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Ajout transformation d'unité d'heures en années

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Guyot 2021-10-20 09:51:14 +02:00
parent 0c5d8fc258
commit 713071f3ed
10 changed files with 36518 additions and 33356 deletions
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130
MecaPres.aux
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\BOOKMARK [3][]{Outline0.1.2.26}{L'infiniment petit}{Outline0.1}% 3
\BOOKMARK [2][]{Outline0.2}{Mouvements}{}% 4
\BOOKMARK [3][]{Outline0.2.1.32}{L'infiniment grand}{Outline0.2}% 5
\BOOKMARK [3][]{Outline0.2.2.47}{L'infiniment petit}{Outline0.2}% 6
\BOOKMARK [3][]{Outline0.2.2.49}{L'infiniment petit}{Outline0.2}% 6
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\BOOKMARK [2][]{Outline1.3}{R\351f\351rences}{Outline1}% 8
\BOOKMARK [2][]{Outline1.4}{Cr\351dits photographiques}{Outline1}% 9

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\beamer@slide {notes}{56}

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MecaPres.tex
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\usepackage{array}
\usepackage{comment}
\usepackage{enumerate}
\usepackage{siunitx} % pour la gestion des unités
\sisetup{
per-mode = symbol-or-fraction,
exponent-product = \cdot,
output-decimal-marker = {,}
}
\begin{document}
@ -517,6 +523,71 @@ Bien d'autres exemples existent et font l'objet d'études approfondies\endnote{\
\end{overlayarea}
\end{frame}
\begin{frame}{Transformation des unités}
Le calcul précédent est intéressant car il montre que les changements d'unités sont omniprésents en physique.
\smallskip
Revenons sur la toute dernière partie du calcul : transformer des heures en années. En y réfléchissant, on comprend vite qu'une clé du calcul sera le chiffre \[r= 24\cdot 365=\SI{8760}{\hour\per an}\]
\smallskip
Voici trois manières de savoir si ce chiffre \(r\) doit diviser ou multiplier le nombre d'heures qu'on veut transformer en années.
\end{frame}
\begin{frame}
\begin{columns}
\begin{column}{0.3\textwidth}
\begin{block}{Rapport de grandeurs}
\scriptsize \textbf{Question}~: dans une année, le nombre d'heures est plus grand que 1 ou plus petit ?
\smallskip
\textbf{Réponse}~: plus grand.
Cela implique que si deux chiffres représentent une durée identique, celui en heures est plus grand que celui en années ou celui en années est plus petit que celui en heures.
\smallskip
\textbf{Conséquence}~: il faut diviser le nombre d'heures par le chiffres rapport r.
\end{block}
\end{column}
\begin{column}{0.3\textwidth}
\begin{block}{Règle de trois}
\scriptsize
\begin{align*}
1 an &\rightarrow \SI{8760}{\hour}\\
? &\leftarrow \SI{4,8e13}{\hour}
\end{align*}
Par produits croisés :
\begin{align*}
? \cdot 8760 &= 1\cdot 4,8\cdot 10^{13}\\
? &= \frac{4,8\cdot 10^{13}}{8760}\\
&=\SI{5,5e9}{ans}
\end{align*}
On a donc bien une division par r.
\end{block}
\end{column}
\begin{column}{0.3\textwidth}
\begin{block}{Unités}
\scriptsize
Les crochets [\dots] signifient~: \og les unités de \fg{}
\begin{align*}
t_h&=\SI{4,8e13}{\hour}\,[t_h]=\si{\hour}\\
r&=\SI{8760}{\hour\per an}\;\;[r]=\si{\hour\per an}
\end{align*}
La question est~:
\(t_{an}=t_h\cdot r\;\text{ou}\;t_{an}=t_h/r\)
\smallskip
Un calcul d'unité donne~:
\begin{align*}
[t_{an}]&=[t_h]\cdot [r]=\si{\hour\cdot \hour\per an}\\
&=\si{\hour\squared\per an}\\
[t_{an}]&=[t_h]/[r]=\si{\hour\per(\hour\per an)}\\
&=\si{\hour\cdot (an\per\hour)}=\si{an}
\end{align*}
Pour avoir des années, il faut donc diviser par r.
\end{block}
\end{column}
\end{columns}
\end{frame}
\subsubsection{Le système solaire}
\begin{frame}{Mouvement du soleil}

16
MecaPres.toc
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\select@language {french}
\babel@toc {french}{}
\beamer@sectionintoc {1}{Structures}{2}{0}{1}
\beamer@subsectionintoc {1}{1}{L'infiniment grand}{2}{0}{1}
\beamer@subsubsectionintoc {1}{1}{1}{L'univers}{3}{0}{1}
@ -14,10 +14,10 @@
\beamer@sectionintoc {2}{Mouvements}{32}{0}{2}
\beamer@subsectionintoc {2}{1}{L'infiniment grand}{32}{0}{2}
\beamer@subsubsectionintoc {2}{1}{1}{Les galaxies}{33}{0}{2}
\beamer@subsubsectionintoc {2}{1}{2}{Le syst\IeC {\`e}me solaire}{38}{0}{2}
\beamer@subsubsectionintoc {2}{1}{3}{La terre}{40}{0}{2}
\beamer@subsubsectionintoc {2}{1}{4}{La lune}{43}{0}{2}
\beamer@subsectionintoc {2}{2}{L'infiniment petit}{47}{0}{2}
\beamer@subsubsectionintoc {2}{2}{1}{Probabilit\IeC {\'e}s}{48}{0}{2}
\beamer@subsubsectionintoc {2}{2}{2}{Principe d'incertitude}{50}{0}{2}
\beamer@subsubsectionintoc {2}{2}{3}{\IeC {\`A} la limite}{51}{0}{2}
\beamer@subsubsectionintoc {2}{1}{2}{Le syst\IeC {\`e}me solaire}{40}{0}{2}
\beamer@subsubsectionintoc {2}{1}{3}{La terre}{42}{0}{2}
\beamer@subsubsectionintoc {2}{1}{4}{La lune}{45}{0}{2}
\beamer@subsectionintoc {2}{2}{L'infiniment petit}{49}{0}{2}
\beamer@subsubsectionintoc {2}{2}{1}{Probabilit\IeC {\'e}s}{50}{0}{2}
\beamer@subsubsectionintoc {2}{2}{2}{Principe d'incertitude}{52}{0}{2}
\beamer@subsubsectionintoc {2}{2}{3}{\IeC {\`A} la limite}{53}{0}{2}