?</title>
+ <title>In a smooth fixed hemisphere, a stick of mass m freely lies so that its angle with the horizon is equal to \alpha , and its end extends beyond the edge of the hemisphere. With what forces does the wand act on the hemisphere at the points of contact between A and B?</title>
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@@ -82,9 +82,9 @@
$$mg = N_A \sin2\alpha +N_B\cos\alpha\quad(1)$$
$$N_A \cos2\alpha = N_B\sin\alpha\quad(2)$$
Moment of forces with respect to point $A$
−$$mg\cos\alpha \cdot \frac{l}{2} = N_B\cdot l_{AB}\quad(3)$$
+$$mg\cos\alpha\cdot \frac{l}{2} = N_B\cdot l_{AB}\quad(3)$$
Alternatively, moment of forces with respect to point $B$
−$$mg\cos\alpha \cdot \left(l_{AB} - \frac{l}{2}\right) = N_A\sin\alpha\cdot l_{AB}\quad(4)$$
+$$mg\cos\alpha\cdot \left(l_{AB} - \frac{l}{2}\right) = N_A\sin\alpha\cdot l_{AB}\quad(4)$$
Substituting in $(2)$, $(3)$ and $(4)$
$$\frac{l}{l_{AB}} = \frac{2\cos2\alpha}{\cos^2 \alpha}$$
$$\boxed{N_A = mg\tan\alpha}$$
@@ -94,7 +94,7 @@
<h4>Answer</h4>
<p>
− $$F_A=mg\operatorname{tg}\alpha; F_B=mg\cos2\alpha/\cos\alpha$$
+ $$F_A=mg\operatorname{tg}\alpha ; F_B=mg\cos2\alpha /\cos\alpha$$
</p>
<p style="text-align: right; font-style: italic; font-size: 14;">
Almaskhan Arsen<br>
unchanged lines 15