Updated greek laters @ latex compiling

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правка #10161 предыдущая #9222 GitHub dbb31ba ← раньше позже →
en/4.2.14.md +4 −4
@@ -81,17 +81,17 @@
From right figure
$$\cos{\theta} = \frac{R}{2R} = 0.5$$
so, $\theta = 60^\circ$. Applying Newton Second Law for submerged trunk on $x$-axis,
− $$N = N_t~\sin{\theta} \;(1)$$
+ $$N = N_t~\sin{\theta} \quad(1)$$
on $y$-axis
$$F_{A1} = mg + N_t~\cos{\theta}$$
− $$\rho_w~g~V = mg + N_t~\cos{\theta} \;(2)$$
+ $$\rho_w~g~V = mg + N_t~\cos{\theta} \quad(2)$$
For half-submerged trunk, on $x$-axis,
$$N = N_t~\sin{\theta}$$
on $y$-axis
$$F_{A2} + N_t~\cos{\theta} = mg$$
− $$\rho_w~g~\frac{V}{2} + N_t~\cos{\theta} = mg \;(3)$$
+ $$\rho_w~g~\frac{V}{2} + N_t~\cos{\theta} = mg \quad(3)$$
Substituting $(2)$ into $(3)$, it is obtained
− $$N_t = \frac{mg}{3~\cos{\theta}} \;(4)$$
+ $$N_t = \frac{mg}{3~\cos{\theta}} \quad(4)$$
Putting $(4)$ into $(1)$
$$N = \frac{mg}{3}~\tan{\theta}$$
$$\boxed{N = \frac{mg}{\sqrt{3}}}$$
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