Beaucoup de modifications pour permettre des exercices OS.
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Annexe-ChuteLune
Annexe-Energies
Annexe-Exercices
Annexe-Incertitudes
Annexe-MRUA
Annexe-Maree
Annexe-MesuresDistances
Annexe-Relativite
Annexe-Rotations
Annexe-Satellites
Annexe-SystemeCoordonnees
Annexe-TravauxPratiques
Annexe-UnitesInternationales
Cinematique
CoursMecaniqueOSDF.auxCoursMecaniqueOSDF.dviCoursMecaniqueOSDF.entCoursMecaniqueOSDF.idxCoursMecaniqueOSDF.lofCoursMecaniqueOSDF.logCoursMecaniqueOSDF.lotCoursMecaniqueOSDF.pdfCoursMecaniqueOSDF.psCoursMecaniqueOSDF.texCoursMecaniqueOSDF.tocDynamique
Energie
EnergieOS
Introduction
Macros.auxMecaniqueDifferentielle
MecaniqueDim
Prefaces
QtiteMvt
Solutions.texSolutionsOS.texThermodynamique
ThermodynamiqueOS
@ -1,18 +1,18 @@
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@ -1,48 +1,40 @@
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@ -853,6 +853,23 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan
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\Opensolutionfile{ansos}[SolutionsOS]
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\begin{exos}
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Un exercice de test.
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Un corrigé de test.
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@ -1357,4 +1374,9 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan
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||||
\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}
|
||||
\contentsline {figure}{\numberline {B.1}{\ignorespaces Syst\IeC {\`e}me de coordonn\IeC {\'e}es circulaires\relax }}{105}
|
||||
\contentsline {figure}{\numberline {B.2}{\ignorespaces Syst\IeC {\`e}me de coordonn\IeC {\'e}es sph\IeC {\'e}riques\relax }}{106}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\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}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\contentsline {figure}{\numberline {D.1}{\ignorespaces Rail horizontal}}{114}
|
||||
\contentsline {figure}{\numberline {D.2}{\ignorespaces Chute libre\relax }}{115}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\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}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {A.1}{\ignorespaces Relation de l'arc de cercle\relax }}{159}
|
||||
\contentsline {figure}{\numberline {F.1}{\ignorespaces \emph {Discours concernant deux sciences nouvelles} de Galil\IeC {\'e}e}}{125}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\contentsline {figure}{\numberline {G.1}{\ignorespaces Chute de la lune\relax }}{127}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\contentsline {figure}{\numberline {H.1}{\ignorespaces Satellite}}{129}
|
||||
\addvspace {10\p@ }
|
||||
\contentsline {figure}{\numberline {D.1}{\ignorespaces Rail horizontal}}{172}
|
||||
\contentsline {figure}{\numberline {D.2}{\ignorespaces Chute libre\relax }}{173}
|
||||
\contentsline {figure}{\numberline {I.1}{\ignorespaces Transformation de galil\IeC {\'e}e}}{132}
|
||||
\contentsline {figure}{\numberline {J.1}{\ignorespaces Mar\IeC {\'e}e}}{137}
|
||||
\addvspace {10\p@ }
|
||||
\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}
|
||||
\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}
|
||||
\addvspace {10\p@ }
|
||||
\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 Graphes horaires du MRU.\relax }}{217}
|
||||
\contentsline {figure}{\numberline {L.4}{\ignorespaces Chute aristot\IeC {\'e}licienne de la tour Eiffel.\relax }}{221}
|
||||
\contentsline {figure}{\numberline {L.5}{\ignorespaces Une fus\IeC {\'e}e.\relax }}{221}
|
||||
\contentsline {figure}{\numberline {L.6}{\ignorespaces Une remorque\relax }}{221}
|
||||
\contentsline {figure}{\numberline {L.7}{\ignorespaces Un ascenseur\relax }}{223}
|
||||
\contentsline {figure}{\numberline {K.1}{\ignorespaces Le barrage du Ch\IeC {\^a}telot}}{145}
|
||||
\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@ }
|
||||
\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}
|
||||
\contentsline {table}{\numberline {D.1}{\ignorespaces Tableau de mesures\relax }}{115}
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
\addvspace {10\p@ }
|
||||
@ -39,6 +28,3 @@
|
||||
\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 }}{231}
|
||||
\contentsline {table}{\numberline {M.2}{\ignorespaces La longueur d'autres baguettes de pain\relax }}{232}
|
||||
|
||||
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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}
|
||||
|
||||
%---------------------------------------------------------------
|
||||
@ -18,6 +18,9 @@
|
||||
\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}
|
||||
\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
|
||||
|
||||
|
||||
@ -89,313 +89,177 @@
|
||||
\contentsline {paragraph}{Exemple}{72}
|
||||
\contentsline {subsubsection}{La force d'un ressort}{72}
|
||||
\contentsline {paragraph}{Exemple}{73}
|
||||
\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}{213}
|
||||
\contentsline {section}{\numberline {L.2}Solutions}{214}
|
||||
\contentsline {chapter}{\numberline {M}Ordre de grandeur, erreur et incertitudes}{231}
|
||||
\contentsline {section}{\numberline {M.1}Ordre de grandeur}{231}
|
||||
\contentsline {section}{\numberline {M.2}\IeC {\'E}cart et erreur}{231}
|
||||
\contentsline {section}{\numberline {M.3}Incertitude}{232}
|
||||
\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}
|
||||
|
||||
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614
Solutions.tex
614
Solutions.tex
@ -1,617 +1,3 @@
|
||||
\begin{Solution}{1}
|
||||
Comme le nombre de \kilo\metre est 1000 fois plus petit que le nombre de mètres et que \(\unit{1}{AL}=\unit{9,46\cdot 10^{15}}{\metre}\), on a :
|
||||
\begin{align*}
|
||||
\unit{4,238}{AL}&=4,238\cdot 9,46\cdot 10^{15}\\
|
||||
&=4\cdot 10^{16}\,m=\unit{4\cdot 10^{13}}{\kilo\metre}
|
||||
\end{align*}
|
||||
Comme \(\unit{1}{pc}\approx \unit{3\cdot 10^{16}}{\metre}\), on a :
|
||||
\[\unit{4\cdot 10^{16}}{\metre}\approx \frac{4\cdot 10^{16}}{3\cdot 10^{16}}=\unit{1,33}{pc}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{2}
|
||||
La distance Terre-Soleil vaut \unit{1,496\cdot 10^{11}}{\metre}. On a donc :
|
||||
\[\unit{1,496\cdot 10^{11}}{\metre}=\unit{1,496\cdot 10^{8}}{\kilo\metre}\]
|
||||
Par ailleurs, par définition de l'unité astronomique (UA), on a :
|
||||
\[\unit{1,496\cdot 10^{11}}{\metre}=\unit{1}{UA}\]
|
||||
Finalement, avec $1\,AL=9,46\cdot 10^{15}\,m$, on a :
|
||||
\begin{align*}
|
||||
\unit{1,496\cdot 10^{11}}{\metre}&=\frac{1,496\cdot 10^{11}}{9,46\cdot 10^{15}}\\
|
||||
&=\unit{1,58\cdot 10^{-5}}{AL}\cong\unit{16}{\micro AL}
|
||||
\end{align*}
|
||||
L'exercice \ref{centaure} nous indique que l'étoile la plus proche de nous est à \unit{4,238}{AL}. On a donc :
|
||||
\[\frac{4,238}{1,58\cdot 10^{-5}}=2,68\cdot 10^5\,\times\]
|
||||
Alpha du Centaure se trouve donc à \(268'228\,\times\) la distance Terre-Soleil.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{3}
|
||||
Le diamètre de notre galaxie est de \unit{80'000}{AL}. L'exercice \ref{centaure} nous indique que la distance à Alpha du Centaure vaut \unit{4,238}{AL}. Ainsi, on a :
|
||||
\[\frac{80'000}{4,238}=18'877\,\times\]
|
||||
Le diamètre de la galaxie représente donc \(18'877\,\times\) la distance à l'étoile la plus proche de nous.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{4}
|
||||
La distance Terre-Lune est beaucoup plus grande que le diamètre de la Lune. L'angle est donc petit et on peut écrire la relation d'arc donnée par l'équation \ref{relationdarc} :
|
||||
\begin{align*}
|
||||
D&=2\cdot R_{Lune}=d\cdot \alpha\;\Rightarrow\;\alpha=\frac{2\cdot R_{Lune}}{d_{Terre-Lune}}\\
|
||||
\alpha&=\frac{2\cdot 0,2725\cdot 6,371\cdot 10^6}{3,84\cdot 10^8}=\unit{0,009}{\rad}
|
||||
\end{align*}
|
||||
Comme \(\unit{180}{\degree}=\unit{\pi}{\rad}\), l'angle considéré est :
|
||||
\[\alpha=0,009\cdot \frac{180}{\pi}=\unit{0,5157}{\degree}\]
|
||||
Comme un degré vaut soixante minutes d'arc, \(\unit{1}{\degree}=\unit{60}{\arcminute}\), on a :
|
||||
\[\alpha=\unit{0,5157}{\degree}=0,5157\cdot 60=\unit{31}{\arcminute}\]
|
||||
et :
|
||||
\[\alpha=\unit{31}{\arcminute}=31\cdot 60=\unit{1860}{\arcsecond}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{5}
|
||||
Dans \unit{1}{\metre\cubed}, on trouve \unit{1000}{\deci\metre\cubed} et \unit{10^6}{\centi\metre\cubed}. Ainsi, dans \unit{1}{\metre\cubed}, on trouve un million de fois plus d'atomes que dans \unit{1}{\centi\metre\cubed}. On a donc par \metre\cubed :
|
||||
\[nb\,atomes=0,1\cdot 10^4\cdot 10^6=10^9\,\text{atomes}\]
|
||||
Et par litre, c'est-à-dire par \deci\metre\cubed :
|
||||
\[nb\,atomes=0,1\cdot 10^4\cdot 10^3=10^6\,\text{atomes}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{6}
|
||||
La relation d'arc donnée par l'équation \ref{relationdarc} nous permet d'écrire :
|
||||
\[L=R\cdot \alpha\,\Rightarrow\,R=\frac{L}{\alpha}\]
|
||||
Avec la longueur \(L\) en \(m\) et l'angle \(\alpha\) en \rad :
|
||||
\begin{align*}
|
||||
L&=5000\cdot 160=\unit{8\cdot 10^5}{\metre}\\
|
||||
\alpha&=7,5\cdot \frac{\pi}{180}=\unit{0,13}{\rad}
|
||||
\end{align*}
|
||||
Ainsi, le rayon de la Terre d'Eratosthène valait :
|
||||
\[R=\frac{8\cdot 10^5}{0,13}=\unit{6'111'550}{\metre}=\unit{6'111,55}{\kilo\metre}\]
|
||||
Sachant que la valeur actuelle du rayon moyen de la Terre vaut :
|
||||
\[R_{Terre}=\unit{6'371,03}{\kilo\metre}\]
|
||||
à l'aide de l'équation \ref{defecart}, on peut déterminer l'écart entre les deux valeurs :
|
||||
\[e=\frac{6'371,03-6'111,55}{6'371,03}\cdot 100=4,1\%\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{7}
|
||||
Par définition, le déplacement se calcule par :
|
||||
\[D=\Delta x=x_f-x_i=-5-0=\unit{-5}{\metre}\]
|
||||
Et la distance parcourue est la distance réellement effectuée :
|
||||
\[d=10+1+11+5=\unit{27}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{8}
|
||||
Pour passer de \kilo\metre\per\hour en \metre\per\second, il faut diviser par un facteur de 3,6. En effet :
|
||||
\[\unit{120}{\kilo\metre\hour}=\frac{120\cdot 10^3\,m/h}{3600\,s/h}=\frac{120}{3,6}=\unit{33,3}{\metre\per\second}\]
|
||||
Ainsi, la distance parcourue en deux secondes est :
|
||||
\[d=v\cdot t=33,3\cdot 2=\unit{66,6}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{9}
|
||||
Comme la position au bout de \unit{10}{\second} se calcule par :
|
||||
\[x(10\,s)=-2\cdot 10+20=\unit{0}{\metre}\]
|
||||
le déplacement est donné par :
|
||||
\[D=\Delta x=x_f-x_i=0-0=\unit{0}{\metre}\]
|
||||
Selon l'équation de la position donnée ici, le mouvement de l'objet est le suivant :
|
||||
\begin{enumerate}
|
||||
\item à la vitesse constante de \unit{2}{\metre\per\second} l'objet se déplace pendant \unit{4}{\second},
|
||||
\item il s'arrête de \unit{4}{} à \unit{6}{\second} et
|
||||
\item il revient en arrière à la vitesse de \unit{-2}{\metre\per\second} de \unit{6}{} à \unit{10}{\second}.
|
||||
\end{enumerate}
|
||||
Ainsi, l'objet parcourt dans un premier temps \(2\cdot 4=\unit{8}{\metre}\) en avant et dans un second temps \unit{8}{\metre} en arrière. La distance parcourue est donc :
|
||||
\[d=8+8=\unit{16}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{10}
|
||||
Deux raisonnements sont possibles :
|
||||
\begin{itemize}
|
||||
\item On s'imagine être dans un train qu'on ne voit pas bouger. Sa vitesse par rapport à nous est nulle. L'autre train se trouve au départ à une distance de \unit{12}{\kilo\metre} et se déplace par rapport à nous à une vitesse relative de \unit{200}{\kilo\metre\per\hour} (sa vitesse et notre vitesse sont cumulées). Ainsi, on peut écrire :
|
||||
\[v=\frac{\Delta x}{t}\;\Rightarrow\;t=\frac{\Delta x}{v}=\frac{12}{200}=\unit{0,06}{\hour}\]
|
||||
\item On définit le zéro du système d'axes à la position du premier train au moment où ils sont séparés de \unit{12}{\kilo\metre}. L'équation de la position du premier train est alors :
|
||||
\[x_1=100\cdot t\]
|
||||
Comme la position initiale du second train vaut \unit{12}{\kilo\metre} et qu'il s'approche, sa vitesse est négative et l'équation de sa position au cours du temps est :
|
||||
\[x_2=-100\cdot t+12\]
|
||||
La condition de rencontre s'écrit alors :
|
||||
\begin{align*}
|
||||
x_1&=x_2\\
|
||||
100\cdot t&=-100\cdot t+12\;\Rightarrow\\
|
||||
200\cdot t&=12\;\Rightarrow\;t=\frac{12}{200}=\unit{0,06}{\hour}
|
||||
\end{align*}
|
||||
\end{itemize}
|
||||
Le premier raisonnement se fait par rapport à l'un des objets en mouvement. Il est dit relatif. Le second raisonnement se fait par rapport à un référentiel commun : le sol. Il est dit absolu.
|
||||
|
||||
Mais quel que soit le référentiel, le résultat est le même.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{11}
|
||||
Deux raisonnements sont possibles :
|
||||
\begin{itemize}
|
||||
\item On s'imagine être dans le camion qu'on ne voit pas bouger. Sa vitesse par rapport à nous est nulle. La voiture, elle, se trouve au départ à une distance de \unit{0,6}{\kilo\metre} et se déplace par rapport à nous à une vitesse relative de \(110-80=\unit{30}{\kilo\metre\per\hour}\) (sa vitesse est diminuée de notre vitesse, puisqu'on la fuit). Ainsi, on peut écrire :
|
||||
\[v=\frac{\Delta x}{t}\;\Rightarrow\;t=\frac{\Delta x}{v}=\frac{0,6}{30}=\unit{0,02}{\hour}\]
|
||||
\item On définit le zéro du système d'axes à la position de la voiture au moment où la voiture et le camion sont séparés de \unit{0,6}{\kilo\metre}. L'équation de la position de la voiture est alors :
|
||||
\[x_v=110\cdot t\]
|
||||
Comme la position initiale du camion vaut \unit{0,6}{\kilo\metre} et qu'il va dans la même direction que la voiture, l'équation de sa position au cours du temps est :
|
||||
\[x_c=80\cdot t+0,6\]
|
||||
La condition de rencontre s'écrit alors :
|
||||
\begin{align*}
|
||||
x_v&=x_c\\
|
||||
110\cdot t&=80\cdot t+0,6\;\Rightarrow\\
|
||||
30\cdot t&=0,6\;\Rightarrow\;t=\frac{0,6}{30}=\unit{0,02}{\hour}
|
||||
\end{align*}
|
||||
\end{itemize}
|
||||
Le premier raisonnement se fait par rapport à l'un des objets en mouvement. Il est dit relatif. Le second raisonnement se fait par rapport à un référentiel commun : le sol. Il est dit absolu.
|
||||
|
||||
Mais quel que soit le référentiel, le résultat est le même.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{12}
|
||||
On sait que le rayon de la Terre vaut environ \unit{6'400}{\kilo\metre}. Sa circonférence vaut donc :
|
||||
\[C=2\cdot \pi\cdot r\approx 2\cdot 3\cdot 6'000=\unit{36'000}{\kilo\metre}\approx \unit{40'000}{\kilo\metre}\]
|
||||
Sa vitesse se calcule donc ainsi :
|
||||
\begin{align*}
|
||||
v&=\frac{C}{t}\approx \frac{40'000}{24}\approx \frac{40'000}{25}\\
|
||||
&=40'000\cdot \frac{4}{100}=400\cdot 4=\unit{1'600}{\kilo\metre\per\hour}
|
||||
\end{align*}
|
||||
En réalité, on a :
|
||||
\[v=\frac{2\cdot \pi\cdot r}{t}=\frac{2\cdot \pi\cdot 6'371}{24}=\unit{1668}{\kilo\metre\per\hour}\]
|
||||
Ce qui correspond à un écart (équation \ref{defecart}) de :
|
||||
\[e=\frac{1668-1600}{1668}\cdot 100=4\%\]
|
||||
Ce qui est un bon écart, compte tenu des grosses approximations faites.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{13}
|
||||
Le temps donné \(t_{tot}\) est constitué du temps \(t_{boule}\) mis par la boule pour aller frapper celle de l'adversaire et du temps \(t_{son}\) mis par le son pour revenir se faire entendre par le joueur. On a donc :
|
||||
\[t_{tot}=1,2=t_{boule}+t_{son}\]
|
||||
Or, pour avoir la vitesse de la boule sur les \unit{9}{\metre} de son parcours, il nous faut \(t_{boule}\). Pour cela, il faut donc calculer \(t_{son}\), qui est le temps mis pas le son pour parcourir \unit{9}{\metre} à la vitesse de \unit{343}{\metre\per\second} :
|
||||
\[v=\frac{d}{t}\;\Rightarrow\;t=\frac{d}{v}=\frac{9}{343}=\unit{0,026}{\second}\]
|
||||
Ainsi, le temps de parcours de la boule est :
|
||||
\[t_{boule}=1,2-t_{son}=1,2-0,026=\unit{1,174}{\second}\]
|
||||
Et la vitesse de la boule est finalement :
|
||||
\[v_{boule}=\frac{9}{1,174}=\unit{7,666}{\metre\per\second}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{14}
|
||||
Par définition de la vitesse moyenne, on a tout simplement :
|
||||
\[v=\frac{x_2-x_1}{t_2-t_1}=\frac{-5,2-3,6}{6,8-3}=\unit{-2,32}{\centi\metre\per\second}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{15}
|
||||
Le rayon du cercle parcouru par le Soleil vaut donc en mètres :
|
||||
\begin{align*}
|
||||
d_{Terre-Soleil}&=\unit{1}{UA}=\unit{1,496\cdot 10^{11}}{\metre}\\
|
||||
&=\unit{1,496\cdot 10^{8}}{\kilo\metre}
|
||||
\end{align*}
|
||||
La distance parcourue par le Soleil est donc de :
|
||||
\[d=2\cdot \pi\cdot d_{Terre-Soleil}=\unit{9,4\cdot 10^8}{\kilo\metre}\]
|
||||
Comme la période de rotation \(T\), c'est-à-dire le temps mis par la Terre pour faire un tour autour du Soleil, est d'une année, soit \unit{365}{jours}, la vitesse moyenne est :
|
||||
\[v=\frac{d}{T}=\frac{9,4\cdot 10^8}{365\cdot 24\cdot 3600}=\unit{29,8}{\kilo\metre\per\second}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{16}
|
||||
On a simplement pour le velociraptor :
|
||||
\[v=\frac{d}{t}=\frac{3,058}{0,284}=\unit{10,8}{\metre\per\second}=\unit{38,8}{\kilo\metre\per\hour}\]
|
||||
Et pour le tyranosaure :
|
||||
\[v=\frac{d}{t}=\frac{9,559}{1,199}=\unit{8}{\metre\per\second}=\unit{28,7}{\kilo\metre\per\hour}\]
|
||||
La comparaison montre que la vitesse d'un sprinter (\(\unit{10}{\metre\per\second}=\unit{36}{\metre\per\second}\) est légèrement inférieure à celle d'un velociraptor.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{17}
|
||||
Par définition de l'accélération, on a :
|
||||
\begin{align*}
|
||||
a&=\frac{v_f-v_i}{t}\;\Rightarrow\\
|
||||
t&=\frac{v_f-v_i}{a}=\frac{0-50/3,6}{-3}=\unit{4,63}{\second}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{18}
|
||||
On a simplement :
|
||||
\[a=\frac{v_f-v_i}{t}=\frac{10-0}{9,9}=\unit{1,01}{\metre\per\second\squared}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{19}
|
||||
On a successivement :
|
||||
\begin{itemize}
|
||||
\item pour le DC 10 :
|
||||
\[a=\frac{350/3,6-0}{50}=\unit{1,94}{\metre\per\second\squared}\]
|
||||
\item pour l'avion sur le porte-avions :
|
||||
\[a=\frac{0-190/3,6}{5}=\unit{-10,56}{\metre\per\second\squared}\]
|
||||
C'est une décélération et l'accélération est donc négative.
|
||||
\item pour la capsule spatiale :
|
||||
\[a=\frac{1450/3,6-0}{3}=\unit{134}{\metre\per\second\squared}\]
|
||||
\end{itemize}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{20}
|
||||
Par définition de la vitesse moyenne, on a :
|
||||
\[v=\frac{x_f-x_i}{t_f-t_i}=\frac{-5-7}{7-3}=\unit{-3}{\metre\per\second}\]
|
||||
Par définition de l'accélération moyenne, on a :
|
||||
\[a=\frac{v_f-v_i}{t_f-t_i}=\frac{-2-4}{7-3}=\unit{-1,5}{\metre\per\second\squared}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{21}
|
||||
Les graphes sont présentés à la figure \ref{graphesmru}.
|
||||
\begin{figure}[!t]
|
||||
\centering
|
||||
\caption{Graphes horaires du MRU.\label{graphesmru}}
|
||||
\includegraphics{GraphesMRU.eps}
|
||||
\end{figure}
|
||||
|
||||
La distance totale parcourue se calcule simplement :
|
||||
\[d=v\cdot t=\frac{50}{3,6}\cdot 5\cdot 60=\unit{4'167}{\metre}\]
|
||||
Sur le graphe de la vitesse en fonction du temps, la distance parcourue apparaît simplement être l'aire sous le graphe. En effet, la base \(t=5\cdot 60=\unit{300}{\second}\) multipliée par la hauteur \(v=50/3,6=\unit{13,9}{\metre\per\second}\) donne bien la distance parcourue.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{22}
|
||||
On va décrire mathématiquement le mouvement des voitures de sport et de police.
|
||||
|
||||
Les deux mouvements sont des MRU. On peut donc écrire, dans un système d'axes dont l'origine est sur la voiture de police au moment où elle entame sa poursuite :
|
||||
\begin{align*}
|
||||
v_{police}&=180\cdot t\\
|
||||
v_{sport}&=160\cdot t+1
|
||||
\end{align*}
|
||||
La condition de rencontre s'écrit alors :
|
||||
\begin{align*}
|
||||
v_{police}=v_{sport}\;\Rightarrow\,180\cdot t&=160\cdot t+1\;\Rightarrow\\
|
||||
20\cdot t&=1\\
|
||||
t&=\frac{1}{20}=\unit{0,05}{\hour}
|
||||
\end{align*}
|
||||
La voiture de police se trouve alors à une distance de l'origine du système d'axes de :
|
||||
\[x_{police}=180\cdot 0,05=\unit{9}{\kilo\metre}\]
|
||||
Alors que la voiture de sport est à la même place :
|
||||
\[x_{sport}=160\cdot 0,05+1=\unit{9}{\kilo\metre}\]
|
||||
Ce qu'il fallait montrer.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{23}
|
||||
Ici, aucune symétrie n'est présente. Comme les deux voitures ne sont pas à vitesse constante, on ne peut calculer de vitesse relative pour résoudre le problème. Il faut donc procéder en décrivant les deux mouvements par rapport au sol. Ainsi, avec \(\unit{144}{\kilo\metre\per\hour}=\unit{40}{\metre\per\second}\), on peut écrire :
|
||||
\begin{align*}
|
||||
MRU\;&\Rightarrow\;x_{chauffard}=40\cdot t\\
|
||||
MRUA\;&\Rightarrow\;x_{police}=\frac{1}{2}\cdot 5\cdot t^2
|
||||
\end{align*}
|
||||
La condition de rencontre permet alors de trouver le temps cherché :
|
||||
\begin{align*}
|
||||
x_{chauffard}&=x_{police}\;\Rightarrow\\
|
||||
40\cdot t&=\frac{1}{2}\cdot 5\cdot t^2\;\Rightarrow\\
|
||||
40&=2,5\cdot t\;\Rightarrow\;t=\unit{16}{\second}
|
||||
\end{align*}
|
||||
car la solution \(t=\unit{0}{\second}\) est à rejeter. En effet, elle correspond au début de la poursuite.
|
||||
|
||||
La position à laquelle se trouvent les deux voitures, qui est en même temps la distance qu'elles ont parcourues, est alors :
|
||||
\begin{align*}
|
||||
x_{chauffard}&=40\cdot 16=640\,m\\
|
||||
x_{police}&=\frac{1}{2}\cdot 5\cdot 16^2=\unit{640}{\metre}
|
||||
\end{align*}
|
||||
Les deux positions sont bien évidemment les mêmes.
|
||||
|
||||
Quant aux vitesse lors de la rencontre, elles sont :
|
||||
\begin{align*}
|
||||
v_{chauffard}&=40\,m/s=144\,km/h\\
|
||||
v_{police}&=5\cdot 16=\unit{80}{\metre\per\second}=\unit{288}{\kilo\metre\per\hour}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{24}
|
||||
On fait l'hypothèse d'un MRUA. La voiture est stoppée sur une distance de \unit{1,5}{\metre}. On peut donc écrire :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
0^2&=(\frac{50}{3,6})^2+2\cdot a\cdot 1,5\;\Rightarrow\\
|
||||
a&=-\frac{13,89^2}{3}=\unit{-64,3}{\metre\per\second\squared}=-6,55\cdot g
|
||||
\end{align*}
|
||||
Le temps de collision est donc de :
|
||||
\begin{align*}
|
||||
a&=\frac{v_f-v_i}{t}\;\Rightarrow\\
|
||||
t&=\frac{v_f-v_i}{a}=\frac{0-50/3,6}{-64,3}=\unit{0,216}{\second}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{25}
|
||||
Oublions la position du kangourou et calculons la distance totale d'arrêt \(d_t\). Elle se compose de la distance de réaction \(d_r\) et la distance de freinage \(d_f\) :
|
||||
\[d_t=d_r+d_f\]
|
||||
Pour la distance de réaction, on a :
|
||||
\[d_r=v\cdot t=40\cdot 0,8=\unit{32}{\metre}\]
|
||||
Pour la distance de freinage, il faut faire l'hypothèse d'un MRUA. Comme le mouvement est une décélération, c'est-à-dire un freinage, l'accélération est négative, et on a :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d_f\;\Rightarrow\\
|
||||
0^2&=40^2+2\cdot (-8)\cdot d_f\;\Rightarrow\\
|
||||
d_f&=\frac{40^2}{16}=\unit{100}{\metre}
|
||||
\end{align*}
|
||||
Ainsi, la distance totale d'arrêt vaut :
|
||||
\[d_t=32+100=\unit{132}{\metre}\]
|
||||
Comme le kangourou se trouve à \unit{70}{\metre}, son avenir serait bien sombre s'il n'avait pas cette prodigieuse capacité à rebondir.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{26}
|
||||
Un objet qui n'est soumis qu'à son poids est en chute libre, même s'il monte. Ainsi, l'accélération du plongeur, comme du dauphin, dans sa phase d'ascension vaut \unit{-9,81}{\metre\per\second\squared}. En effet, on a une décélération. Comme celle-ci est constante et que la vitesse au sommet est nulle, on peut écrire pour le plongeur :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot h\;\Rightarrow\\
|
||||
0^2&=v_o^2+2\cdot (-9,81)\cdot 0,5\;\Rightarrow\\
|
||||
v_o&=\sqrt{2\cdot 9,81\cdot 0,5}=\unit{3,132}{\metre\per\second}=\unit{11,3}{\kilo\metre\per\hour}
|
||||
\end{align*}
|
||||
Et de la même manière, pour le dauphin :
|
||||
\[v_o=\sqrt{2\cdot 9,81\cdot 6}=\unit{10,85}{\metre\per\second}=\unit{39}{\kilo\metre\per\hour}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{27}
|
||||
Le plongeur est en chute libre. Son accélération vaut donc \(g=\unit{9,81}{\metre\per\second\squared}\). On fixe un axe vertical dont l'origine se situe à \unit{10}{\metre} et qui pointe vers le bas. On peut alors écrire :
|
||||
\begin{align*}
|
||||
x&=\frac{1}{2}\cdot g\cdot t^2+v_{o\,verticale}\cdot t\;\Rightarrow\\
|
||||
10&=\frac{1}{2}\cdot 9,81\cdot t^2+v_{o\,verticale}\cdot t
|
||||
\end{align*}
|
||||
Avec dans le premier cas, comme dans le second, une vitesse initiale verticale nulle, on peut écrire :
|
||||
\begin{align*}
|
||||
10&=\frac{1}{2}\cdot 9,81\cdot t^2\;\Rightarrow\\
|
||||
t&=\sqrt{\frac{2\cdot 10}{9,81}}=\unit{1,43}{\second}
|
||||
\end{align*}
|
||||
Ce qui donne une vitesse juste avant d'entrer dans l'eau de :
|
||||
\[v=a\cdot t=9,81\cdot 1,43=\unit{14}{\metre\per\second}=\unit{50,5}{\kilo\metre\per\hour}\]
|
||||
Le premier et le second cas ne sont pas différents du point de vue du temps de chute. Néanmoins, la distance parcourue par le plongeur qui se déplace horizontalement est plus grande que celle du plongeur qui se laisse tomber. Mais sa vitesse totale (horizontale et verticale) est aussi plus grande. On peut ainsi comprendre qu'ils arriveraient en bas simultanément s'ils partaient en même temps.
|
||||
|
||||
Le troisième cas est plus complexe puisqu'il faut tenir compte d'une vitesse \(v_o=\unit{-1}{\metre\per\second}\) dans le sens contraire de l'axe :
|
||||
\begin{align*}
|
||||
10&=\frac{1}{2}\cdot 9,81\cdot t^2-1\cdot t\;\Rightarrow\\
|
||||
0&=4,905\cdot t^2-t-10
|
||||
\end{align*}
|
||||
Ce qui constitue une équation à une inconnue (\(t\)), mais du second degré. Sa solution est donnée par :
|
||||
\begin{align*}
|
||||
t&=\frac{1\pm \sqrt{1^2-4\cdot 4,905\cdot (-10)}}{2\cdot 4,905}\\
|
||||
&=\frac{1\pm 14}{9,81}=\begin{cases}\unit{1,53}{\second}\\\unit{-1,33}{\second}\end{cases}
|
||||
\end{align*}
|
||||
Évidemment, la solution négative est à rejeter et la solution positive est supérieure au temps de chute calculé précédemment puisque le plongeur parcourt une certaine distance vers le haut avant de tomber.
|
||||
|
||||
En ce qui concerne la vitesse, dans le troisième cas on peut simplement déterminer la vitesse par :
|
||||
\[v=a\cdot t=9,81\cdot 1,53-1=\unit{14}{\metre\per\second}=\unit{50,5}{\kilo\metre\per\hour}\]
|
||||
Ce qui donne la même valeur que précedemment en raison de la faible vitesse verticale initiale et de l'arrondi. Celle-ci doit cependant être comptée et doit l'être négativement (\(v_o=\unit{-1}{\metre\per\second}\)), car elle est vers le haut alors que l'axe est vers le bas.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{28}
|
||||
Cet objet est en chute libre. Son accélération vaut donc \(g\). On peut écrire pour un MRUA :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot h\;\Rightarrow\\
|
||||
v&=\sqrt{2\cdot g\cdot h}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{29}
|
||||
Par définition de l'accélération, on a :
|
||||
\[a=\frac{v-v_o}{t}=\frac{100/3,6-0}{4}=\unit{6,94}{\metre\per\second\squared}\]
|
||||
La distance parcourue est alors :
|
||||
\[d=\frac{1}{2}\cdot 6,94\cdot 4^2=\unit{55,56}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{30}
|
||||
Le temps n'est pas donné. On doit donc écrire :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
(100/3,6)^2&=(50/3,6)^2+2\cdot a\cdot 59\;\Rightarrow\\
|
||||
a&=\frac{(100/3,6)^2-(50/3,6)^2}{2\cdot 59}\\
|
||||
&=\unit{4,905}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
Ce qui représente une accélération d'un demi \(g\).
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{31}
|
||||
Le temps de chute est le même que celui d'un objet tombant verticalement. En effet, seul le poids est présent et l'objet est en chute libre. Ainsi, on peut écrire :
|
||||
\begin{align*}
|
||||
h&=\frac{1}{2}\cdot g\cdot t^2\;\Rightarrow\;5=\frac{1}{2}\cdot 9,81\cdot t^2\;\Rightarrow\\
|
||||
t&=\sqrt{\frac{2\cdot 5}{9,81}}=\unit{1,01}{\second}
|
||||
\end{align*}
|
||||
Si la vitesse horizontale est constante, on peut encore écrire pour la distance horizontale \(d\) parcourue :
|
||||
\[d=v_{horiz}\cdot t=2\cdot 1,01=\unit{2,02}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{32}
|
||||
Commençons par calculer la distance qu'elle a parcouru pendant la phase de poussée. Pour cela, on a la vitesse moyenne \(\overline{v}\) et le temps que dure le mouvement. Ainsi, on peut poser :
|
||||
\[d_{pouss\acute ee}=\overline{v}\cdot t=3\cdot 2\cdot 60=\unit{360}{\metre}\]
|
||||
A ce moment-là, au bout de deux minutes et à \unit{360}{\metre} d'altitude, la poussée cesse (le moteur s'arrête). Si on imagine un axe \(y\) orienté vers le haut et dont l'origine se situe au sol, on a donc une fusée qui se situe en \(y_o=\unit{360}{\metre}\) avec une vitesse \(v_o=\unit{4}{\metre\per\second}\) et qui n'est plus soumise qu'à son poids. Elle est donc en chute libre, même si elle monte, et son accélération dirigée vers le bas, dans le sens contraire du mouvement, est une décélération qui vaut : \(g=\unit{-9,81}{\metre\per\second\squared}\). Pendant quelques instants, elle va donc encore monter jusqu'à s'arrêter. Pour calculer la distance sur laquelle elle s'arrête, comme on ne dispose pas du temps qu'elle met pour le faire, on doit écrire :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
0^2&=4^2+2\cdot (-9,81)\cdot d\;\Rightarrow\\
|
||||
d&=\frac{16}{2\cdot 9,81}=\unit{0,8155}{\metre}=\unit{81,55}{\centi\metre}
|
||||
\end{align*}
|
||||
Ainsi la hauteur totale à laquelle est parvenue la fusée vaut :
|
||||
\[h_{tot}=360+0,8155=\unit{360,8155}{\metre}\]
|
||||
Pour déterminer le temps de vol, on dispose en premier lieu du temps de poussée qui est de deux minutes. Il faut encore calculer le temps de chute de la fusée entre le moment ou la poussée cesse et celui ou elle arrive au sol. Pour cela, il faut écrire :
|
||||
\begin{align*}
|
||||
y&=\frac{1}{2}\cdot a\cdot t^2+v_o\cdot t+y_o\;\Rightarrow\\
|
||||
y&=\frac{1}{2}\cdot (-9,81)\cdot t^2+4\cdot t+360\;\Rightarrow\\
|
||||
0&=-4,905\cdot t^2+4\cdot t+360
|
||||
\end{align*}
|
||||
car on cherche le temps mis pour arriver au sol, soit à \(y=0\). C'est une équation du second degré à une inconnue, dont la solution est :
|
||||
\begin{align*}
|
||||
t&=\frac{-4\pm \sqrt{4^2-4\cdot (-4,905)\cdot 360}}{2\cdot (-4,905)}\\
|
||||
&=\frac{-4\pm 84,14}{-9,81}=\begin{cases}\unit{-8,17}{\second}\\\unit{8,98}{\second}\end{cases}
|
||||
\end{align*}
|
||||
La solution \(t=\unit{8,98}{\second}\) est évidemment la bonne.
|
||||
|
||||
Le temps total est donc finalement de :
|
||||
\[t_{tot}=2\cdot 60+8,98=\unit{128,98}{\second}\simeq \unit{2}{\minute}\unit{9}{\second}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{33}
|
||||
Pour Aristote, au moment où l'obus est sorti du canon, plus aucune action horizontale vers l'avant ne s'exerce sur lui. Il cessera donc de se déplacer horizontalement et retombera exactement là où il a quitté le canon.
|
||||
|
||||
Pendant l'élévation et la chute de l'obus, le scooter avance à vitesse constante. La distance dont il s'est déplacé par rapport à l'obus (qui n'a selon Aristote pas bougé horizontalement) est donc de :
|
||||
\[d=v\cdot t=\frac{5}{3,6}\cdot 2=\unit{2,76}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{34}
|
||||
Rappelons que selon Aristote, dès le moment où on a lâché le couteau, plus aucune force horizontale ne s'exerce sur lui et il va tomber parfaitement verticalement. Or, le bateau avance pendant ce temps. La distance au pied du mât à laquelle tombe le couteau est donc de :
|
||||
\[d=v\cdot t=\frac{8}{3,6}\cdot 0,8=\unit{1,78}{\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{35}
|
||||
Pour connaître la vitesse de rotation de la Terre à Paris, il faut connaître la distance parcourue en \unit{24}{\hour}. Pour cela, il faut connaître sa distance \(r\) à l'axe de rotation de la Terre (voir figure \ref{eiffelmecanique}).
|
||||
\begin{figure}[!t]
|
||||
\centering
|
||||
\caption{Chute aristotélicienne de la tour Eiffel.\label{eiffelmecanique}}
|
||||
\includegraphics{EiffelMecanique.eps}
|
||||
\end{figure}
|
||||
On a d'après la figure \ref{eiffelmecanique} que :
|
||||
\[r=R\cdot \cos(\beta)=6'371\cdot \cos(48,8^{\circ})=\unit{4'197}{\kilo\metre}\]
|
||||
car :
|
||||
\begin{align*}
|
||||
R&=R_{Terre}=\unit{6'371}{\kilo\metre}\\
|
||||
\beta&=\unit{48}{\degree}\unit{48}{\arcminute}=\unit{48,8}{\degree}
|
||||
\end{align*}
|
||||
Ainsi, la vitesse de la tour Eiffel est :
|
||||
\begin{align*}
|
||||
v&=\frac{2\cdot \pi\cdot r}{t}=\frac{2\cdot \pi\cdot 4'197}{24}\\
|
||||
&=\unit{1099}{\kilo\metre\per\hour}=\unit{305}{\metre\per\second}
|
||||
\end{align*}
|
||||
et, selon Aristote, pendant la chute de la pièce, la Tour Eiffel devrait s'être déplacée de :
|
||||
\[d=v\cdot t=305\cdot 2,1=\unit{640,5}{\metre}\]
|
||||
Ce n'est évidemment pas le cas. L'inertie de la pièce l'en empêche.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{36}
|
||||
Le schéma de la situation est donné dans la figure \ref{fusee}.
|
||||
\begin{figure}[!t]
|
||||
\centering
|
||||
\caption{Une fusée.\label{fusee}}
|
||||
\includegraphics{Fusee.eps}
|
||||
\end{figure}
|
||||
La seconde équation de Newton s'écrit :
|
||||
\[\overrightarrow F+\overrightarrow P=m\cdot \overrightarrow a\]
|
||||
En projection sur l'axe et en raison de la définition du poids, on a :
|
||||
\[F-P=m\cdot a\;\Rightarrow\;F=m\cdot a+m\cdot g\]
|
||||
Or, comme l'accélération vaut :
|
||||
\[a=\frac{v_f-v_i}{t}=\frac{1000/3,6-0}{60}=\unit{4,63}{\metre\per\second\squared}\]
|
||||
on a :
|
||||
\[F=60\cdot 10^3\cdot 4,63+60\cdot 10^3\cdot 9,81=\unit{866'400}{\newton}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{37}
|
||||
Le schéma de la situation est donné par la figure \ref{remorque}.
|
||||
\begin{figure}[!t]
|
||||
\centering
|
||||
\caption{Une remorque\label{remorque}}
|
||||
\includegraphics[width=6cm]{Remorque.eps}
|
||||
\end{figure}
|
||||
|
||||
La remorque avance à vitesse constante. La première loi de Newton nous indique alors que la somme des forces qui s'exercent sur elle est nulle. On peut considérer successivement le cas des forces verticales et celui des forces horizontales.
|
||||
|
||||
Verticalement, la position de la voiture ne change pas. Elle est verticalement à l'arrêt. La réaction du sol \(\overrightarrow R\) est donc égale en grandeur, mais opposée, au poids \(\overrightarrow P\), comme présenté dans la figure \ref{remorque}.
|
||||
|
||||
Horizontalement par contre, la remorque se déplace. Mais elle le fait à vitesse constante et donc, là encore, la somme des forces horizontales qui s'exercent sur elle est nulle. La force de frottement \(\overrightarrow F_{fr}\) est égale en grandeur et opposée à la force \(\overrightarrow F\) exercée par la voiture pour tirer la remorque. Ainsi :
|
||||
\[F=F_{fr}=\unit{500}{\newton}\]
|
||||
|
||||
Si la voiture a une accélération, la situation des forces verticales ne change pas. On a toujours : \(\overrightarrow R=-\overrightarrow P\). Par contre, la sommes des forces horizontales n'est plus nulle. On a, selon l'axe de la figure \ref{remorque} :
|
||||
\begin{align*}
|
||||
F-F_{fr}&=m\cdot a\;\Rightarrow\\
|
||||
F&=m\cdot a+F_{fr}=500\cdot 5+500=\unit{3000}{\newton}
|
||||
\end{align*}
|
||||
et la somme des forces qui s'exercent sur la remorque est :
|
||||
\[F-F_{fr}=m\cdot a=500\cdot 5=\unit{2500}{\newton}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{38}
|
||||
Ce problème est identique au problème \ref{exfusee} de la fusée. Il suffit de remplacer la fusée par l'ascenseur et de considérer la force de propulsion de la fusée comme la force de traction du câble. Considérons donc la figure \ref{fusee}. Selon l'axe considéré, on a :
|
||||
\begin{align*}
|
||||
F-P&=m\cdot a\,\Rightarrow\\
|
||||
F&=m\cdot a+m\cdot g=260\cdot 4+260\cdot 9,81\\
|
||||
&=\unit{3590,6}{\newton}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{39}
|
||||
Pour que la voiture ralentisse, il faut que la force qui s'exerce sur elle soit vers l'arrière. C'est la force de frottement du sol sur les roues qui la freine. En effet, sur la glace elle ne s'exerce pas et la voiture ne peut freiner.
|
||||
|
||||
Tant la force que l'accélération sont donc dirigées vers l'arrière. La décélération se calculant par :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
a&=\frac{0^2-(50/3,6)^2}{2\cdot 40}=\unit{-2,4}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
on trouve aisément la force de frottement de la route sur les pneus qui ralentit la voiture :
|
||||
\[F_{fr}=m\cdot a=2000\cdot (-2,4)=\unit{-4'822,5}{\newton}\]
|
||||
Elle est négative, donc bien dirigée vers l'arrière.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{40}
|
||||
Ce problème illustre bien l'importance du choix du système. Comme tout se déroule horizontalement, on ne va considérer que les forces horizontales. Les verticales existent, mais n'interviennent pas.
|
||||
\begin{enumerate}
|
||||
\item Comme on cherche la force nécessaire à l'augmentation de vitesse du train dans son entier, considérons pour système le train entier. Sa masse totale est \(M=\unit{300\cdot 10^3}{\kilo\gram}\). Son accélération est :
|
||||
\[a=\frac{v_f-v_i}{t}=\frac{10/3,6-0}{60}=\unit{0,046}{\metre\per\second\squared}\]
|
||||
On peut donc écrire :
|
||||
\[F_{tot}=M\cdot a=300\cdot 10^3\cdot 0,046=\unit{13'889}{\newton}\]
|
||||
\item Cette fois-ci, on cherche la force exercée sur une partie du train : les wagons. On ne va donc considérer comme système que les wagons. Une seule force \(F\) les tire vers l'avant avec la même accélération que celle du train dans son ensemble. Leur masse est \(m=\unit{250\cdot 10^3}{\kilo\gram}\). On a donc :
|
||||
\[F=m\cdot a=250\cdot 10^3\cdot 0,046=\unit{11'500}{\newton}\]
|
||||
Valeur inférieure à celle du point précédent, car il ne faut pas tirer la locomotive.
|
||||
\item Ici, le système est évidemment la locomotive seule de masse \(m'=\unit{50\cdot 10^3}{\kilo\gram}\). On peut donc calculer l'accélération :
|
||||
\begin{align*}
|
||||
F_{tot}&=m'\cdot a\;\Rightarrow\\
|
||||
a&=\frac{F_{tot}}{m'}=\frac{13'889}{50\cdot 10^3}=\unit{0,28}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
et finalement le temps :
|
||||
\[a=\frac{v_f-v_i}{t}\;\Rightarrow\;t=\frac{10/3,6-0}{0,28}=\unit{10}{\second}\]
|
||||
\end{enumerate}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{41}
|
||||
Pendant la montée, la balle subit deux forces extérieures vers le bas : son poids \(P=m\cdot g\) et la force de frottement \(F_{fr}\). En prenant un axe vertical dirigé vers le haut, on peut donc écrire :
|
||||
\begin{align*}
|
||||
\sum F^{ext}=-m\cdot g-F_{fr}&=m\cdot a\;\Rightarrow\\
|
||||
-0,1\cdot 9,81-0,05&=0,1\cdot a\;\Rightarrow\\
|
||||
a&=\unit{-10,31}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
La balle a donc une décélération constante. Ainsi il s'agit d'un MRUA et, connaissant les vitesses initiale et finale et l'accélération, on peut écrire :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot h\;\Rightarrow\\
|
||||
0&=2^2-2\cdot 10,31\cdot h\;\Rightarrow\\
|
||||
h&=\unit{0,194}{\metre}=\unit{19,4}{\centi\metre}
|
||||
\end{align*}
|
||||
Évidemment, elle monte moins haut que s'il n'y avait pas de frottements.
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{42}
|
||||
La première phase du mouvement se déroule à vitesse constante. La distance parcourue pendant cinq minutes, c'est-à-dire \(1/12\,h\), est donc donnée par :
|
||||
\[d_{MRU}=v_o\cdot t=10'000\cdot \frac{1}{12}=\unit{833,3}{\kilo\metre}\]
|
||||
La seconde phase du mouvement se déroule à accélération constante. En effet, la force de poussée et la masse étant constantes, on peut écrire :
|
||||
\begin{align*}
|
||||
\sum F^{ext}=P&=m\cdot a\;\Rightarrow\\
|
||||
1000&=9'000\cdot a\;\Rightarrow\\
|
||||
a&=\unit{0,111}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
Connaissant l'accélération, on peut ensuite calculer la distance parcourue en MRUA grâce au temps de poussée :
|
||||
\begin{align*}
|
||||
d_{MRUA}&=\frac{1}{2}\cdot a\cdot t^2+v_o\cdot t\\
|
||||
&=\frac{1}{2}\cdot 0,111\cdot 30^2+\frac{10'000}{3,6}\cdot 30\\
|
||||
&=83'383,3\,m=\unit{83,4}{\kilo\metre}
|
||||
\end{align*}
|
||||
Au total, la distance parcourue est donc de :
|
||||
\[d_{tot}=d_{MRU}+d_{MRUA}=833,3+83,4=\unit{916,7}{\kilo\metre}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{43}
|
||||
Son accélération, supposée constante, est donnée par :
|
||||
\begin{align*}
|
||||
v^2&=v_o^2+2\cdot a\cdot d\;\Rightarrow\\
|
||||
(0,01\cdot 3\cdot 10^8)^2&=0^2+2\cdot a\cdot 30\;\Rightarrow\\
|
||||
a&=\unit{1,5\cdot 10^{11}}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
La force totale qui s'exerce sur lui est alors donnée par :
|
||||
\[F_{tot}=m\cdot a=9,1\cdot 10^{-31}\cdot 1,5\cdot 10^{11}=\unit{1,37\cdot 10^{-19}}{\newton}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{44}
|
||||
Tant que l'araignée ne bouge pas, la force exercée par le fil est égale à son poids, c'est-à-dire :
|
||||
\[F=m\cdot g=0,005\cdot 9,81=\unit{0,049}{\newton}\]
|
||||
Pendant sa chute, la seconde loi de Newton permet d'écrire, en utilisant un axe dans le sens de la chute :
|
||||
\begin{align*}
|
||||
\sum F^{ext}=m\cdot g-F&=m\cdot a\;\Rightarrow\\
|
||||
0,005\cdot 9,81-0,01&=0.005\cdot a\;\Rightarrow\\
|
||||
a&=\unit{7,81}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
Avec une vitesse initiale nulle, le temps de chute sur une hauteur de \unit{2}{\metre} est :
|
||||
\begin{align*}
|
||||
h&=\frac{1}{2}\cdot a\cdot t^2\;\Rightarrow\\
|
||||
t&=\sqrt{\frac{2\cdot h}{a}}=\sqrt{\frac{2\cdot 2}{7,81}}=\unit{0,716}{\second}
|
||||
\end{align*}
|
||||
Et la vitesse finale est alors :
|
||||
\[v=a\cdot t=7,81\cdot 0,716=\unit{5,59}{\metre\per\second}\]
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{45}
|
||||
L'ensemble se comporte comme un système en une dimension dont l'accélération se fait dans le sens de la masse la plus grande et qui est freiné par la masse la plus faible. Si on définit le sens positif de l'axe dans le sens du mouvement, on peut écrire :
|
||||
\begin{align*}
|
||||
\sum F^{ext}=m_2\cdot g-m_1\cdot g&=(m_1+m_2)\cdot a\;\Rightarrow\\
|
||||
3\cdot 9,81-2\cdot 9,81&=(2+3)\cdot a\;\Rightarrow\\
|
||||
a&=\unit{1,962}{\metre\per\second\squared}
|
||||
\end{align*}
|
||||
|
||||
\end{Solution}
|
||||
\begin{Solution}{46}
|
||||
La figure \ref{ascenseur} présente la situation.
|
||||
\begin{figure}[!t]
|
||||
|
||||
4
SolutionsOS.tex
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4
SolutionsOS.tex
Normal file
@ -0,0 +1,4 @@
|
||||
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|
||||
Un corrigé de test.
|
||||
|
||||
\end{SolutionOS}
|
||||
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Loading…
Reference in New Issue
Block a user