\babel@toc {french}{}
\contentsline {chapter}{\numberline {1}Introduction}{21}% 
\contentsline {section}{\numberline {1.1}Du temps}{21}% 
\contentsline {section}{\numberline {1.2}De l'infiniment grand \IeC {\`a} l'infiniment petit}{21}% 
\contentsline {subsection}{\numberline {1.2.1}L'Univers}{21}% 
\contentsline {subsection}{\numberline {1.2.2}Les amas de galaxies}{22}% 
\contentsline {subsection}{\numberline {1.2.3}Les galaxies}{23}% 
\contentsline {subsection}{\numberline {1.2.4}Les \IeC {\'e}toiles}{24}% 
\contentsline {subsection}{\numberline {1.2.5}Le syst\IeC {\`e}me solaire}{24}% 
\contentsline {subsection}{\numberline {1.2.6}La Terre et la Lune}{26}% 
\contentsline {subsubsection}{La Terre}{26}% 
\contentsline {subsubsection}{La Lune}{27}% 
\contentsline {subsubsection}{Les mar\IeC {\'e}es}{29}% 
\contentsline {subsection}{\numberline {1.2.7}Le monde subatomique}{32}% 
\contentsline {subsubsection}{Conclusion}{36}% 
\contentsline {chapter}{\numberline {2}La cin\IeC {\'e}matique}{37}% 
\contentsline {section}{\numberline {2.1}Introduction}{37}% 
\contentsline {section}{\numberline {2.2}Position}{37}% 
\contentsline {subsection}{\numberline {2.2.1}Dimensions}{37}% 
\contentsline {subsection}{\numberline {2.2.2}Syst\IeC {\`e}me d'axes}{37}% 
\contentsline {subsection}{\numberline {2.2.3}Position}{37}% 
\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}% 
\contentsline {subsection}{\numberline {2.4.2}Exemples}{39}% 
\contentsline {subsubsection}{Exemple 1}{39}% 
\contentsline {subsubsection}{Exemple 2}{39}% 
\contentsline {subsubsection}{Remarque~:}{39}% 
\contentsline {subsection}{\numberline {2.4.3}L'acc\IeC {\'e}l\IeC {\'e}ration instantan\IeC {\'e}e}{39}% 
\contentsline {section}{\numberline {2.5}Mouvements simples}{39}% 
\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}% 
\contentsline {subsection}{\numberline {J.3.2}Force d'inertie}{136}% 
\contentsline {section}{\numberline {J.4}Poids relatif}{137}% 
\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}% 
\contentsline {subsection}{\numberline {J.6.6}Retards et mar\IeC {\'e}es c\IeC {\^o}ti\IeC {\`e}res}{139}% 
\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}% 
\contentsline {subsection}{\numberline {K.3.1}R\IeC {\`e}gle de Betz}{144}% 
\contentsline {subsection}{\numberline {K.3.2}\IeC {\'E}oliennes}{145}% 
\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}% 
\contentsline {subsection}{\numberline {L.1.6}Relatif au MRUA}{149}% 
\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}% 
\contentsline {section}{\numberline {L.2}Solutions}{154}%