From 31b21a3b2bc3836c0826c0411d5d2acf54037eab Mon Sep 17 00:00:00 2001 From: guyotv Date: Fri, 12 Aug 2022 20:40:42 +0200 Subject: [PATCH] Ajout des deux premiers exos de thermo. --- Annexe-Exercices/Annexe-Exercices.tex | 33 ++++++++++++++++++++++ Annexe-Exercices/Annexe-Exercices.tex.bak | 33 ++++++++++++++++++++++ CoursMecaniqueOS.pdf | Bin 12797365 -> 12800285 bytes CoursMecaniqueOSDF.pdf | Bin 12797365 -> 12800285 bytes Solutions.tex | 16 +++++++++++ 5 files changed, 82 insertions(+) diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index 1e320d9..a2ab483 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -1,4 +1,12 @@ \myclearpage +%%% Mise en place des exercices de DF %%% +%%% --------------------------------- %%% +%\begin{ex}\label{centaure} +% Énoncé +% \begin{sol} +% Solution +% \end{sol} +%\end{ex} %%% Mise en place des exercices d'OS %%% %%% -------------------------------- %%% @@ -2311,6 +2319,31 @@ Les exercices suivants doivent être réalisés si possible sans la théorie de \end{sol} \end{ex} +\subsection{Relatifs à la thermodynamique} + +\begin{ex}\label{centaure} + Une règle en aluminium est construite pour faire \SI{30}{\centi\metre} à \SI{20}{\celsius}. Si on la chauffe à \SI{40}{\celsius}, quelle sera alors sa longueur réelle ? Réponse~: \SI{30,014}{\centi\metre}. + \begin{sol} + La variation de longueur est aisément calculable par~: + \begin{equation*} + \Delta L=L_0\cdot\alpha\cdot\Delta\theta=30\cdot 23,1\cdot 10^{-6}\cdot (40-20)=\SI{0,014}{\centi\metre} + \end{equation*} + Sa longueur totale sera donc de \SI{30,014}{\centi\metre}. + \end{sol} +\end{ex} + +\begin{ex}\label{centaure} + On veut faire entrer un objet en verre de \SI{20}{\metre} à \SI{15}{\celsius} dans une boite en fer de \SI{20,005}{\metre} à \SI{10}{\celsius} pour conserver le tout à \SI{20}{\celsius}. Est-ce possible ? + \begin{sol} + En chauffant l'objet en verre de \SI{5}{\celsius}, il va se dilater de~: + \[\Delta L=L_0\cdot\alpha\cdot\Delta\theta=20\cdot 68\cdot 10^{-6}\cdot (20-15)=\SI{6,8}{\milli\metre}\] + Ainsi, sa taille sera de \(20+0,0068=\SI{20,0068}{\metre}\). Au premier abord, cela semble donc impossible. Mais, en passant de \SI{10}{\celsius} à \SI{20}{\celsius}, la boite en fer voit sa taille augmenter de~: + \[\Delta L=20,005\cdot 12\cdot 10^{-6}\cdot (20-10)=\SI{2,4}{\milli\metre}\] + Ainsi, la boite en fer fera \SI{20,0074}{\metre} et l'objet en verre pourra s'y placer. + \end{sol} +\end{ex} + + \Closesolutionfile{ansos} % ferme le fichier SolutionsOS.tex qui contient les solutions OS. \Closesolutionfile{ans} % ferme le fichier Solutions.tex qui contient les solutions \vfill diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index 1e320d9..a2ab483 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -1,4 +1,12 @@ \myclearpage +%%% Mise en place des exercices de DF %%% +%%% --------------------------------- %%% +%\begin{ex}\label{centaure} +% Énoncé +% \begin{sol} +% Solution +% \end{sol} +%\end{ex} %%% Mise en place des exercices d'OS %%% %%% -------------------------------- %%% @@ -2311,6 +2319,31 @@ Les exercices suivants doivent être réalisés si possible sans la théorie de \end{sol} \end{ex} +\subsection{Relatifs à la thermodynamique} + +\begin{ex}\label{centaure} + Une règle en aluminium est construite pour faire \SI{30}{\centi\metre} à \SI{20}{\celsius}. Si on la chauffe à \SI{40}{\celsius}, quelle sera alors sa longueur réelle ? Réponse~: \SI{30,014}{\centi\metre}. + \begin{sol} + La variation de longueur est aisément calculable par~: + \begin{equation*} + \Delta L=L_0\cdot\alpha\cdot\Delta\theta=30\cdot 23,1\cdot 10^{-6}\cdot (40-20)=\SI{0,014}{\centi\metre} + \end{equation*} + Sa longueur totale sera donc de \SI{30,014}{\centi\metre}. + \end{sol} +\end{ex} + +\begin{ex}\label{centaure} + On veut faire entrer un objet en verre de \SI{20}{\metre} à \SI{15}{\celsius} dans une boite en fer de \SI{20,005}{\metre} à \SI{10}{\celsius} pour conserver le tout à \SI{20}{\celsius}. Est-ce possible ? + \begin{sol} + En chauffant l'objet en verre de \SI{5}{\celsius}, il va se dilater de~: + \[\Delta L=L_0\cdot\alpha\cdot\Delta\theta=20\cdot 68\cdot 10^{-6}\cdot (20-15)=\SI{6,8}{\milli\metre}\] + Ainsi, sa taille sera de \(20+0,0068=\SI{20,0068}{\metre}\). Au premier abord, cela semble donc impossible. Mais, en passant de \SI{10}{\celsius} à \SI{20}{\celsius}, la boite en fer voit sa taille augmenter de~: + \[\Delta L=20,005\cdot 12\cdot 10^{-6}\cdot (20-10)=\SI{2,4}{\milli\metre}\] + Ainsi, la boite en fer fera \SI{20,0074}{\metre} et l'objet en verre pourra s'y placer. + \end{sol} +\end{ex} + + \Closesolutionfile{ansos} % ferme le fichier SolutionsOS.tex qui contient les solutions OS. \Closesolutionfile{ans} % ferme le fichier Solutions.tex qui contient les solutions \vfill diff --git a/CoursMecaniqueOS.pdf b/CoursMecaniqueOS.pdf index fac45369e26c0b139de1b8daa7dc41fa159fa884..2d251cd0dad75ec82c5479427287d0132b99f8df 100644 GIT binary patch delta 249557 zcmXWhLy#s~kOknf*=5_dZQHhO{$<;?ZQHhO8(r?2Hxsk?B66K^7dK9x*63J>+@e^B z2J9rjbkg=1T3GWL4Jqs$hGT?3J?;F{d2ZB=76&U)mUCSdXA7gyz%jCHL=BF=5rziKbqcb#Tq0h4vETbg{${cSN zE|V#$!fXaJXF*i6t#feiI~G_Nv+M61!?-t}&Jg34x1g*Scr4Q1 z9TPb$x1ma9UJ={ME=ID?`Tt(V9pjp~HMa^%toOp@Cw;QyR7O`zCa6Xd2aCb1l_C{e+VcA-&(Fy%yoTAvDuGjtdI{% 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z^V<*Vvx+JW)h9mpNqva1q_nW5cpymQa0O=`=kZjQT;p#v@xz*cDN)a7f>;%~gi(zS zR_$2Ljsf;+_TUgSkE6P^nif*SVXaxsStGb+h$py8<^Oj?+w@hcq#rn_W7wc!VO_eW SCj)|dDtr18C2BSdN&kP38ZLqW diff --git a/Solutions.tex b/Solutions.tex index 75a943c..3b47242 100644 --- a/Solutions.tex +++ b/Solutions.tex @@ -1023,3 +1023,19 @@ On a successivement~: \[P=\frac{E}{t}=\frac{1'098,4}{24\cdot 365}=\SI{125,4}{\kilo\watt}\] \end{Solution} +\begin{Solution}{71} + La variation de longueur est aisément calculable par~: + \begin{equation*} + \Delta L=L_0\cdot\alpha\cdot\Delta\theta=30\cdot 23,1\cdot 10^{-6}\cdot (40-20)=\SI{0,014}{\centi\metre} + \end{equation*} + Sa longueur totale sera donc de \SI{30,014}{\centi\metre}. + +\end{Solution} +\begin{Solution}{72} + En chauffant l'objet en verre de \SI{5}{\celsius}, il va se dilater de~: + \[\Delta L=L_0\cdot\alpha\cdot\Delta\theta=20\cdot 68\cdot 10^{-6}\cdot (20-15)=\SI{6,8}{\milli\metre}\] + Ainsi, sa taille sera de \(20+0,0068=\SI{20,0068}{\metre}\). Au premier abord, cela semble donc impossible. Mais, en passant de \SI{10}{\celsius} à \SI{20}{\celsius}, la boite en fer voit sa taille augmenter de~: + \[\Delta L=20,005\cdot 12\cdot 10^{-6}\cdot (20-10)=\SI{2,4}{\milli\metre}\] + Ainsi, la boite en fer fera \SI{20,0074}{\metre} et l'objet en verre pourra s'y placer. + +\end{Solution}