From e3289441a5182aa1ec40b1e11663f051b9a4d86c Mon Sep 17 00:00:00 2001 From: guyotv Date: Wed, 24 Aug 2022 14:25:11 +0200 Subject: [PATCH] =?UTF-8?q?Correction=20d'un=20exo=20et=20corrig=C3=A9=20d?= =?UTF-8?q?'un=20autre=20(satellite=20non=20g=C3=A9ostationnaire)?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Annexe-Exercices/Annexe-Exercices.tex | 18 +++++++++++----- Annexe-Exercices/Annexe-Exercices.tex.bak | 25 +++++++++++++++------- CoursMecaniqueOS.pdf | Bin 12815398 -> 12817205 bytes CoursMecaniqueOSDF.pdf | Bin 12815398 -> 12817205 bytes SolutionsOS.tex | 14 +++++++++--- 5 files changed, 41 insertions(+), 16 deletions(-) diff --git a/Annexe-Exercices/Annexe-Exercices.tex b/Annexe-Exercices/Annexe-Exercices.tex index a7d84c0..8793650 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex +++ b/Annexe-Exercices/Annexe-Exercices.tex @@ -1857,9 +1857,16 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{exos} \begin{exos} - Un satellite en orbite basse (non géostationnaire) se trouve à une altitude de \SI{5}{\kilo\metre} au-dessus de la surface de la Terre. À quelle vitesse par rapport au sol se déplace-t-il ? + Un satellite en orbite basse (non géostationnaire) se trouve à une altitude de \SI{5}{\kilo\metre} au-dessus du plus haut sommet terrestre (Everest~: \SI{8}{\kilo\metre}). À quelle vitesse par rapport au sol se déplace-t-il ? On suppose le mouvement circulaire uniforme. Réponse~: \SI{28433}{\kilo\metre\per\hour}. \begin{solos} - Un autre corrigé de test. + La seconde loi de Newton est constituée de la force de gravitation qui maintient le satellite en rotation et d'une accélération considérée comme issue d'un mouvement circulaire uniforme de rayon~: + \[r=R_{Terre}+r_{Everest}+r_{sat.}=6371+8+5=\SI{6384}{\kilo\metre}\] + Ainsi, elle s'écrit~: + \begin{align*} + F&=G\cdot \frac{m_{sat.}\cdot M_{Terre}}{r^2}=m_{sat.}\cdot\frac{v^2}{r}=m\cdot a\\ + &\rightarrow 6,67\cdot 10^{-11}\cdot\frac{5,97\cdot 10^{24}}{6384\cdot 10^3}=v^2\\ + &\rightarrow v=\SI{7898}{\metre\per\second}=\SI{28433}{\kilo\metre\per\hour} + \end{align*} \end{solos} \end{exos} @@ -1991,7 +1998,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \item Quelle est l'énergie perdue par le bob pendant les descentes et d'où vient-elle ? \item Estimez la force de frottement qui s'exerce sur le bob si on imagine que la vitesse finale du bob est de \SI{200}{\kilo\metre\per\hour}. \end{enumerate} - Réponses~: \SI{2452500}{\joule} et \SI{106,3}{\newton} + Réponses~: \SI{2452500}{\joule} et \SI{139,6}{\newton} \begin{solos} Le travail de l'équipe pour remonter le bobsleigh du bas de la piste à son point de départ sert à augmenter l'énergie potentielle du bob. On néglige les frottement exercés sur le véhicule de transport. Ainsi, on a~: \begin{align*} @@ -2013,12 +2020,13 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco qui est bien supérieure à celle fournie pour augmenter la vitesse. \medskip - La différence d'énergie potentielle et cinétique, soit 1'117'200-925'926 = \SI{191274}{\joule}, est perdue dans le frottement. + La différence d'énergie potentielle et cinétique, soit d'énergie mécanique~:\[\Delta E_{mec}=1'117'200-925'926 = \SI{251274}{\joule}\] + est perdue dans le frottement. Comme la distance sur laquelle il s'exerce est de \SI{1800}{\metre}, on peut calculer la force de frottement moyenne par~: \begin{align*} A_{fr}&=F_fr\cdot d\;\Rightarrow\\ - F_{fr}&=\frac{A_{fr}}{d}=\frac{191'274}{1'800}=\SI{106,3}{\newton} + F_{fr}&=\frac{A_{fr}}{d}=\frac{251'274}{1'800}=\SI{139,6}{\newton} \end{align*} C'est évidemment une estimation. \end{solos} diff --git a/Annexe-Exercices/Annexe-Exercices.tex.bak b/Annexe-Exercices/Annexe-Exercices.tex.bak index f2a3d0b..8793650 100644 --- a/Annexe-Exercices/Annexe-Exercices.tex.bak +++ b/Annexe-Exercices/Annexe-Exercices.tex.bak @@ -1857,9 +1857,16 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \end{exos} \begin{exos} - Un satellite en orbite basse (non géostationnaire) se trouve à une altitude de \SI{5}{\kilo\metre} au-dessus de la surface de la Terre. À quelle vitesse par rapport au sol se déplace-t-il ? + Un satellite en orbite basse (non géostationnaire) se trouve à une altitude de \SI{5}{\kilo\metre} au-dessus du plus haut sommet terrestre (Everest~: \SI{8}{\kilo\metre}). À quelle vitesse par rapport au sol se déplace-t-il ? On suppose le mouvement circulaire uniforme. Réponse~: \SI{28433}{\kilo\metre\per\hour}. \begin{solos} - Un autre corrigé de test. + La seconde loi de Newton est constituée de la force de gravitation qui maintient le satellite en rotation et d'une accélération considérée comme issue d'un mouvement circulaire uniforme de rayon~: + \[r=R_{Terre}+r_{Everest}+r_{sat.}=6371+8+5=\SI{6384}{\kilo\metre}\] + Ainsi, elle s'écrit~: + \begin{align*} + F&=G\cdot \frac{m_{sat.}\cdot M_{Terre}}{r^2}=m_{sat.}\cdot\frac{v^2}{r}=m\cdot a\\ + &\rightarrow 6,67\cdot 10^{-11}\cdot\frac{5,97\cdot 10^{24}}{6384\cdot 10^3}=v^2\\ + &\rightarrow v=\SI{7898}{\metre\per\second}=\SI{28433}{\kilo\metre\per\hour} + \end{align*} \end{solos} \end{exos} @@ -1991,7 +1998,7 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco \item Quelle est l'énergie perdue par le bob pendant les descentes et d'où vient-elle ? \item Estimez la force de frottement qui s'exerce sur le bob si on imagine que la vitesse finale du bob est de \SI{200}{\kilo\metre\per\hour}. \end{enumerate} - Réponses~: \SI{2452500}{\joule} et \SI{106,3}{\newton} + Réponses~: \SI{2452500}{\joule} et \SI{139,6}{\newton} \begin{solos} Le travail de l'équipe pour remonter le bobsleigh du bas de la piste à son point de départ sert à augmenter l'énergie potentielle du bob. On néglige les frottement exercés sur le véhicule de transport. Ainsi, on a~: \begin{align*} @@ -2013,12 +2020,13 @@ On lâche la première à vitesse initiale nulle. Calculez la vitesse de la seco qui est bien supérieure à celle fournie pour augmenter la vitesse. \medskip - La différence d'énergie potentielle et cinétique, soit 1'117'200-925'926 = \SI{191274}{\joule}, est perdue dans le frottement. + La différence d'énergie potentielle et cinétique, soit d'énergie mécanique~:\[\Delta E_{mec}=1'117'200-925'926 = \SI{251274}{\joule}\] + est perdue dans le frottement. Comme la distance sur laquelle il s'exerce est de \SI{1800}{\metre}, on peut calculer la force de frottement moyenne par~: \begin{align*} A_{fr}&=F_fr\cdot d\;\Rightarrow\\ - F_{fr}&=\frac{A_{fr}}{d}=\frac{191'274}{1'800}=\SI{106,3}{\newton} + F_{fr}&=\frac{A_{fr}}{d}=\frac{251'274}{1'800}=\SI{139,6}{\newton} \end{align*} C'est évidemment une estimation. \end{solos} @@ -2484,14 +2492,15 @@ Les valeurs des c\oe fficients de dilatation thermique sont celles du tableau \r Le bilan thermique s'écrit~: \begin{align*} m_{eau}\cdot c_{eau}\cdot (\theta_{eq.}-20)+m_?\cdot c_?\cdot (\theta_{eq.}-80)&=0\\ - 0,2\cdot 4180\cdot (21,55-20)&\\ - +0,05\cdot c_?\cdot (21,55-80)&=0\\ + 0,2\cdot 4180\cdot (21,55-20)&+\\ + 0,05\cdot c_?\cdot (21,55-80)&=0\\ 1295,8-2,92\cdot c_?&=0 \end{align*} Ainsi, la chaleur massique vaut~: \[c_?=\frac{1295,8}{2,92}=\SI{444}{\joule\celsius\per\kilo\gram}\] + En consultant le tableau \ref{tabchaleurmassique}, page \pageref{tabchaleurmassique}, on constate qu'il s'agit de fer. \end{solos} - En consultant le tableau \ref{chaleurmassique}, page \pageref{chaleurmassique}, on constate qu'il s'agit de fer. + \end{exos} } diff --git a/CoursMecaniqueOS.pdf b/CoursMecaniqueOS.pdf index 10a0829596da1c07c5125d402db380612889521d..88d7e72950bf099e124f30d8bf66c9210dc6290c 100644 GIT binary patch delta 68634 zcmWjIQ*0)T5(ePfw(WLn+qP}nZohhK+qP}nTidpc^Ph_+b34i8&15pA>9G(krLhq8 za=_q+hg`dBNy@-A_x5wAv%XY=0AU>VwyqZ@%m5`OB zlkqB?-sc6D!wD1Ly{EC5K!g{MhkQ`f=j&e88f{(vY{j|H%ZXT4@uwuOyO`(97ek(b zo(D!N^FcbVw`oBzy;nBnFEID}`hkK7{=BK~jFKOJ8sHI2v7tE6-Yr&pvlBRXD%iT5 zcIe#AVUSkzCM`KB0|XbCEw}~bZwmU|MejM)YLr@W-59K5mlKkg{`T**wJ;Z*RcD zjMgJbMIyQ07=s_JS*yS>MMw|M!wU4AdFcdcEZRO%NlhQ8+j zbqk~idoyUFP>^L?rpNm~i&X%=UVtA;lJdaip(~$)d=%qnQ9FOe#3vG(E}s@HMcL6k z=^NL~!P};d6$N||p}_EGi2KLe?6Z`-bR^M3y!Xn>+wOY=V(kc7%gg?oeeVPGR$U5P z65r2(ww&^`GU0E;Z)S}0d*C_`;42MqJm;un^@gZ%a%(hhR%-rC?Ay}FU)Qhc_jUYi zmD`+`!rA**pd>ex>4_Qp5>+$o#eC)0{g*@IcBk*-?V>7}y(!bS_)bcJARMoB9W;iG 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