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Modifications exercices OS 2,3 et 6

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Guyot 2022-03-27 11:32:59 +02:00
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@ -986,7 +986,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan
\end{exos}
\begin{exos}
Une lampe de \SI{7}{\kilo\gram} est suspendue entre deux murs par deux câbles souples sans masse qui font un angle de \SI{20}{\degree} et \SI{30}{\degree}.
Une lampe de \SI{7}{\kilo\gram} est suspendue entre deux murs par deux câbles souples sans masse qui font un angle de \SI{20}{\degree} et \SI{30}{\degree} par rapport à l'horizontale.
Quelles sont les tensions exercées par chaque câble sur les murs ? Réponses~: \SI{77,63}{\newton} et \SI{84,24}{\newton}.
\begin{solos}
@ -1031,7 +1031,7 @@ Attention, cette ``procédure\index{procédure}'', qui présente beaucoup d'avan
\end{exos}
\begin{exos}
Soient deux masses, la première, de valeur M=\SI{5}{\kilo\gram}, posée sur un plan horizontal sans frottements et la seconde, m=\SI{2}{\kilo\gram}, reliée à la première par une corde sans masse et pendant dans le vide, comme présenté sur la figure \ref{pendante}.
Soient deux masses, la première, de valeur M=\SI{3}{\kilo\gram}, posée sur un plan horizontal sans frottements et la seconde, m=\SI{2}{\kilo\gram}, reliée à la première par une corde sans masse et pendant dans le vide, comme présenté sur la figure \ref{pendante}.
\begin{figure}[ht]
\caption[Masse pendante]{La masse pendante}\label{pendante}
\smallskip
@ -1203,7 +1203,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco
\end{exos}
\begin{exos}
Un parachutiste de \SI{70}{\kilo\gram} saute d'un avion et ouvre immédiatement son parachute. Sa vitesse augmente d'abord progressivement, puis se stabilise à une valeur à déterminer par le fait qu'en deçà de \SI{2}{\metre}, une personne normale peut atterrir sans risque d'un saut à vitesse initiale nulle.
Un parachutiste de \SI{70}{\kilo\gram} saute d'un avion et ouvre immédiatement son parachute. Sa vitesse augmente d'abord progressivement, puis se stabilise à une valeur qui devient rapidement constante. Celle-ci doit être assez faible pour qu'arrivé au sol, le parachutiste puisse se réceptionner sans dommages. Or, on sait que, lâchée en deçà de \SI{2}{\metre} au-dessus du sol, une personne normale peut atterrir sans risques. Au-dessus de cette hauteur, ce n'est pas possible.
Calculez la vitesse de descente du parachutiste pour qu'il puisse atterrir en toute sécurité. Puis déterminez la tension exercée par le parachute sur le parachutiste pendant sa descente. Réponses~: \SI{6,26}{\metre\per\second} et \SI{686,7}{\newton}.
\begin{solos}

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\contentsline {subsection}{\numberline {2.2.4}D\IeC {\'e}placement}{38}%
\contentsline {subsection}{\numberline {2.2.5}Distance parcourue}{38}%
\contentsline {section}{\numberline {2.3}Vitesse}{38}%
\contentsline {subsection}{\numberline {2.3.1}Vitesse moyenne}{38}%
\contentsline {subsection}{\numberline {2.3.2}Exemples}{38}%
\contentsline {subsubsection}{Exemple 1}{38}%
\contentsline {subsubsection}{Exemple 2}{38}%
\contentsline {subsection}{\numberline {2.3.3}Vitesse instantan\IeC {\'e}e}{38}%
\contentsline {section}{\numberline {2.4}Acc\IeC {\'e}l\IeC {\'e}ration}{39}%
\contentsline {subsection}{\numberline {2.4.1}Acc\IeC {\'e}l\IeC {\'e}ration moyenne}{39}%
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\contentsline {subsubsection}{Exemple 1}{39}%
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\contentsline {subsection}{\numberline {2.4.3}L'acc\IeC {\'e}l\IeC {\'e}ration instantan\IeC {\'e}e}{39}%
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\contentsline {subsection}{\numberline {2.5.1}Le mouvement rectiligne uniforme}{39}%
\contentsline {subsubsection}{D\IeC {\'e}finition}{39}%
\contentsline {subsubsection}{Propri\IeC {\'e}t\IeC {\'e}s}{39}%
\contentsline {subsubsection}{Un exemple~: Apollo en route vers la Lune}{40}%
\contentsline {subsubsection}{Autre exemple~: le d\IeC {\'e}placement d'Androm\IeC {\`e}de}{41}%
\contentsline {subsection}{\numberline {2.5.2}Mouvement rectiligne uniform\IeC {\'e}ment acc\IeC {\'e}l\IeC {\'e}r\IeC {\'e} (MRUA)}{41}%
\contentsline {subsubsection}{D\IeC {\'e}finition}{41}%
\contentsline {subsubsection}{Propri\IeC {\'e}t\IeC {\'e}s}{41}%
\contentsline {subsection}{\numberline {2.5.3}La chute libre}{42}%
\contentsline {paragraph}{D\IeC {\'e}finition}{42}%
\contentsline {paragraph}{Propri\IeC {\'e}t\IeC {\'e}s}{42}%
\contentsline {paragraph}{Exp\IeC {\'e}rience}{42}%
\contentsline {paragraph}{Calculs}{42}%
\contentsline {paragraph}{Analyse des r\IeC {\'e}sultats}{43}%
\contentsline {paragraph}{Conclusions}{44}%
\contentsline {subsection}{\numberline {2.5.4}Balistique}{44}%
\contentsline {paragraph}{D\IeC {\'e}finition}{44}%
\contentsline {paragraph}{Propri\IeC {\'e}t\IeC {\'e}s}{44}%
\contentsline {paragraph}{\IeC {\'E}quations}{44}%
\contentsline {paragraph}{Premier exemple}{45}%
\contentsline {paragraph}{Second exemple}{45}%
\contentsline {subsection}{\numberline {2.5.5}La chute libre ... de la Lune}{45}%
\contentsline {subsection}{\numberline {2.5.6}Mouvement circulaire uniforme (MCU)}{47}%
\contentsline {subsubsection}{Relation importante}{47}%
\contentsline {subsection}{\numberline {2.5.7}Lois de Kepler}{48}%
\contentsline {chapter}{\numberline {3}La m\IeC {\'e}canique}{51}%
\contentsline {section}{\numberline {3.1}La \FB@og m\IeC {\'e}canique\fg {} d'Aristote}{51}%
\contentsline {subsection}{\numberline {3.1.1}Introduction}{51}%
\contentsline {subsection}{\numberline {3.1.2}Platon}{51}%
\contentsline {subsection}{\numberline {3.1.3}Aristote}{52}%
\contentsline {subsubsection}{Cin\IeC {\'e}matique}{52}%
\contentsline {subsubsection}{Dynamique}{52}%
\contentsline {section}{\numberline {3.2}M\IeC {\'e}canique de Newton}{55}%
\contentsline {subsection}{\numberline {3.2.1}Introduction}{55}%
\contentsline {subsection}{\numberline {3.2.2}M\IeC {\'e}canique}{55}%
\contentsline {subsubsection}{Les trois lois de Newton}{55}%
\contentsline {subsubsection}{Force ext\IeC {\'e}rieure}{56}%
\contentsline {subsubsection}{Exemples}{57}%
\contentsline {subsection}{\numberline {3.2.3}Types de forces}{57}%
\contentsline {subsubsection}{Loi de la gravitation universelle}{58}%
\contentsline {subsubsection}{Le poids}{58}%
\contentsline {paragraph}{Exemple}{59}%
\contentsline {subsubsection}{Masse et poids}{60}%
\contentsline {subsubsection}{Poids apparent}{60}%
\contentsline {subsubsection}{Gravitation et MCU}{62}%
\contentsline {subsubsection}{Troisi\IeC {\`e}me loi de Kepler}{63}%
\contentsline {subsubsection}{Les mar\IeC {\'e}es}{65}%
\contentsline {subsubsection}{Le frottement}{69}%
\contentsline {paragraph}{Exemple}{70}%
\contentsline {subsubsection}{La force d'un ressort}{70}%
\contentsline {paragraph}{Exemple}{70}%
\contentsline {chapter}{\numberline {4}L'\IeC {\'e}nergie}{73}%
\contentsline {section}{\numberline {4.1}Introduction}{73}%
\contentsline {section}{\numberline {4.2}Travail}{73}%
\contentsline {section}{\numberline {4.3}Puissance}{74}%
\contentsline {section}{\numberline {4.4}\IeC {\'E}nergie potentielle}{74}%
\contentsline {section}{\numberline {4.5}\IeC {\'E}nergie cin\IeC {\'e}tique}{75}%
\contentsline {section}{\numberline {4.6}Th\IeC {\'e}or\IeC {\`e}me de l'\IeC {\'e}nergie cin\IeC {\'e}tique}{75}%
\contentsline {section}{\numberline {4.7}Conservation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{75}%
\contentsline {section}{\numberline {4.8}Variation de l'\IeC {\'e}nergie m\IeC {\'e}canique}{77}%
\contentsline {section}{\numberline {4.9}\IeC {\'E}nergies renouvelables}{77}%
\contentsline {subsection}{\numberline {4.9.1}\IeC {\'E}nergie hydraulique}{77}%
\contentsline {subsubsection}{Exemple}{78}%
\contentsline {subsubsection}{Types de turbines}{79}%
\contentsline {subsubsection}{Alternateur}{79}%
\contentsline {subsubsection}{Probl\IeC {\`e}mes rencontr\IeC {\'e}s}{80}%
\contentsline {subsection}{\numberline {4.9.2}\IeC {\'E}nergie \IeC {\'e}olienne}{80}%
\contentsline {subsection}{\numberline {4.9.3}\IeC {\'E}nergie solaire}{81}%
\contentsline {subsubsection}{\IeC {\'E}nergie solaire thermique}{81}%
\contentsline {subsubsection}{\IeC {\'E}nergie solaire \IeC {\'e}lectrique}{83}%
\contentsline {subsection}{\numberline {4.9.4}\IeC {\'E}nergie g\IeC {\'e}othermique}{84}%
\contentsline {section}{\numberline {4.10}\IeC {\'E}nergies non renouvelables}{84}%
\contentsline {subsection}{\numberline {4.10.1}\IeC {\'E}nergie nucl\IeC {\'e}aire}{85}%
\contentsline {subsubsection}{Fission}{85}%
\contentsline {paragraph}{D\IeC {\'e}chets radioactifs}{86}%
\contentsline {paragraph}{Accidents nucl\IeC {\'e}aires}{87}%
\contentsline {subsubsection}{Fusion}{87}%
\contentsline {subsection}{\numberline {4.10.2}\IeC {\'E}nergie de combustion~: p\IeC {\'e}trole et gaz}{87}%
\contentsline {chapter}{\numberline {5}Thermodynamique}{91}%
\contentsline {section}{\numberline {5.1}Introduction}{91}%
\contentsline {section}{\numberline {5.2}Temp\IeC {\'e}rature}{91}%
\contentsline {subsection}{\numberline {5.2.1}Celsius}{91}%
\contentsline {subsection}{\numberline {5.2.2}Fahrenheit}{91}%
\contentsline {subsection}{\numberline {5.2.3}Kelvin}{92}%
\contentsline {subsection}{\numberline {5.2.4}Agitation mol\IeC {\'e}culaire}{92}%
\contentsline {section}{\numberline {5.3}Dilatation}{92}%
\contentsline {section}{\numberline {5.4}Chaleur}{93}%
\contentsline {subsection}{\numberline {5.4.1}Chaleur sp\IeC {\'e}cifique}{93}%
\contentsline {subsection}{\numberline {5.4.2}Chaleur latente}{93}%
\contentsline {section}{\numberline {5.5}\IeC {\'E}nergie thermique}{94}%
\contentsline {subsection}{\numberline {5.5.1}Premier principe}{95}%
\contentsline {chapter}{\numberline {A}Syst\IeC {\`e}mes d'unit\IeC {\'e}s}{97}%
\contentsline {section}{\numberline {A.1}Introduction}{97}%
\contentsline {section}{\numberline {A.2}Op\IeC {\'e}rateur d'unit\IeC {\'e}s}{97}%
\contentsline {section}{\numberline {A.3}Analyse dimensionnelle}{98}%
\contentsline {section}{\numberline {A.4}Les unit\IeC {\'e}s du Syst\IeC {\`e}me International}{99}%
\contentsline {subsection}{\numberline {A.4.1}Exemple}{99}%
\contentsline {section}{\numberline {A.5}Conversions}{99}%
\contentsline {section}{\numberline {A.6}Sous-multiples}{100}%
\contentsline {section}{\numberline {A.7}Notation scientifique}{100}%
\contentsline {section}{\numberline {A.8}R\IeC {\`e}gles de calcul}{101}%
\contentsline {chapter}{\numberline {B}Deux syst\IeC {\`e}mes de coordonn\IeC {\'e}es}{103}%
\contentsline {section}{\numberline {B.1}Le syst\IeC {\`e}me de coordonn\IeC {\'e}es circulaires}{103}%
\contentsline {subsection}{\numberline {B.1.1}Introduction}{103}%
\contentsline {subsection}{\numberline {B.1.2}Description}{103}%
\contentsline {section}{\numberline {B.2}Coordonn\IeC {\'e}es sph\IeC {\'e}riques}{103}%
\contentsline {subsection}{\numberline {B.2.1}Introduction}{103}%
\contentsline {subsection}{\numberline {B.2.2}Description}{103}%
\contentsline {subsection}{\numberline {B.2.3}Latitude et longitude}{104}%
\contentsline {chapter}{\numberline {C}Mesures de distances}{105}%
\contentsline {section}{\numberline {C.1}La taille de la Terre}{105}%
\contentsline {subsection}{\numberline {C.1.1}Le principe}{105}%
\contentsline {subsection}{\numberline {C.1.2}Techniquement}{106}%
\contentsline {section}{\numberline {C.2}La taille de la Lune}{107}%
\contentsline {section}{\numberline {C.3}La distance Terre-Lune}{107}%
\contentsline {section}{\numberline {C.4}La distance Terre-Soleil}{108}%
\contentsline {section}{\numberline {C.5}La distance des \IeC {\'e}toiles}{110}%
\contentsline {chapter}{\numberline {D}Travaux pratiques}{111}%
\contentsline {section}{\numberline {D.1}Le rapport de laboratoire}{111}%
\contentsline {subsection}{\numberline {D.1.1}Plan d'un rapport de travail pratique}{112}%
\contentsline {subsubsection}{Pr\IeC {\'e}liminaires}{112}%
\contentsline {subsubsection}{R\IeC {\'e}sum\IeC {\'e}}{112}%
\contentsline {subsubsection}{But}{112}%
\contentsline {subsubsection}{Th\IeC {\'e}orie}{112}%
\contentsline {subsubsection}{Description de l'exp\IeC {\'e}rience}{112}%
\contentsline {subsubsection}{R\IeC {\'e}sultats}{112}%
\contentsline {subsubsection}{Discussion}{114}%
\contentsline {subsubsection}{Conclusion}{114}%
\contentsline {subsubsection}{Annexes}{114}%
\contentsline {section}{\numberline {D.2}La n\IeC {\'e}buleuse du Crabe}{115}%
\contentsline {subsection}{\numberline {D.2.1}Introduction}{115}%
\contentsline {subsection}{\numberline {D.2.2}But du travail pratique}{115}%
\contentsline {subsection}{\numberline {D.2.3}Dispositif exp\IeC {\'e}rimental}{115}%
\contentsline {subsection}{\numberline {D.2.4}Mesures}{115}%
\contentsline {subsection}{\numberline {D.2.5}R\IeC {\'e}sultats}{115}%
\contentsline {subsection}{\numberline {D.2.6}Analyse}{115}%
\contentsline {section}{\numberline {D.3}Le pendule simple}{115}%
\contentsline {subsection}{\numberline {D.3.1}Les mesures}{115}%
\contentsline {subsection}{\numberline {D.3.2}Organisation des donn\IeC {\'e}es et graphiques}{117}%
\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}{118}%
\contentsline {subsection}{\numberline {D.5.3}Les mesures}{118}%
\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}{135}%
\contentsline {section}{\numberline {J.1}Introduction}{135}%
\contentsline {section}{\numberline {J.2}Centre de gravit\IeC {\'e}}{135}%
\contentsline {section}{\numberline {J.3}Force d'inertie}{136}%
\contentsline {subsection}{\numberline {J.3.1}Vitesse angulaire}{136}%
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\contentsline {section}{\numberline {J.5}Analyse diff\IeC {\'e}rentielle}{137}%
\contentsline {section}{\numberline {J.6}Autres rythmes}{137}%
\contentsline {subsection}{\numberline {J.6.1}D\IeC {\'e}calages}{138}%
\contentsline {subsection}{\numberline {J.6.2}Mar\IeC {\'e}es de vives et mortes eaux}{138}%
\contentsline {subsection}{\numberline {J.6.3}Mar\IeC {\'e}es d'\IeC {\'e}quinoxes}{138}%
\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}{139}%
\contentsline {subsection}{\numberline {J.6.5}Mar\IeC {\'e}es de d\IeC {\'e}clinaison}{139}%
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\contentsline {section}{\numberline {J.7}Limite de Roche}{139}%
\contentsline {subsection}{\numberline {J.7.1}Mod\IeC {\`e}le simplifi\IeC {\'e}}{140}%
\contentsline {subsection}{\numberline {J.7.2}Exemples}{141}%
\contentsline {chapter}{\numberline {K}\IeC {\'E}nergies}{143}%
\contentsline {section}{\numberline {K.1}Introduction}{143}%
\contentsline {section}{\numberline {K.2}\IeC {\'E}nergie hydraulique}{143}%
\contentsline {section}{\numberline {K.3}\IeC {\'E}nergie \IeC {\'e}olienne}{144}%
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\contentsline {subsubsection}{\IeC {\'E}olienne de Collonges-Dor\IeC {\'e}naz}{145}%
\contentsline {subsubsection}{\IeC {\'E}oliennes du Mont Soleil (Jura suisse)}{145}%
\contentsline {section}{\numberline {K.4}G\IeC {\'e}othermie}{145}%
\contentsline {section}{\numberline {K.5}\IeC {\'E}nergie de combustion des d\IeC {\'e}chets}{146}%
\contentsline {chapter}{\numberline {L}Exercices}{147}%
\contentsline {section}{\numberline {L.1}Probl\IeC {\`e}mes}{147}%
\contentsline {subsection}{\numberline {L.1.1}Relatifs \IeC {\`a} la conversion d'unit\IeC {\'e}s et \IeC {\`a} la notation scientifique}{147}%
\contentsline {subsection}{\numberline {L.1.2}Relatifs aux notions de d\IeC {\'e}placement, position et distance parcourue}{147}%
\contentsline {subsection}{\numberline {L.1.3}Relatifs \IeC {\`a} la notion de vitesse}{148}%
\contentsline {subsection}{\numberline {L.1.4}Relatif \IeC {\`a} la notion d'acc\IeC {\'e}l\IeC {\'e}ration}{148}%
\contentsline {subsection}{\numberline {L.1.5}Relatif au MRU}{149}%
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\contentsline {subsection}{\numberline {L.1.7}Relatifs \IeC {\`a} la physique aristot\IeC {\'e}licienne}{150}%
\contentsline {subsection}{\numberline {L.1.8}Relatifs \IeC {\`a} la physique newtonienne}{150}%
\contentsline {subsection}{\numberline {L.1.9}Relatifs aux forces}{151}%
\contentsline {subsection}{\numberline {L.1.10}Relatifs \IeC {\`a} l'\IeC {\'e}nergie}{152}%
\contentsline {subsection}{\numberline {L.1.11}Relatifs \IeC {\`a} la conservation de l'\IeC {\'e}nergie}{152}%
\contentsline {subsection}{\numberline {L.1.12}Relatifs \IeC {\`a} l'\IeC {\'e}nergie hydraulique}{153}%
\contentsline {subsection}{\numberline {L.1.13}Relatifs \IeC {\`a} l'\IeC {\'e}nergie \IeC {\'e}olienne}{153}%
\contentsline {subsection}{\numberline {L.1.14}Relatifs \IeC {\`a} l'\IeC {\'e}nergie solaire}{153}%
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