Création du premier problème d'OS.
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@ -858,6 +858,32 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan
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\optv{OS}{
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\Opensolutionfile{ansos}[SolutionsOS]
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\begin{exos}
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Soient deux masses, la première, de valeur M=\unit{5}{\kilo\gram}, posée sur un plan horizontal sans frottements et la seconde, m=\unit{2}{\kilo\gram}, reliée à la première par une corde sans masse et pendant dans le vide, comme présenté sur la figure \ref{pendante}.
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On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seconde alors que la première à parcouru une distance de \unit{50}{\centi\metre}. Réponse~:\unit{2,8}{\metre\per\second}.
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\begin{solos}
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On commence par choisir le système. Pour éviter de devoir calculer la tension dans la corde, on le choisit comme constitué de la corde et des deux masses M et m.
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Les forces extérieures sont alors au nombre de trois. Le plan horizontal exerce sur la masse M une force de soutient verticale égale et opposée à son poids (mais qui ne sont pas l'action et la réaction l'une de l'autre), puisque la masse se déplace horizontalement. Ces deux forces s'annulent donc. Reste le poids de la masse m, seule force extérieure à agir pour accélérer le système.
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On peut donc écrire, selon la seconde loi de Newton~:
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\[\sum F^{ext}=m\cdot g=(M+m)\cdot a\]
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où M+m est la masse du système. Ainsi, finalement, on peut calculer la valeur de l'accélération~:
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\begin{align*}
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&m\cdot g=(M+m)\cdot a\;\Rightarrow\\
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&a=\frac{m}{M+m}\cdot g=\frac{2}{5}\cdot 9,81=\unit{3,924}{\metre\per\second\squared}
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\end{align*}
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\medskip
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À partir de l'accélération, on peut ensuite calculer la vitesse au bout d'un mètre, grâce à l'équation du MRUA~:
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\begin{align*}
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v^2&=v_0^2+2\cdot a\cdot d\;\Rightarrow\\
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v^2&=0+2\cdot 3,924\cdot 1\;\Rightarrow\\
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v&=\sqrt{2\cdot 3,924}=\unit{2,8}{\metre\per\second}
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\end{align*}
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\end{solos}
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\end{exos}
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\begin{exos}
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Un exercice de test.
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\contentsline {figure}{\numberline {7.5}{\ignorespaces Ancienne turbine Pelton}}{107}
|
||||
\contentsline {figure}{\numberline {7.6}{\ignorespaces \IeC {\'E}olienne}}{108}
|
||||
\contentsline {figure}{\numberline {7.7}{\ignorespaces Pale d'\IeC {\'e}olienne}}{108}
|
||||
\contentsline {figure}{\numberline {7.8}{\ignorespaces Tube de vent\relax }}{109}
|
||||
\contentsline {figure}{\numberline {7.9}{\ignorespaces Solaire thermique}}{111}
|
||||
\contentsline {figure}{\numberline {7.10}{\ignorespaces Effet photo\IeC {\'e}lectrique}}{111}
|
||||
\contentsline {figure}{\numberline {7.11}{\ignorespaces Cellule photo\IeC {\'e}lectrique}}{112}
|
||||
\contentsline {figure}{\numberline {7.12}{\ignorespaces Applications de la g\IeC {\'e}othermie}}{113}
|
||||
\contentsline {figure}{\numberline {7.13}{\ignorespaces Fission de l'uranium\relax }}{114}
|
||||
\contentsline {figure}{\numberline {7.14}{\ignorespaces R\IeC {\'e}acteur nucl\IeC {\'e}aire\relax }}{114}
|
||||
\contentsline {figure}{\numberline {7.15}{\ignorespaces Combustion du m\IeC {\'e}thane}}{116}
|
||||
\contentsline {figure}{\numberline {7.16}{\ignorespaces R\IeC {\'e}sum\IeC {\'e} de l'\IeC {\'e}nergie\relax }}{117}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {C.1}{\ignorespaces Taille de la terre\relax }}{107}
|
||||
\contentsline {figure}{\numberline {C.2}{\ignorespaces Taille de la lune}}{109}
|
||||
\contentsline {figure}{\numberline {C.3}{\ignorespaces Parallaxe de Mars}}{110}
|
||||
\contentsline {figure}{\numberline {8.1}{\ignorespaces \IeC {\'E}nergie et vitesse\relax }}{119}
|
||||
\contentsline {figure}{\numberline {8.2}{\ignorespaces Balance \IeC {\`a} fl\IeC {\'e}au\relax }}{119}
|
||||
\contentsline {figure}{\numberline {8.3}{\ignorespaces Travail simple\relax }}{120}
|
||||
\contentsline {figure}{\numberline {8.4}{\ignorespaces Travail et produit scalaire\relax }}{120}
|
||||
\contentsline {figure}{\numberline {8.5}{\ignorespaces Travail en g\IeC {\'e}n\IeC {\'e}ral\relax }}{121}
|
||||
\contentsline {figure}{\numberline {8.6}{\ignorespaces Travail du poids\relax }}{125}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {D.1}{\ignorespaces Rail horizontal}}{114}
|
||||
\contentsline {figure}{\numberline {D.2}{\ignorespaces Chute libre\relax }}{115}
|
||||
\contentsline {figure}{\numberline {9.1}{\ignorespaces Thermom\IeC {\`e}tres}}{128}
|
||||
\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Fahrenheit}}}{128}
|
||||
\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Kelvin}}}{128}
|
||||
\contentsline {figure}{\numberline {9.2}{\ignorespaces Changements d'\IeC {\'e}tats\relax }}{130}
|
||||
\contentsline {figure}{\numberline {9.3}{\ignorespaces R\IeC {\'e}sum\IeC {\'e} de thermodynamique\relax }}{132}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {E.1}{\ignorespaces Le syst\IeC {\`e}me g\IeC {\'e}ocentrique de Tycho Brah\IeC {\'e}}}{122}
|
||||
\contentsline {figure}{\numberline {E.2}{\ignorespaces Le Soleil dans la Voie Lact\IeC {\'e}e}}{123}
|
||||
\contentsline {figure}{\numberline {10.1}{\ignorespaces Dilatation lin\IeC {\'e}aire\relax }}{134}
|
||||
\contentsline {figure}{\numberline {10.2}{\ignorespaces Fusible bilame\relax }}{134}
|
||||
\contentsline {figure}{\numberline {10.3}{\ignorespaces Dilatation volumique\relax }}{134}
|
||||
\contentsline {figure}{\numberline {10.4}{\ignorespaces Travail et diagramme P-V\relax }}{142}
|
||||
\contentsline {figure}{\numberline {10.5}{\ignorespaces Transformation isobare\relax }}{144}
|
||||
\contentsline {figure}{\numberline {10.6}{\ignorespaces Transformation isochore\relax }}{145}
|
||||
\contentsline {figure}{\numberline {10.7}{\ignorespaces Transformation isotherme\relax }}{145}
|
||||
\contentsline {figure}{\numberline {10.8}{\ignorespaces Transformation adiabatique\relax }}{146}
|
||||
\contentsline {figure}{\numberline {10.9}{\ignorespaces Moteur thermique}}{149}
|
||||
\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Chargement}}}{149}
|
||||
\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Chauffage}}}{149}
|
||||
\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {D\IeC {\'e}chargement}}}{149}
|
||||
\contentsline {subfigure}{\numberline {(d)}{\ignorespaces {Refroidissement}}}{149}
|
||||
\contentsline {figure}{\numberline {10.10}{\ignorespaces Diagramme d'\IeC {\'e}tat\relax }}{149}
|
||||
\contentsline {figure}{\numberline {10.11}{\ignorespaces Diagramme d'\IeC {\'e}tat\relax }}{150}
|
||||
\contentsline {figure}{\numberline {10.12}{\ignorespaces Diagramme d'\IeC {\'e}tat\relax }}{150}
|
||||
\contentsline {figure}{\numberline {10.13}{\ignorespaces Moteur \IeC {\`a} explosion}}{151}
|
||||
\contentsline {subfigure}{\numberline {(a)}{\ignorespaces {Admission}}}{151}
|
||||
\contentsline {subfigure}{\numberline {(b)}{\ignorespaces {Compression}}}{151}
|
||||
\contentsline {subfigure}{\numberline {(c)}{\ignorespaces {Allumage}}}{151}
|
||||
\contentsline {subfigure}{\numberline {(d)}{\ignorespaces {Temps moteur}}}{151}
|
||||
\contentsline {subfigure}{\numberline {(e)}{\ignorespaces {\IeC {\'E}chappement}}}{151}
|
||||
\contentsline {subfigure}{\numberline {(f)}{\ignorespaces {\IeC {\'E}vacuation}}}{151}
|
||||
\contentsline {figure}{\numberline {10.14}{\ignorespaces Diagramme d'\IeC {\'e}tat\relax }}{152}
|
||||
\contentsline {figure}{\numberline {10.15}{\ignorespaces Diagramme d'\IeC {\'e}tat\relax }}{152}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {F.1}{\ignorespaces \emph {Discours concernant deux sciences nouvelles} de Galil\IeC {\'e}e}}{125}
|
||||
\contentsline {figure}{\numberline {A.1}{\ignorespaces Relation de l'arc de cercle\relax }}{159}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {G.1}{\ignorespaces Chute de la lune\relax }}{127}
|
||||
\contentsline {figure}{\numberline {B.1}{\ignorespaces Syst\IeC {\`e}me de coordonn\IeC {\'e}es circulaires\relax }}{163}
|
||||
\contentsline {figure}{\numberline {B.2}{\ignorespaces Syst\IeC {\`e}me de coordonn\IeC {\'e}es sph\IeC {\'e}riques\relax }}{164}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {H.1}{\ignorespaces Satellite}}{129}
|
||||
\contentsline {figure}{\numberline {C.1}{\ignorespaces Taille de la terre\relax }}{165}
|
||||
\contentsline {figure}{\numberline {C.2}{\ignorespaces Taille de la lune}}{167}
|
||||
\contentsline {figure}{\numberline {C.3}{\ignorespaces Parallaxe de Mars}}{168}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {I.1}{\ignorespaces Transformation de galil\IeC {\'e}e}}{132}
|
||||
\contentsline {figure}{\numberline {J.1}{\ignorespaces Mar\IeC {\'e}e}}{137}
|
||||
\contentsline {figure}{\numberline {D.1}{\ignorespaces Rail horizontal}}{172}
|
||||
\contentsline {figure}{\numberline {D.2}{\ignorespaces Chute libre\relax }}{173}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {J.2}{\ignorespaces Syst\IeC {\`e}me Terre-Lune\relax }}{138}
|
||||
\contentsline {figure}{\numberline {J.3}{\ignorespaces Syst\IeC {\`e}me Terre-Lune-eau\relax }}{138}
|
||||
\contentsline {figure}{\numberline {J.4}{\ignorespaces D\IeC {\'e}calage horaire}}{140}
|
||||
\contentsline {figure}{\numberline {J.5}{\ignorespaces Vives et mortes eaux}}{140}
|
||||
\contentsline {figure}{\numberline {J.6}{\ignorespaces Limite de Roche}}{142}
|
||||
\contentsline {figure}{\numberline {J.7}{\ignorespaces Limite de Roche}}{143}
|
||||
\contentsline {figure}{\numberline {E.1}{\ignorespaces Le syst\IeC {\`e}me g\IeC {\'e}ocentrique de Tycho Brah\IeC {\'e}}}{180}
|
||||
\contentsline {figure}{\numberline {E.2}{\ignorespaces Le Soleil dans la Voie Lact\IeC {\'e}e}}{181}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {K.1}{\ignorespaces Le barrage du Ch\IeC {\^a}telot}}{145}
|
||||
\contentsline {figure}{\numberline {F.1}{\ignorespaces \emph {Discours concernant deux sciences nouvelles} de Galil\IeC {\'e}e}}{183}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {G.1}{\ignorespaces Chute de la lune\relax }}{185}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {H.1}{\ignorespaces Satellite}}{187}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {I.1}{\ignorespaces Transformation de galil\IeC {\'e}e}}{190}
|
||||
\contentsline {figure}{\numberline {J.1}{\ignorespaces Mar\IeC {\'e}e}}{195}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {J.2}{\ignorespaces Syst\IeC {\`e}me Terre-Lune\relax }}{196}
|
||||
\contentsline {figure}{\numberline {J.3}{\ignorespaces Syst\IeC {\`e}me Terre-Lune-eau\relax }}{196}
|
||||
\contentsline {figure}{\numberline {J.4}{\ignorespaces D\IeC {\'e}calage horaire}}{198}
|
||||
\contentsline {figure}{\numberline {J.5}{\ignorespaces Vives et mortes eaux}}{198}
|
||||
\contentsline {figure}{\numberline {J.6}{\ignorespaces Limite de Roche}}{200}
|
||||
\contentsline {figure}{\numberline {J.7}{\ignorespaces Limite de Roche}}{201}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {K.1}{\ignorespaces Le barrage du Ch\IeC {\^a}telot}}{203}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {L.1}{\ignorespaces Le rayon de la Terre par Eratosth\IeC {\`e}ne\relax }}{208}
|
||||
\contentsline {figure}{\numberline {L.2}{\ignorespaces La poulie}}{212}
|
||||
\contentsline {figure}{\numberline {L.3}{\ignorespaces Un ascenseur\relax }}{214}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {L.1}{\ignorespaces Le rayon de la Terre par Eratosth\IeC {\`e}ne\relax }}{150}
|
||||
\contentsline {figure}{\numberline {L.2}{\ignorespaces La poulie}}{154}
|
||||
\contentsline {figure}{\numberline {L.3}{\ignorespaces Un ascenseur\relax }}{156}
|
||||
|
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||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {5.1}{\ignorespaces C\oe fficient de dilatation lin\IeC {\'e}aire\relax }}{95}
|
||||
\contentsline {table}{\numberline {5.2}{\ignorespaces Chaleur sp\IeC {\'e}cifique\relax }}{95}
|
||||
\contentsline {table}{\numberline {5.3}{\ignorespaces Chaleur latente\relax }}{96}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {A.1}{\ignorespaces Les unit\IeC {\'e}s du Syst\IeC {\`e}me International\relax }}{102}
|
||||
\contentsline {table}{\numberline {A.2}{\ignorespaces Conversions d'unit\IeC {\'e}s\relax }}{102}
|
||||
\contentsline {table}{\numberline {A.3}{\ignorespaces Quelques \IeC {\'e}quivalents\relax }}{102}
|
||||
\contentsline {table}{\numberline {A.4}{\ignorespaces Multiples et sous-multiples\relax }}{103}
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {D.1}{\ignorespaces Tableau de mesures\relax }}{115}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {9.1}{\ignorespaces C\oe fficient de dilatation lin\IeC {\'e}aire\relax }}{129}
|
||||
\contentsline {table}{\numberline {9.2}{\ignorespaces Chaleur sp\IeC {\'e}cifique\relax }}{129}
|
||||
\contentsline {table}{\numberline {9.3}{\ignorespaces Chaleur latente\relax }}{130}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {10.1}{\ignorespaces Coefficient de dilatation lin\IeC {\'e}aire\relax }}{134}
|
||||
\contentsline {table}{\numberline {10.2}{\ignorespaces Coefficient de dilatation volumique\relax }}{135}
|
||||
\contentsline {table}{\numberline {10.3}{\ignorespaces Chaleur massique\relax }}{136}
|
||||
\contentsline {table}{\numberline {10.4}{\ignorespaces Chaleur latente\relax }}{137}
|
||||
\contentsline {table}{\numberline {10.5}{\ignorespaces \IeC {\'E}tats caract\IeC {\'e}ristiques\relax }}{148}
|
||||
\contentsline {table}{\numberline {10.6}{\ignorespaces Grandeurs caract\IeC {\'e}ristiques\relax }}{150}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {A.1}{\ignorespaces Les unit\IeC {\'e}s du Syst\IeC {\`e}me International\relax }}{160}
|
||||
\contentsline {table}{\numberline {A.2}{\ignorespaces Conversions d'unit\IeC {\'e}s\relax }}{160}
|
||||
\contentsline {table}{\numberline {A.3}{\ignorespaces Quelques \IeC {\'e}quivalents\relax }}{160}
|
||||
\contentsline {table}{\numberline {A.4}{\ignorespaces Multiples et sous-multiples\relax }}{161}
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {D.1}{\ignorespaces Tableau de mesures\relax }}{173}
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
@ -28,3 +39,6 @@
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {table}{\numberline {M.1}{\ignorespaces La longueur des baguettes de pain\relax }}{221}
|
||||
\contentsline {table}{\numberline {M.2}{\ignorespaces La longueur d'autres baguettes de pain\relax }}{222}
|
||||
|
||||
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CoursMecaniqueOSDF.ps
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|
||||
\usepackage[arrow,matrix,tips,frame]{xy}
|
||||
%\renewcommand{\bibname}{Bibliographie}
|
||||
|
||||
\usepackage[DF]{optional} % Pour réaliser le cours de base de Discipline Fondamentale (DF)
|
||||
%\usepackage[OS]{optional} % Pour réaliser le cours complet d'Option Spécifique (OS)
|
||||
%\usepackage[DF]{optional} % Pour réaliser le cours de base de Discipline Fondamentale (DF)
|
||||
\usepackage[OS]{optional} % Pour réaliser le cours complet d'Option Spécifique (OS)
|
||||
% La commande pour ajouter les parties d'OS est \opt{OS}{parties}
|
||||
|
||||
%---------------------------------------------------------------
|
||||
@ -18,8 +18,8 @@
|
||||
\Newassociation{sol}{Solution}{ans} % définition de l'étiquette Solution du module answers
|
||||
\newtheorem{exc}{Exercice} % définition de l'étiquette Exercice du module answers
|
||||
\newenvironment{ex}{\begin{exc}\normalfont}{\end{exc}} % cela (\normalfont) annule l'italique des énoncés des exercices
|
||||
\Newassociation{solos}{SolutionOS}{ansos}
|
||||
\newtheorem{exosc}{ExerciceOS}
|
||||
\Newassociation{solos}{Solution OS}{ansos}
|
||||
\newtheorem{exosc}{Exercice OS}
|
||||
\newenvironment{exos}{\begin{exosc}\normalfont}{\end{exosc}}
|
||||
|
||||
\setlength{\headheight}{12.2pt} % spécifie la hauteur de l'entête pour qu'elle ne couvre pas le titre
|
||||
|
||||
@ -89,177 +89,314 @@
|
||||
\contentsline {paragraph}{Exemple}{72}
|
||||
\contentsline {subsubsection}{La force d'un ressort}{72}
|
||||
\contentsline {paragraph}{Exemple}{73}
|
||||
\contentsline {chapter}{\numberline {4}L'\IeC {\'e}nergie}{75}
|
||||
\contentsline {section}{\numberline {4.1}Introduction}{75}
|
||||
\contentsline {section}{\numberline {4.2}Travail}{75}
|
||||
\contentsline {section}{\numberline {4.3}Puissance}{76}
|
||||
\contentsline {section}{\numberline {4.4}\IeC {\'E}nergie potentielle}{76}
|
||||
\contentsline {section}{\numberline {4.5}\IeC {\'E}nergie cin\IeC {\'e}tique}{77}
|
||||
\contentsline {section}{\numberline {4.6}Th\IeC {\'e}or\IeC {\`e}me de l'\IeC {\'e}nergie cin\IeC {\'e}tique}{77}
|
||||
\contentsline {section}{\numberline {4.7}Conservation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{77}
|
||||
\contentsline {section}{\numberline {4.8}Variation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{79}
|
||||
\contentsline {section}{\numberline {4.9}\IeC {\'E}nergies renouvelables}{79}
|
||||
\contentsline {subsection}{\numberline {4.9.1}\IeC {\'E}nergie hydraulique}{80}
|
||||
\contentsline {subsubsection}{Exemple}{81}
|
||||
\contentsline {subsubsection}{Types de turbines}{81}
|
||||
\contentsline {subsubsection}{Alternateur}{81}
|
||||
\contentsline {subsubsection}{Probl\IeC {\`e}mes rencontr\IeC {\'e}s}{82}
|
||||
\contentsline {subsection}{\numberline {4.9.2}\IeC {\'E}nergie \IeC {\'e}olienne}{82}
|
||||
\contentsline {subsection}{\numberline {4.9.3}\IeC {\'E}nergie solaire}{83}
|
||||
\contentsline {subsubsection}{\IeC {\'E}nergie solaire thermique}{84}
|
||||
\contentsline {subsubsection}{\IeC {\'E}nergie solaire \IeC {\'e}lectrique}{85}
|
||||
\contentsline {subsection}{\numberline {4.9.4}\IeC {\'E}nergie g\IeC {\'e}othermique}{86}
|
||||
\contentsline {section}{\numberline {4.10}\IeC {\'E}nergies non renouvelables}{87}
|
||||
\contentsline {subsection}{\numberline {4.10.1}\IeC {\'E}nergie nucl\IeC {\'e}aire}{87}
|
||||
\contentsline {subsubsection}{Fission}{87}
|
||||
\contentsline {paragraph}{D\IeC {\'e}chets radioactifs}{89}
|
||||
\contentsline {paragraph}{Accidents nucl\IeC {\'e}aires}{89}
|
||||
\contentsline {subsubsection}{Fusion}{89}
|
||||
\contentsline {subsection}{\numberline {4.10.2}\IeC {\'E}nergie de combustion : p\IeC {\'e}trole et gaz}{90}
|
||||
\contentsline {chapter}{\numberline {5}Thermodynamique}{93}
|
||||
\contentsline {section}{\numberline {5.1}Introduction}{93}
|
||||
\contentsline {section}{\numberline {5.2}Temp\IeC {\'e}rature}{93}
|
||||
\contentsline {subsection}{\numberline {5.2.1}Celsius}{93}
|
||||
\contentsline {subsection}{\numberline {5.2.2}Fahrenheit}{93}
|
||||
\contentsline {subsection}{\numberline {5.2.3}Kelvin}{94}
|
||||
\contentsline {subsection}{\numberline {5.2.4}Agitation mol\IeC {\'e}culaire}{94}
|
||||
\contentsline {section}{\numberline {5.3}Dilatation}{94}
|
||||
\contentsline {section}{\numberline {5.4}Chaleur}{95}
|
||||
\contentsline {subsection}{\numberline {5.4.1}Chaleur sp\IeC {\'e}cifique}{95}
|
||||
\contentsline {subsection}{\numberline {5.4.2}Chaleur latente}{95}
|
||||
\contentsline {section}{\numberline {5.5}\IeC {\'E}nergie thermique}{96}
|
||||
\contentsline {subsection}{\numberline {5.5.1}Premier principe}{97}
|
||||
\contentsline {chapter}{\numberline {A}Syst\IeC {\`e}mes d'unit\IeC {\'e}s}{99}
|
||||
\contentsline {section}{\numberline {A.1}Introduction}{99}
|
||||
\contentsline {section}{\numberline {A.2}Op\IeC {\'e}rateur d'unit\IeC {\'e}s}{99}
|
||||
\contentsline {section}{\numberline {A.3}Analyse dimentionnelle}{100}
|
||||
\contentsline {section}{\numberline {A.4}Les unit\IeC {\'e}s du Syst\IeC {\`e}me International}{101}
|
||||
\contentsline {subsection}{\numberline {A.4.1}Exemple}{101}
|
||||
\contentsline {section}{\numberline {A.5}Conversions}{101}
|
||||
\contentsline {section}{\numberline {A.6}Sous-multiples}{102}
|
||||
\contentsline {section}{\numberline {A.7}Notation scientifique}{102}
|
||||
\contentsline {section}{\numberline {A.8}R\IeC {\`e}gles de calcul}{103}
|
||||
\contentsline {chapter}{\numberline {B}Deux syst\IeC {\`e}mes de coordonn\IeC {\'e}es}{105}
|
||||
\contentsline {section}{\numberline {B.1}Le syst\IeC {\`e}me de coordonn\IeC {\'e}es circulaires}{105}
|
||||
\contentsline {subsection}{\numberline {B.1.1}Introduction}{105}
|
||||
\contentsline {subsection}{\numberline {B.1.2}Description}{105}
|
||||
\contentsline {section}{\numberline {B.2}Coordonn\IeC {\'e}es sph\IeC {\'e}riques}{105}
|
||||
\contentsline {subsection}{\numberline {B.2.1}Introduction}{105}
|
||||
\contentsline {subsection}{\numberline {B.2.2}Description}{105}
|
||||
\contentsline {subsection}{\numberline {B.2.3}Latitude et longitude}{106}
|
||||
\contentsline {chapter}{\numberline {C}Mesures de distances}{107}
|
||||
\contentsline {section}{\numberline {C.1}La taille de la Terre}{107}
|
||||
\contentsline {subsection}{\numberline {C.1.1}Le principe}{107}
|
||||
\contentsline {subsection}{\numberline {C.1.2}Techniquement}{108}
|
||||
\contentsline {section}{\numberline {C.2}La taille de la Lune}{109}
|
||||
\contentsline {section}{\numberline {C.3}La distance Terre-Lune}{109}
|
||||
\contentsline {section}{\numberline {C.4}La distance Terre-Soleil}{110}
|
||||
\contentsline {section}{\numberline {C.5}La distance des \IeC {\'e}toiles}{112}
|
||||
\contentsline {chapter}{\numberline {D}Travaux pratiques}{113}
|
||||
\contentsline {section}{\numberline {D.1}Le rapport de laboratoire}{113}
|
||||
\contentsline {subsection}{\numberline {D.1.1}Plan d'un rapport de travail pratique}{114}
|
||||
\contentsline {subsubsection}{Pr\IeC {\'e}liminaires}{114}
|
||||
\contentsline {subsubsection}{R\IeC {\'e}sum\IeC {\'e}}{114}
|
||||
\contentsline {subsubsection}{But}{114}
|
||||
\contentsline {subsubsection}{Th\IeC {\'e}orie}{114}
|
||||
\contentsline {subsubsection}{Description de l'exp\IeC {\'e}rience}{114}
|
||||
\contentsline {subsubsection}{R\IeC {\'e}sultats}{114}
|
||||
\contentsline {subsubsection}{Discussion}{116}
|
||||
\contentsline {subsubsection}{Conclusion}{116}
|
||||
\contentsline {subsubsection}{Annexes}{116}
|
||||
\contentsline {section}{\numberline {D.2}La n\IeC {\'e}buleuse du Crabe}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.1}Introduction}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.2}But du travail pratique}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.3}Dispositif exp\IeC {\'e}rimental}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.4}Mesures}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.5}R\IeC {\'e}sultats}{117}
|
||||
\contentsline {subsection}{\numberline {D.2.6}Analyse}{117}
|
||||
\contentsline {section}{\numberline {D.3}Le pendule simple}{117}
|
||||
\contentsline {subsection}{\numberline {D.3.1}Les mesures}{117}
|
||||
\contentsline {subsection}{\numberline {D.3.2}Organisation des donn\IeC {\'e}es et graphiques}{118}
|
||||
\contentsline {section}{\numberline {D.4}Mouvement simple : MRU}{118}
|
||||
\contentsline {subsection}{\numberline {D.4.1}Les mesures}{118}
|
||||
\contentsline {subsection}{\numberline {D.4.2}Organisation des donn\IeC {\'e}es et graphiques}{118}
|
||||
\contentsline {subsection}{\numberline {D.4.3}Analyse des r\IeC {\'e}sultats}{118}
|
||||
\contentsline {section}{\numberline {D.5}Mouvement simple :\\MRUA}{118}
|
||||
\contentsline {subsection}{\numberline {D.5.1}But}{118}
|
||||
\contentsline {subsection}{\numberline {D.5.2}Th\IeC {\'e}orie}{119}
|
||||
\contentsline {subsection}{\numberline {D.5.3}Les mesures}{119}
|
||||
\contentsline {subsection}{\numberline {D.5.4}Organisation des donn\IeC {\'e}es et graphiques}{119}
|
||||
\contentsline {subsection}{\numberline {D.5.5}Galil\IeC {\'e}e et le plan inclin\IeC {\'e}}{119}
|
||||
\contentsline {section}{\numberline {D.6}La chute libre}{119}
|
||||
\contentsline {subsection}{\numberline {D.6.1}Cette exp\IeC {\'e}rience donnant lieu \IeC {\`a} un rapport not\IeC {\'e}, elle n'est pas d\IeC {\'e}crite.}{119}
|
||||
\contentsline {subsection}{\numberline {D.6.2}R\IeC {\'e}sultats}{119}
|
||||
\contentsline {section}{\numberline {D.7}Le canon horizontal}{119}
|
||||
\contentsline {section}{\numberline {D.8}Le chariot \IeC {\`a} masse pendante}{120}
|
||||
\contentsline {chapter}{\numberline {E}Rotations}{121}
|
||||
\contentsline {section}{\numberline {E.1}Rotation de la Terre sur elle-m\IeC {\^e}me}{121}
|
||||
\contentsline {section}{\numberline {E.2}Rotation de la Terre autour du Soleil}{121}
|
||||
\contentsline {section}{\numberline {E.3}Rotation du Soleil dans la Voie Lact\IeC {\'e}e}{123}
|
||||
\contentsline {section}{\numberline {E.4}Vitesse et r\IeC {\'e}f\IeC {\'e}rentiel}{123}
|
||||
\contentsline {chapter}{\numberline {F}MRUA d\IeC {\'e}veloppements}{125}
|
||||
\contentsline {section}{\numberline {F.1}La position}{125}
|
||||
\contentsline {section}{\numberline {F.2}Une autre relation bien pratique}{125}
|
||||
\contentsline {subsection}{\numberline {F.2.1}Cin\IeC {\'e}matique}{125}
|
||||
\contentsline {subsection}{\numberline {F.2.2}\IeC {\'E}nergie}{126}
|
||||
\contentsline {chapter}{\numberline {G}Chute de la Lune}{127}
|
||||
\contentsline {section}{\numberline {G.1}Introduction}{127}
|
||||
\contentsline {section}{\numberline {G.2}Acc\IeC {\'e}l\IeC {\'e}ration}{127}
|
||||
\contentsline {section}{\numberline {G.3}Force de gravitation}{128}
|
||||
\contentsline {chapter}{\numberline {H}Satellite en orbite g\IeC {\'e}ostationnaire}{129}
|
||||
\contentsline {section}{\numberline {H.1}Introduction}{129}
|
||||
\contentsline {section}{\numberline {H.2}Th\IeC {\'e}oriquement}{129}
|
||||
\contentsline {section}{\numberline {H.3}Num\IeC {\'e}riquement}{130}
|
||||
\contentsline {section}{\numberline {H.4}Loi de Kepler}{130}
|
||||
\contentsline {chapter}{\numberline {I}Relativit\IeC {\'e}}{131}
|
||||
\contentsline {section}{\numberline {I.1}Relativit\IeC {\'e} galil\IeC {\'e}enne}{131}
|
||||
\contentsline {section}{\numberline {I.2}Transformation galil\IeC {\'e}enne}{132}
|
||||
\contentsline {section}{\numberline {I.3}Invariance}{133}
|
||||
\contentsline {section}{\numberline {I.4}Forces inertielles}{133}
|
||||
\contentsline {subsection}{\numberline {I.4.1}Force d'inertie}{133}
|
||||
\contentsline {subsection}{\numberline {I.4.2}Force centrifuge}{134}
|
||||
\contentsline {chapter}{\numberline {J}Mar\IeC {\'e}es}{137}
|
||||
\contentsline {section}{\numberline {J.1}Introduction}{137}
|
||||
\contentsline {section}{\numberline {J.2}Centre de gravit\IeC {\'e}}{137}
|
||||
\contentsline {section}{\numberline {J.3}Force d'inertie}{138}
|
||||
\contentsline {subsection}{\numberline {J.3.1}Vitesse angulaire}{138}
|
||||
\contentsline {subsection}{\numberline {J.3.2}Force d'inertie}{138}
|
||||
\contentsline {section}{\numberline {J.4}Poids relatif}{139}
|
||||
\contentsline {section}{\numberline {J.5}Analyse diff\IeC {\'e}rentielle}{139}
|
||||
\contentsline {section}{\numberline {J.6}Autres rythmes}{139}
|
||||
\contentsline {subsection}{\numberline {J.6.1}D\IeC {\'e}calages}{140}
|
||||
\contentsline {subsection}{\numberline {J.6.2}Mar\IeC {\'e}es de vives et mortes eaux}{140}
|
||||
\contentsline {subsection}{\numberline {J.6.3}Mar\IeC {\'e}es d'\IeC {\'e}quinoxes}{140}
|
||||
\contentsline {subsection}{\numberline {J.6.4}Mar\IeC {\'e}es de p\IeC {\'e}rig\IeC {\'e}e et p\IeC {\'e}rih\IeC {\'e}lie}{141}
|
||||
\contentsline {subsection}{\numberline {J.6.5}Mar\IeC {\'e}es de d\IeC {\'e}clinaison}{141}
|
||||
\contentsline {subsection}{\numberline {J.6.6}Retards et mar\IeC {\'e}es c\IeC {\^o}ti\IeC {\`e}res}{141}
|
||||
\contentsline {section}{\numberline {J.7}Limite de Roche}{141}
|
||||
\contentsline {subsection}{\numberline {J.7.1}Mod\IeC {\`e}le simplifi\IeC {\'e}}{142}
|
||||
\contentsline {subsection}{\numberline {J.7.2}Exemples}{143}
|
||||
\contentsline {chapter}{\numberline {K}\IeC {\'E}nergies}{145}
|
||||
\contentsline {section}{\numberline {K.1}Introduction}{145}
|
||||
\contentsline {section}{\numberline {K.2}\IeC {\'E}nergie hydraulique}{145}
|
||||
\contentsline {section}{\numberline {K.3}\IeC {\'E}nergie \IeC {\'e}olienne}{146}
|
||||
\contentsline {subsection}{\numberline {K.3.1}R\IeC {\`e}gle de Betz}{146}
|
||||
\contentsline {subsection}{\numberline {K.3.2}\IeC {\'E}oliennes}{147}
|
||||
\contentsline {subsubsection}{\IeC {\'E}olienne de Collonges-Dor\IeC {\'e}naz}{147}
|
||||
\contentsline {subsubsection}{\IeC {\'E}oliennes du Mont Soleil (Jura suisse)}{147}
|
||||
\contentsline {section}{\numberline {K.4}G\IeC {\'e}othermie}{147}
|
||||
\contentsline {section}{\numberline {K.5}\IeC {\'E}nergie de combustion des d\IeC {\'e}chets}{148}
|
||||
\contentsline {chapter}{\numberline {L}Exercices}{149}
|
||||
\contentsline {section}{\numberline {L.1}Probl\IeC {\`e}mes}{149}
|
||||
\contentsline {subsection}{\numberline {L.1.1}Relatifs \IeC {\`a} la conversion d'unit\IeC {\'e}s et \IeC {\`a} la notation scientifique}{149}
|
||||
\contentsline {subsection}{\numberline {L.1.2}Relatifs aux notions de d\IeC {\'e}placement, position et distance parcourue}{150}
|
||||
\contentsline {subsection}{\numberline {L.1.3}Relatifs \IeC {\`a} la notion de vitesse}{150}
|
||||
\contentsline {subsection}{\numberline {L.1.4}Relatif \IeC {\`a} la notion d'acc\IeC {\'e}l\IeC {\'e}ration}{150}
|
||||
\contentsline {subsection}{\numberline {L.1.5}Relatif au MRU}{151}
|
||||
\contentsline {subsection}{\numberline {L.1.6}Relatif au MRUA}{151}
|
||||
\contentsline {subsection}{\numberline {L.1.7}Relatifs \IeC {\`a} la physique aristot\IeC {\'e}licienne}{152}
|
||||
\contentsline {subsection}{\numberline {L.1.8}Relatifs \IeC {\`a} la physique newtonienne}{152}
|
||||
\contentsline {subsection}{\numberline {L.1.9}Relatifs aux forces}{154}
|
||||
\contentsline {subsection}{\numberline {L.1.10}Relatifs \IeC {\`a} l'\IeC {\'e}nergie}{154}
|
||||
\contentsline {subsection}{\numberline {L.1.11}Relatifs \IeC {\`a} la conservation de l'\IeC {\'e}nergie}{155}
|
||||
\contentsline {subsection}{\numberline {L.1.12}Relatifs \IeC {\`a} l'\IeC {\'e}nergie hydraulique}{155}
|
||||
\contentsline {subsection}{\numberline {L.1.13}Relatifs \IeC {\`a} l'\IeC {\'e}nergie \IeC {\'e}olienne}{155}
|
||||
\contentsline {subsection}{\numberline {L.1.14}Relatifs \IeC {\`a} l'\IeC {\'e}nergie solaire}{155}
|
||||
\contentsline {section}{\numberline {L.2}Solutions}{156}
|
||||
\contentsline {chapter}{\numberline {4}M\IeC {\'e}canique en plusieurs dimensions}{75}
|
||||
\contentsline {section}{\numberline {4.1}Pr\IeC {\'e}liminaires}{75}
|
||||
\contentsline {subsection}{\numberline {4.1.1}Dimensions}{75}
|
||||
\contentsline {subsection}{\numberline {4.1.2}Syst\IeC {\`e}me d'axes}{75}
|
||||
\contentsline {section}{\numberline {4.2}Notion de vecteur en physique}{75}
|
||||
\contentsline {subsection}{\numberline {4.2.1}Norme d'un vecteur}{75}
|
||||
\contentsline {subsection}{\numberline {4.2.2}Op\IeC {\'e}rations vectorielles}{75}
|
||||
\contentsline {subsubsection}{produit scalaire}{76}
|
||||
\contentsline {subsubsection}{Produit vectoriel}{76}
|
||||
\contentsline {section}{\numberline {4.3}M\IeC {\'e}canique}{76}
|
||||
\contentsline {subsection}{\numberline {4.3.1}Cin\IeC {\'e}matique}{76}
|
||||
\contentsline {subsubsection}{Position}{76}
|
||||
\contentsline {subsubsection}{Vitesse}{77}
|
||||
\contentsline {subsubsection}{Acc\IeC {\'e}l\IeC {\'e}ration}{77}
|
||||
\contentsline {subsection}{\numberline {4.3.2}Dynamique}{77}
|
||||
\contentsline {subsubsection}{Premi\IeC {\`e}re loi}{77}
|
||||
\contentsline {subsubsection}{Seconde loi}{77}
|
||||
\contentsline {subsubsection}{Troisi\IeC {\`e}me loi}{77}
|
||||
\contentsline {section}{\numberline {4.4}Exemples}{77}
|
||||
\contentsline {subsection}{\numberline {4.4.1}Statique}{77}
|
||||
\contentsline {subsection}{\numberline {4.4.2}Plan inclin\IeC {\'e}}{78}
|
||||
\contentsline {subsection}{\numberline {4.4.3}Balistique}{80}
|
||||
\contentsline {subsection}{\numberline {4.4.4}Mouvement circulaire uniforme : MCU}{82}
|
||||
\contentsline {subsubsection}{D\IeC {\'e}finition}{82}
|
||||
\contentsline {subsubsection}{Cin\IeC {\'e}matique}{82}
|
||||
\contentsline {subsubsection}{Relation importante}{83}
|
||||
\contentsline {subsubsection}{Dynamique}{84}
|
||||
\contentsline {subsubsection}{Virages inclin\IeC {\'e}s}{84}
|
||||
\contentsline {paragraph}{Vitesses minimales}{84}
|
||||
\contentsline {paragraph}{Vitesses maximales}{85}
|
||||
\contentsline {subsection}{\numberline {4.4.5}Satellite en orbite g\IeC {\'e}ostationnaire}{86}
|
||||
\contentsline {subsubsection}{Introduction}{86}
|
||||
\contentsline {subsubsection}{Th\IeC {\'e}oriquement}{86}
|
||||
\contentsline {subsubsection}{Num\IeC {\'e}riquement}{86}
|
||||
\contentsline {subsection}{\numberline {4.4.6}Mouvement central}{87}
|
||||
\contentsline {subsubsection}{Mouvement kepleriens}{87}
|
||||
\contentsline {subsubsection}{Loi de Kepler}{87}
|
||||
\contentsline {chapter}{\numberline {5}M\IeC {\'e}canique diff\IeC {\'e}rentielle}{89}
|
||||
\contentsline {section}{\numberline {5.1}Introduction}{89}
|
||||
\contentsline {section}{\numberline {5.2}Cin\IeC {\'e}matique}{89}
|
||||
\contentsline {subsection}{\numberline {5.2.1}Exemples}{90}
|
||||
\contentsline {subsubsection}{Mouvement rectiligne uniform\IeC {\'e}ment acc\IeC {\'e}l\IeC {\'e}r\IeC {\'e} : MRUA}{90}
|
||||
\contentsline {subsubsection}{Port\IeC {\'e} maximum en balistique}{90}
|
||||
\contentsline {section}{\numberline {5.3}Dynamique}{91}
|
||||
\contentsline {subsection}{\numberline {5.3.1}Int\IeC {\'e}gration}{91}
|
||||
\contentsline {subsubsection}{Chute libre}{91}
|
||||
\contentsline {subsubsection}{Freinage}{91}
|
||||
\contentsline {subsection}{\numberline {5.3.2}\IeC {\'E}quation diff\IeC {\'e}rentielle}{91}
|
||||
\contentsline {subsubsection}{Chute dans un fluide visqueux}{91}
|
||||
\contentsline {subsubsection}{Mouvement harmonique}{93}
|
||||
\contentsline {subsubsection}{Mouvement harmonique d'une masse pendante}{94}
|
||||
\contentsline {subsubsection}{Mouvement non lin\IeC {\'e}aire}{95}
|
||||
\contentsline {chapter}{\numberline {6}Impulsion et quantit\IeC {\'e} de mouvement}{97}
|
||||
\contentsline {section}{\numberline {6.1}Introduction}{97}
|
||||
\contentsline {section}{\numberline {6.2}Quantit\IeC {\'e} de mouvement}{97}
|
||||
\contentsline {subsection}{\numberline {6.2.1}Masse d'inertie}{97}
|
||||
\contentsline {section}{\numberline {6.3}\IeC {\'E}nergie cin\IeC {\'e}tique}{98}
|
||||
\contentsline {section}{\numberline {6.4}Choc parfaitement \IeC {\'e}lastique}{98}
|
||||
\contentsline {subsection}{\numberline {6.4.1}Exemple}{98}
|
||||
\contentsline {section}{\numberline {6.5}Choc parfaitement mou}{99}
|
||||
\contentsline {subsection}{\numberline {6.5.1}Exemple}{99}
|
||||
\contentsline {section}{\numberline {6.6}choc bidimentionnel}{100}
|
||||
\contentsline {subsection}{\numberline {6.6.1}Exemple}{100}
|
||||
\contentsline {section}{\numberline {6.7}Impulsion}{100}
|
||||
\contentsline {section}{\numberline {6.8}Impulsion et quantit\IeC {\'e} de mouvement}{100}
|
||||
\contentsline {chapter}{\numberline {7}L'\IeC {\'e}nergie}{101}
|
||||
\contentsline {section}{\numberline {7.1}Introduction}{101}
|
||||
\contentsline {section}{\numberline {7.2}Travail}{101}
|
||||
\contentsline {section}{\numberline {7.3}Puissance}{102}
|
||||
\contentsline {section}{\numberline {7.4}\IeC {\'E}nergie potentielle}{102}
|
||||
\contentsline {section}{\numberline {7.5}\IeC {\'E}nergie cin\IeC {\'e}tique}{103}
|
||||
\contentsline {section}{\numberline {7.6}Th\IeC {\'e}or\IeC {\`e}me de l'\IeC {\'e}nergie cin\IeC {\'e}tique}{103}
|
||||
\contentsline {section}{\numberline {7.7}Conservation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{103}
|
||||
\contentsline {section}{\numberline {7.8}Variation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{105}
|
||||
\contentsline {section}{\numberline {7.9}\IeC {\'E}nergies renouvelables}{105}
|
||||
\contentsline {subsection}{\numberline {7.9.1}\IeC {\'E}nergie hydraulique}{106}
|
||||
\contentsline {subsubsection}{Exemple}{107}
|
||||
\contentsline {subsubsection}{Types de turbines}{107}
|
||||
\contentsline {subsubsection}{Alternateur}{107}
|
||||
\contentsline {subsubsection}{Probl\IeC {\`e}mes rencontr\IeC {\'e}s}{108}
|
||||
\contentsline {subsection}{\numberline {7.9.2}\IeC {\'E}nergie \IeC {\'e}olienne}{108}
|
||||
\contentsline {subsection}{\numberline {7.9.3}\IeC {\'E}nergie solaire}{109}
|
||||
\contentsline {subsubsection}{\IeC {\'E}nergie solaire thermique}{110}
|
||||
\contentsline {subsubsection}{\IeC {\'E}nergie solaire \IeC {\'e}lectrique}{111}
|
||||
\contentsline {subsection}{\numberline {7.9.4}\IeC {\'E}nergie g\IeC {\'e}othermique}{112}
|
||||
\contentsline {section}{\numberline {7.10}\IeC {\'E}nergies non renouvelables}{113}
|
||||
\contentsline {subsection}{\numberline {7.10.1}\IeC {\'E}nergie nucl\IeC {\'e}aire}{113}
|
||||
\contentsline {subsubsection}{Fission}{113}
|
||||
\contentsline {paragraph}{D\IeC {\'e}chets radioactifs}{115}
|
||||
\contentsline {paragraph}{Accidents nucl\IeC {\'e}aires}{115}
|
||||
\contentsline {subsubsection}{Fusion}{115}
|
||||
\contentsline {subsection}{\numberline {7.10.2}\IeC {\'E}nergie de combustion : p\IeC {\'e}trole et gaz}{116}
|
||||
\contentsline {chapter}{\numberline {8}L'\IeC {\'e}nergie}{119}
|
||||
\contentsline {section}{\numberline {8.1}Introduction}{119}
|
||||
\contentsline {section}{\numberline {8.2}Le travail}{119}
|
||||
\contentsline {subsection}{\numberline {8.2.1}Historiquement}{119}
|
||||
\contentsline {subsection}{\numberline {8.2.2}D\IeC {\'e}finition}{120}
|
||||
\contentsline {subsubsection}{Travail simple}{120}
|
||||
\contentsline {subsubsection}{Travail et produit scalaire}{120}
|
||||
\contentsline {subsubsection}{Travail cas g\IeC {\'e}n\IeC {\'e}ral}{120}
|
||||
\contentsline {section}{\numberline {8.3}L'\IeC {\'e}nergie}{121}
|
||||
\contentsline {subsection}{\numberline {8.3.1}Introduction}{121}
|
||||
\contentsline {subsection}{\numberline {8.3.2}\IeC {\'E}nergie potentielle}{122}
|
||||
\contentsline {subsection}{\numberline {8.3.3}\IeC {\'E}nergie cin\IeC {\'e}tique}{122}
|
||||
\contentsline {subsection}{\numberline {8.3.4}\IeC {\'E}nergie m\IeC {\'e}canique}{122}
|
||||
\contentsline {subsection}{\numberline {8.3.5}Exemple}{122}
|
||||
\contentsline {section}{\numberline {8.4}Conservation de l'\IeC {\'e}nergie}{123}
|
||||
\contentsline {subsection}{\numberline {8.4.1}Introduction}{123}
|
||||
\contentsline {subsection}{\numberline {8.4.2}Th\IeC {\'e}or\IeC {\`e}me de conservation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{123}
|
||||
\contentsline {subsection}{\numberline {8.4.3}Exemples}{123}
|
||||
\contentsline {section}{\numberline {8.5}Limite du th\IeC {\'e}or\IeC {\`e}me de conservation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{124}
|
||||
\contentsline {section}{\numberline {8.6}Forces conservatives}{124}
|
||||
\contentsline {subsection}{\numberline {8.6.1}D\IeC {\'e}finition}{124}
|
||||
\contentsline {subsection}{\numberline {8.6.2}Exemple}{124}
|
||||
\contentsline {chapter}{\numberline {9}Thermodynamique}{127}
|
||||
\contentsline {section}{\numberline {9.1}Introduction}{127}
|
||||
\contentsline {section}{\numberline {9.2}Temp\IeC {\'e}rature}{127}
|
||||
\contentsline {subsection}{\numberline {9.2.1}Celsius}{127}
|
||||
\contentsline {subsection}{\numberline {9.2.2}Fahrenheit}{127}
|
||||
\contentsline {subsection}{\numberline {9.2.3}Kelvin}{128}
|
||||
\contentsline {subsection}{\numberline {9.2.4}Agitation mol\IeC {\'e}culaire}{128}
|
||||
\contentsline {section}{\numberline {9.3}Dilatation}{128}
|
||||
\contentsline {section}{\numberline {9.4}Chaleur}{129}
|
||||
\contentsline {subsection}{\numberline {9.4.1}Chaleur sp\IeC {\'e}cifique}{129}
|
||||
\contentsline {subsection}{\numberline {9.4.2}Chaleur latente}{129}
|
||||
\contentsline {section}{\numberline {9.5}\IeC {\'E}nergie thermique}{130}
|
||||
\contentsline {subsection}{\numberline {9.5.1}Premier principe}{131}
|
||||
\contentsline {chapter}{\numberline {10}Thermodynamique}{133}
|
||||
\contentsline {section}{\numberline {10.1}Temp\IeC {\'e}rature et dilatation}{133}
|
||||
\contentsline {subsection}{\numberline {10.1.1}Temp\IeC {\'e}rature}{133}
|
||||
\contentsline {subsection}{\numberline {10.1.2}Dilatation}{133}
|
||||
\contentsline {section}{\numberline {10.2}Chaleurs sp\IeC {\'e}cifique et latente}{135}
|
||||
\contentsline {subsection}{\numberline {10.2.1}Introduction}{135}
|
||||
\contentsline {subsection}{\numberline {10.2.2}Chaleur sp\IeC {\'e}cifique}{135}
|
||||
\contentsline {subsubsection}{Chaleur massique}{135}
|
||||
\contentsline {subsubsection}{Capacit\IeC {\'e} thermique}{136}
|
||||
\contentsline {subsubsection}{Notion de mole}{136}
|
||||
\contentsline {subsubsection}{Chaleur molaire}{136}
|
||||
\contentsline {subsubsection}{Relation entre chaleur massique et molaire}{137}
|
||||
\contentsline {subsubsection}{Chaleur latente}{137}
|
||||
\contentsline {subsubsection}{\IeC {\'E}vaporation}{137}
|
||||
\contentsline {subsection}{\numberline {10.2.3}Bilan thermique}{138}
|
||||
\contentsline {section}{\numberline {10.3}Loi des gaz parfaits}{139}
|
||||
\contentsline {subsection}{\numberline {10.3.1}\IeC {\'E}quation d'\IeC {\'e}tat}{139}
|
||||
\contentsline {subsubsection}{Pression}{139}
|
||||
\contentsline {subsubsection}{\IeC {\'E}tat d'un gaz parfait}{139}
|
||||
\contentsline {subsubsection}{Approche intuitive}{139}
|
||||
\contentsline {subsubsection}{Approche mol\IeC {\'e}culaire}{140}
|
||||
\contentsline {subsection}{\numberline {10.3.2}Gaz parfait}{141}
|
||||
\contentsline {section}{\numberline {10.4}Premier principe}{141}
|
||||
\contentsline {subsection}{\numberline {10.4.1}Chaleur}{141}
|
||||
\contentsline {subsection}{\numberline {10.4.2}Travail}{142}
|
||||
\contentsline {subsection}{\numberline {10.4.3}\IeC {\'E}nergie interne}{142}
|
||||
\contentsline {subsubsection}{\IeC {\'E}quipartition de l'\IeC {\'e}nergie}{143}
|
||||
\contentsline {subsection}{\numberline {10.4.4}Premier principe}{143}
|
||||
\contentsline {subsection}{\numberline {10.4.5}Changements d'\IeC {\'e}tats}{143}
|
||||
\contentsline {subsubsection}{Transformation isobare}{144}
|
||||
\contentsline {subsubsection}{Transformation isochore}{144}
|
||||
\contentsline {subsubsection}{Transformation isotherme}{145}
|
||||
\contentsline {subsubsection}{Transformation adiabatique}{146}
|
||||
\contentsline {subsection}{\numberline {10.4.6}Chaleurs sp\IeC {\'e}cifiques}{147}
|
||||
\contentsline {section}{\numberline {10.5}Machines thermiques}{148}
|
||||
\contentsline {subsection}{\numberline {10.5.1}Machine simple}{148}
|
||||
\contentsline {subsection}{\numberline {10.5.2}Moteur \IeC {\`a} explosion}{150}
|
||||
\contentsline {subsection}{\numberline {10.5.3}Moteur Diesel}{152}
|
||||
\contentsline {subsection}{\numberline {10.5.4}Machine de Stirling}{154}
|
||||
\contentsline {subsection}{\numberline {10.5.5}Climatiseur}{154}
|
||||
\contentsline {subsection}{\numberline {10.5.6}R\IeC {\'e}frig\IeC {\'e}rateur}{154}
|
||||
\contentsline {subsection}{\numberline {10.5.7}Pompe \IeC {\`a} chaleur}{154}
|
||||
\contentsline {subsection}{\numberline {10.5.8}Cycle de Carnot}{154}
|
||||
\contentsline {section}{\numberline {10.6}Thermodynamique statistique}{154}
|
||||
\contentsline {section}{\numberline {10.7}Second principe}{155}
|
||||
\contentsline {chapter}{\numberline {A}Syst\IeC {\`e}mes d'unit\IeC {\'e}s}{157}
|
||||
\contentsline {section}{\numberline {A.1}Introduction}{157}
|
||||
\contentsline {section}{\numberline {A.2}Op\IeC {\'e}rateur d'unit\IeC {\'e}s}{157}
|
||||
\contentsline {section}{\numberline {A.3}Analyse dimentionnelle}{158}
|
||||
\contentsline {section}{\numberline {A.4}Les unit\IeC {\'e}s du Syst\IeC {\`e}me International}{159}
|
||||
\contentsline {subsection}{\numberline {A.4.1}Exemple}{159}
|
||||
\contentsline {section}{\numberline {A.5}Conversions}{159}
|
||||
\contentsline {section}{\numberline {A.6}Sous-multiples}{160}
|
||||
\contentsline {section}{\numberline {A.7}Notation scientifique}{160}
|
||||
\contentsline {section}{\numberline {A.8}R\IeC {\`e}gles de calcul}{161}
|
||||
\contentsline {chapter}{\numberline {B}Deux syst\IeC {\`e}mes de coordonn\IeC {\'e}es}{163}
|
||||
\contentsline {section}{\numberline {B.1}Le syst\IeC {\`e}me de coordonn\IeC {\'e}es circulaires}{163}
|
||||
\contentsline {subsection}{\numberline {B.1.1}Introduction}{163}
|
||||
\contentsline {subsection}{\numberline {B.1.2}Description}{163}
|
||||
\contentsline {section}{\numberline {B.2}Coordonn\IeC {\'e}es sph\IeC {\'e}riques}{163}
|
||||
\contentsline {subsection}{\numberline {B.2.1}Introduction}{163}
|
||||
\contentsline {subsection}{\numberline {B.2.2}Description}{163}
|
||||
\contentsline {subsection}{\numberline {B.2.3}Latitude et longitude}{164}
|
||||
\contentsline {chapter}{\numberline {C}Mesures de distances}{165}
|
||||
\contentsline {section}{\numberline {C.1}La taille de la Terre}{165}
|
||||
\contentsline {subsection}{\numberline {C.1.1}Le principe}{165}
|
||||
\contentsline {subsection}{\numberline {C.1.2}Techniquement}{166}
|
||||
\contentsline {section}{\numberline {C.2}La taille de la Lune}{167}
|
||||
\contentsline {section}{\numberline {C.3}La distance Terre-Lune}{167}
|
||||
\contentsline {section}{\numberline {C.4}La distance Terre-Soleil}{168}
|
||||
\contentsline {section}{\numberline {C.5}La distance des \IeC {\'e}toiles}{170}
|
||||
\contentsline {chapter}{\numberline {D}Travaux pratiques}{171}
|
||||
\contentsline {section}{\numberline {D.1}Le rapport de laboratoire}{171}
|
||||
\contentsline {subsection}{\numberline {D.1.1}Plan d'un rapport de travail pratique}{172}
|
||||
\contentsline {subsubsection}{Pr\IeC {\'e}liminaires}{172}
|
||||
\contentsline {subsubsection}{R\IeC {\'e}sum\IeC {\'e}}{172}
|
||||
\contentsline {subsubsection}{But}{172}
|
||||
\contentsline {subsubsection}{Th\IeC {\'e}orie}{172}
|
||||
\contentsline {subsubsection}{Description de l'exp\IeC {\'e}rience}{172}
|
||||
\contentsline {subsubsection}{R\IeC {\'e}sultats}{172}
|
||||
\contentsline {subsubsection}{Discussion}{174}
|
||||
\contentsline {subsubsection}{Conclusion}{174}
|
||||
\contentsline {subsubsection}{Annexes}{174}
|
||||
\contentsline {section}{\numberline {D.2}La n\IeC {\'e}buleuse du Crabe}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.1}Introduction}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.2}But du travail pratique}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.3}Dispositif exp\IeC {\'e}rimental}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.4}Mesures}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.5}R\IeC {\'e}sultats}{175}
|
||||
\contentsline {subsection}{\numberline {D.2.6}Analyse}{175}
|
||||
\contentsline {section}{\numberline {D.3}Le pendule simple}{175}
|
||||
\contentsline {subsection}{\numberline {D.3.1}Les mesures}{175}
|
||||
\contentsline {subsection}{\numberline {D.3.2}Organisation des donn\IeC {\'e}es et graphiques}{176}
|
||||
\contentsline {section}{\numberline {D.4}Mouvement simple : MRU}{176}
|
||||
\contentsline {subsection}{\numberline {D.4.1}Les mesures}{176}
|
||||
\contentsline {subsection}{\numberline {D.4.2}Organisation des donn\IeC {\'e}es et graphiques}{176}
|
||||
\contentsline {subsection}{\numberline {D.4.3}Analyse des r\IeC {\'e}sultats}{176}
|
||||
\contentsline {section}{\numberline {D.5}Mouvement simple :\\MRUA}{176}
|
||||
\contentsline {subsection}{\numberline {D.5.1}But}{176}
|
||||
\contentsline {subsection}{\numberline {D.5.2}Th\IeC {\'e}orie}{177}
|
||||
\contentsline {subsection}{\numberline {D.5.3}Les mesures}{177}
|
||||
\contentsline {subsection}{\numberline {D.5.4}Organisation des donn\IeC {\'e}es et graphiques}{177}
|
||||
\contentsline {subsection}{\numberline {D.5.5}Galil\IeC {\'e}e et le plan inclin\IeC {\'e}}{177}
|
||||
\contentsline {section}{\numberline {D.6}La chute libre}{177}
|
||||
\contentsline {subsection}{\numberline {D.6.1}Cette exp\IeC {\'e}rience donnant lieu \IeC {\`a} un rapport not\IeC {\'e}, elle n'est pas d\IeC {\'e}crite.}{177}
|
||||
\contentsline {subsection}{\numberline {D.6.2}R\IeC {\'e}sultats}{177}
|
||||
\contentsline {section}{\numberline {D.7}Le canon horizontal}{177}
|
||||
\contentsline {section}{\numberline {D.8}Le chariot \IeC {\`a} masse pendante}{178}
|
||||
\contentsline {chapter}{\numberline {E}Rotations}{179}
|
||||
\contentsline {section}{\numberline {E.1}Rotation de la Terre sur elle-m\IeC {\^e}me}{179}
|
||||
\contentsline {section}{\numberline {E.2}Rotation de la Terre autour du Soleil}{179}
|
||||
\contentsline {section}{\numberline {E.3}Rotation du Soleil dans la Voie Lact\IeC {\'e}e}{181}
|
||||
\contentsline {section}{\numberline {E.4}Vitesse et r\IeC {\'e}f\IeC {\'e}rentiel}{181}
|
||||
\contentsline {chapter}{\numberline {F}MRUA d\IeC {\'e}veloppements}{183}
|
||||
\contentsline {section}{\numberline {F.1}La position}{183}
|
||||
\contentsline {section}{\numberline {F.2}Une autre relation bien pratique}{183}
|
||||
\contentsline {subsection}{\numberline {F.2.1}Cin\IeC {\'e}matique}{183}
|
||||
\contentsline {subsection}{\numberline {F.2.2}\IeC {\'E}nergie}{184}
|
||||
\contentsline {chapter}{\numberline {G}Chute de la Lune}{185}
|
||||
\contentsline {section}{\numberline {G.1}Introduction}{185}
|
||||
\contentsline {section}{\numberline {G.2}Acc\IeC {\'e}l\IeC {\'e}ration}{185}
|
||||
\contentsline {section}{\numberline {G.3}Force de gravitation}{186}
|
||||
\contentsline {chapter}{\numberline {H}Satellite en orbite g\IeC {\'e}ostationnaire}{187}
|
||||
\contentsline {section}{\numberline {H.1}Introduction}{187}
|
||||
\contentsline {section}{\numberline {H.2}Th\IeC {\'e}oriquement}{187}
|
||||
\contentsline {section}{\numberline {H.3}Num\IeC {\'e}riquement}{188}
|
||||
\contentsline {section}{\numberline {H.4}Loi de Kepler}{188}
|
||||
\contentsline {chapter}{\numberline {I}Relativit\IeC {\'e}}{189}
|
||||
\contentsline {section}{\numberline {I.1}Relativit\IeC {\'e} galil\IeC {\'e}enne}{189}
|
||||
\contentsline {section}{\numberline {I.2}Transformation galil\IeC {\'e}enne}{190}
|
||||
\contentsline {section}{\numberline {I.3}Invariance}{191}
|
||||
\contentsline {section}{\numberline {I.4}Forces inertielles}{191}
|
||||
\contentsline {subsection}{\numberline {I.4.1}Force d'inertie}{191}
|
||||
\contentsline {subsection}{\numberline {I.4.2}Force centrifuge}{192}
|
||||
\contentsline {chapter}{\numberline {J}Mar\IeC {\'e}es}{195}
|
||||
\contentsline {section}{\numberline {J.1}Introduction}{195}
|
||||
\contentsline {section}{\numberline {J.2}Centre de gravit\IeC {\'e}}{195}
|
||||
\contentsline {section}{\numberline {J.3}Force d'inertie}{196}
|
||||
\contentsline {subsection}{\numberline {J.3.1}Vitesse angulaire}{196}
|
||||
\contentsline {subsection}{\numberline {J.3.2}Force d'inertie}{196}
|
||||
\contentsline {section}{\numberline {J.4}Poids relatif}{197}
|
||||
\contentsline {section}{\numberline {J.5}Analyse diff\IeC {\'e}rentielle}{197}
|
||||
\contentsline {section}{\numberline {J.6}Autres rythmes}{197}
|
||||
\contentsline {subsection}{\numberline {J.6.1}D\IeC {\'e}calages}{198}
|
||||
\contentsline {subsection}{\numberline {J.6.2}Mar\IeC {\'e}es de vives et mortes eaux}{198}
|
||||
\contentsline {subsection}{\numberline {J.6.3}Mar\IeC {\'e}es d'\IeC {\'e}quinoxes}{198}
|
||||
\contentsline {subsection}{\numberline {J.6.4}Mar\IeC {\'e}es de p\IeC {\'e}rig\IeC {\'e}e et p\IeC {\'e}rih\IeC {\'e}lie}{199}
|
||||
\contentsline {subsection}{\numberline {J.6.5}Mar\IeC {\'e}es de d\IeC {\'e}clinaison}{199}
|
||||
\contentsline {subsection}{\numberline {J.6.6}Retards et mar\IeC {\'e}es c\IeC {\^o}ti\IeC {\`e}res}{199}
|
||||
\contentsline {section}{\numberline {J.7}Limite de Roche}{199}
|
||||
\contentsline {subsection}{\numberline {J.7.1}Mod\IeC {\`e}le simplifi\IeC {\'e}}{200}
|
||||
\contentsline {subsection}{\numberline {J.7.2}Exemples}{201}
|
||||
\contentsline {chapter}{\numberline {K}\IeC {\'E}nergies}{203}
|
||||
\contentsline {section}{\numberline {K.1}Introduction}{203}
|
||||
\contentsline {section}{\numberline {K.2}\IeC {\'E}nergie hydraulique}{203}
|
||||
\contentsline {section}{\numberline {K.3}\IeC {\'E}nergie \IeC {\'e}olienne}{204}
|
||||
\contentsline {subsection}{\numberline {K.3.1}R\IeC {\`e}gle de Betz}{204}
|
||||
\contentsline {subsection}{\numberline {K.3.2}\IeC {\'E}oliennes}{205}
|
||||
\contentsline {subsubsection}{\IeC {\'E}olienne de Collonges-Dor\IeC {\'e}naz}{205}
|
||||
\contentsline {subsubsection}{\IeC {\'E}oliennes du Mont Soleil (Jura suisse)}{205}
|
||||
\contentsline {section}{\numberline {K.4}G\IeC {\'e}othermie}{205}
|
||||
\contentsline {section}{\numberline {K.5}\IeC {\'E}nergie de combustion des d\IeC {\'e}chets}{206}
|
||||
\contentsline {chapter}{\numberline {L}Exercices}{207}
|
||||
\contentsline {section}{\numberline {L.1}Probl\IeC {\`e}mes}{207}
|
||||
\contentsline {subsection}{\numberline {L.1.1}Relatifs \IeC {\`a} la conversion d'unit\IeC {\'e}s et \IeC {\`a} la notation scientifique}{207}
|
||||
\contentsline {subsection}{\numberline {L.1.2}Relatifs aux notions de d\IeC {\'e}placement, position et distance parcourue}{208}
|
||||
\contentsline {subsection}{\numberline {L.1.3}Relatifs \IeC {\`a} la notion de vitesse}{208}
|
||||
\contentsline {subsection}{\numberline {L.1.4}Relatif \IeC {\`a} la notion d'acc\IeC {\'e}l\IeC {\'e}ration}{208}
|
||||
\contentsline {subsection}{\numberline {L.1.5}Relatif au MRU}{209}
|
||||
\contentsline {subsection}{\numberline {L.1.6}Relatif au MRUA}{209}
|
||||
\contentsline {subsection}{\numberline {L.1.7}Relatifs \IeC {\`a} la physique aristot\IeC {\'e}licienne}{210}
|
||||
\contentsline {subsection}{\numberline {L.1.8}Relatifs \IeC {\`a} la physique newtonienne}{210}
|
||||
\contentsline {subsection}{\numberline {L.1.9}Relatifs aux forces}{212}
|
||||
\contentsline {subsection}{\numberline {L.1.10}Relatifs \IeC {\`a} l'\IeC {\'e}nergie}{212}
|
||||
\contentsline {subsection}{\numberline {L.1.11}Relatifs \IeC {\`a} la conservation de l'\IeC {\'e}nergie}{213}
|
||||
\contentsline {subsection}{\numberline {L.1.12}Relatifs \IeC {\`a} l'\IeC {\'e}nergie hydraulique}{213}
|
||||
\contentsline {subsection}{\numberline {L.1.13}Relatifs \IeC {\`a} l'\IeC {\'e}nergie \IeC {\'e}olienne}{213}
|
||||
\contentsline {subsection}{\numberline {L.1.14}Relatifs \IeC {\`a} l'\IeC {\'e}nergie solaire}{214}
|
||||
\contentsline {section}{\numberline {L.2}Solutions}{214}
|
||||
\contentsline {section}{\numberline {L.3}Solutions OS}{220}
|
||||
\contentsline {chapter}{\numberline {M}Ordre de grandeur, erreur et incertitudes}{221}
|
||||
\contentsline {section}{\numberline {M.1}Ordre de grandeur}{221}
|
||||
\contentsline {section}{\numberline {M.2}\IeC {\'E}cart et erreur}{221}
|
||||
\contentsline {section}{\numberline {M.3}Incertitude}{222}
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||||
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||||
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\begin{Solution OS}{1}
|
||||
On commence par choisir le système. Pour éviter de devoir calculer la tension dans la corde, on le choisit comme constitué de la corde et des deux masses M et m.
|
||||
|
||||
Les forces extérieures sont alors au nombre de trois. Le plan horizontal exerce sur la masse M une force de soutient verticale égale et opposée à son poids (mais qui ne sont pas l'action et la réaction l'une de l'autre), puisque la masse se déplace horizontalement. Ces deux forces s'annulent donc. Reste le poids de la masse m, seule force extérieure à agir pour accélérer le système.
|
||||
|
||||
On peut donc écrire, selon la seconde loi de Newton~:
|
||||
\[\sum F^{ext}=m\cdot g=(M+m)\cdot a\]
|
||||
où M+m est la masse du système. Ainsi, finalement, on peut calculer la valeur de l'accélération~:
|
||||
\begin{align*}
|
||||
&m\cdot g=(M+m)\cdot a\;\Rightarrow\\
|
||||
&a=\frac{m}{M+m}\cdot g=\frac{2}{5}\cdot 9,81=\unit{3,924}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
\medskip
|
||||
À partir de l'accélération, on peut ensuite calculer la vitesse au bout d'un mètre, grâce à l'équation du MRUA~:
|
||||
\begin{align*}
|
||||
v^2&=v_0^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
v^2&=0+2\cdot 3,924\cdot 1\;\Rightarrow\\
|
||||
v&=\sqrt{2\cdot 3,924}=\unit{2,8}{\metre\per\second}
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||||
\end{align*}
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||||
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||||
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\begin{Solution OS}{2}
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||||
Un corrigé de test.
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Loading…
Reference in New Issue
Block a user