From 4ecc08f81d3b4c0ad3669fe1427e6251d91e2fa3 Mon Sep 17 00:00:00 2001 From: Gregory Trullemans Date: Mon, 12 Aug 2024 17:52:27 +0200 Subject: [PATCH] Corrections et optimisations --- Img/sustentation_2_without.png | Bin 22105 -> 21548 bytes Img/sustentation_2_without.psd | Bin 138214 -> 114906 bytes Syllabus/bases_mecanique.tex | 11 ++++++----- Syllabus/chap_corps.tex | 2 +- Syllabus/chap_dynamique.tex | 16 +++++++++------- Syllabus/chap_referentiel_force.tex | 18 +++++++++--------- Syllabus/chap_statique.tex | 28 ++++++++++++++-------------- Syllabus/layout_syllabus_ffg | 2 +- 8 files changed, 40 insertions(+), 37 deletions(-) diff --git a/Img/sustentation_2_without.png b/Img/sustentation_2_without.png index e09015149ddf7f7a0a1a661a3dd10ce0870e60e5..fe9db44e36daab83cf88843058a587efcfb11885 100644 GIT binary patch literal 21548 zcmdRVg;y3|*zJq7l$4ZoD2RY`BNBolDj|rZbcb{+-6dU8f>I*V4N5oCE!`zu-}C;y zd)K=E!euQM!_1kPGv}PA_TDGxrQ#F3o0K;Z2n3$IoU{@GaibT3K(WWdfHOR*4Vmx< 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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Paramètre du document fichier PDF généré % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\def\formationType{MSAn} % Type de formation : MSIn, MSam, ... -\def\discipline{GAF-GAM-TRA} % Discipline : GAF, GAM, Tr, Tu, ... -\def\disciplineAcronym{GAF - GAM - TRA} % Acronyme de la discipline -\def\moduleTitle{Bases de la mécanique} % Titre du module de la formation +\def\formationType{Initiateur} % Type de formation : MSIn, MSam, ... +\def\discipline{Trampoline} % Discipline : GAF, GAM, Tr, Tu, ... +\def\disciplineAcronym{TRA} % Acronyme de la discipline +\def\moduleTitle{Bases de la mécanique} % Titre du module de la formation \def\writer{Trullemans Gregory} % auteur (actuel) du syllabus % mots clés séparé par une virgule @@ -56,7 +56,8 @@ \begin{itemize} \item Version 2021 : Trullemans Gregory, juillet 2021 \item Version 2022 : Trullemans Gregory, juillet 2022 - \item Version 2023 : Trullemans Gregory, le \today + \item Version 2023 : Trullemans Gregory, juillet 2023 + \item Version 2024 : Trullemans Gregory, le \today \end{itemize} \end{document} \ No newline at end of file diff --git a/Syllabus/chap_corps.tex b/Syllabus/chap_corps.tex index fa838cc..aaf510e 100644 --- a/Syllabus/chap_corps.tex +++ b/Syllabus/chap_corps.tex @@ -161,7 +161,7 @@ Quel(s) est/sont le(s) "rôle(s)" du centre de gravité dans le mouvement ? (plu \subsection*{Question 6} \vspace{-0.2cm} -Qu'est ce qu'un corps isolé ? (plusieurs réponses possibles) +Qu'est-ce qu'un corps isolé ? (plusieurs réponses possibles) \begin{enumerate} \item Un corps qui ne touche rien. \item Un corps seul dans un référentiel. diff --git a/Syllabus/chap_dynamique.tex b/Syllabus/chap_dynamique.tex index 443d1c8..c39b724 100644 --- a/Syllabus/chap_dynamique.tex +++ b/Syllabus/chap_dynamique.tex @@ -107,8 +107,8 @@ Où : Où : \begin{itemize} - \item $\vec{F_t}$ : force tengeantielle ($N.m$) - \item $\vec{a_t}$ : accélération tengeantielle (en $m.s^2$) + \item $\vec{F_t}$ : force tengentielle ($N.m$) + \item $\vec{a_t}$ : accélération tengentielle (en $m.s^2$) \end{itemize} \[ ~~\rightarrow~~ \vec{\mathcal{L}} = m \times \vec{a_t} \times r \] @@ -213,7 +213,9 @@ Pour un corps isolé ou pseudo-isolé, la quantité de mouvement reste constant \[ \mybox{ {p'} = \vec{F} } \] - où $F$ est la résultante des forces agissant sur p ; cette équation est l’\textit{équation de conservation de la quantité de mouvement} : en fait, on voit que si $f = 0$, le vecteur quantité de mouvement a dérivée nulle, et donc il est constant. + où $F$ est la résultante des forces agissant sur le corps. + Cette équation est l’\textit{\textbf{équation de conservation de la quantité de mouvement}}. + On voit que si $F = 0$, la dérivée du vecteur \textit{quantité de mouvement} est nulle ; il est donc constant. \end{morebox} \section{Impulsion} @@ -239,11 +241,11 @@ Pour maximiser l'impulsion, il faut donc que la force appliquée soit la plus gr \begin{morebox} Les notions d'impulsion et de quantité de mouvement sont équivalentes lorsque la vitesse est linéaire (i.e. non angulaire) : - \[I = F \times t ~~et~~ F = m \times \| \vec{a} \| ~~\rightarrow~~ I = m \times \| \vec{a} \| \times t\] + \[I = F \times t ~~et~~ F = m \times a ~~\rightarrow~~ I = m \times a \times t\] Or - \[\vec{a} = \frac{\vec{v}}{t} ~~\rightarrow~~ \| \vec{a} \| = \frac{\| \vec{v} \|}{t} \] + \[a = \frac{v}{t} \] Donc - \[I = m \times \frac{\| \vec{v} \|}{\cancel{t}} \times \cancel{t} = m \times \| \vec{v} \| = P\] + \[I = m \times \frac{v}{\cancel{t}} \times \cancel{t} = m \times v = P\] \end{morebox} \newpage @@ -309,7 +311,7 @@ L'inertie d'un corps est : \end{enumerate} \subsection*{Question 5} -Qu'est ce qu'un moment d'inertie ? +Qu'est-ce qu'un moment d'inertie ? \begin{enumerate} \item Une grandeur proportionnelle au carré de la masse. \item Un élément cinématique proportionnel à la quantité de mouvement. diff --git a/Syllabus/chap_referentiel_force.tex b/Syllabus/chap_referentiel_force.tex index 465bb9f..7ae1f91 100644 --- a/Syllabus/chap_referentiel_force.tex +++ b/Syllabus/chap_referentiel_force.tex @@ -32,7 +32,7 @@ Mais avant même de parler d'axes, simplifions les choses et parlons d'abord de \newpage -Pour décrire les mouvements simples (voire simplistes) du corps humain, trois plans imaginaires appelés \textit{plans anatomiques du corps humain} sont utilisés : +Pour décrire les mouvements simples du corps humain, trois plans imaginaires appelés \textit{plans anatomiques du corps humain} sont utilisés : \bigskip \begin{minipage}[c]{.30\linewidth} @@ -120,7 +120,7 @@ Et, pour être certain de bien comprendre cette définition, nous devons égalem \newpage \subsection{Caractéristiques d'une force} -Les forces sont schématisées par des flèches appelées \textbf{vecteurs}. Ce mode de représentation permet de stocker dans un dessins très simple les quatre caractéristiques de l'action d'une force : +Les forces sont schématisées par des flèches appelées \textbf{vecteurs}. Ce mode de représentation permet de stocker dans un dessin très simple les quatre caractéristiques de l'action d'une force : \begin{itemize} \item \textbf{point d'application} : endroit où la force agit. \item \textbf{droite d'action} : droite suivant laquelle va s'exercer la force. @@ -200,10 +200,10 @@ En biomécanique, le plus souvent, son point d'application est ramené au \texti \subsection{Multiplication de force} Comme nous l'avons vu, les forces sont schématisées par des vecteurs. -Cela permet de les additions ou de les décomposer facilement. +Cela permet de les additionner ou de les décomposer facilement. Il est également possible de multiplier des vecteurs et donc des forces. \begin{definition} - le produit vectoriel, noté $\wedge$, de deux vecteurs $\vec{a}$ et $\vec{b}$ non colinéaires se définit comme l'unique vecteur $\vec{c}$ tel que : + Le produit vectoriel, noté $\wedge$, de deux vecteurs $\vec{a}$ et $\vec{b}$ non colinéaires se définit comme l'unique vecteur $\vec{c}$ tel que : \begin{itemize} \item le vecteur $\vec{c}$ est orthogonal aux deux vecteurs donnés ; \item $\parallel\vec{c}\parallel = \parallel\vec{a}\parallel ~ \parallel\vec{b}\parallel ~ |sin (\widehat{\vec{a}, \vec{b}})|$ @@ -217,7 +217,7 @@ Il est également possible de multiplier des vecteurs et donc des forces. \subsubsection*{Sens direct} La multiplication de deux nombres $x$ et $y$ est symétrique. -Cela signifique que : +Cela signifie que : \[x \times y = y \times x\] Pour la multiplication de vecteur ce n'est pas le cas : multiplier $\vec{a}$ par $\vec{b}$ n'équivaut pas à multiplier $\vec{b}$ par $\vec{a}$ @@ -231,7 +231,7 @@ Le \underline{sens direct} de l'espace correspond au mouvement d'une vis. Prenons le dessin de droite comme exemple. \bigskip - A l'aplomb du plan formé par $\color{red}\vec{a}$ et $\color{blue}\vec{b}$, si pour aller de $\color{red}\vec{a}$ à $\color{blue}\vec{b}$ nous tournons dans le sens \underline{inverse} des aiguille d'une montre (nous dévissons) $\color{green}\vec{c}$ sort (monte/se retire) du plan $ab$ par le haut. + A l'aplomb du plan formé par $\color{red}\vec{a}$ et $\color{blue}\vec{b}$, si pour aller de $\color{red}\vec{a}$ à $\color{blue}\vec{b}$ nous tournons dans le sens \underline{inverse} des aiguilles d'une montre (nous dévissons) $\color{green}\vec{c}$ sort (monte/se retire) du plan $ab$ par le haut. \bigskip Par contre si nous multiplions $\color{blue}\vec{b}$ par $\color{red}\vec{a}$ (c-à-d. nous allons de $\color{blue}\vec{b}$ vers $\color{red}\vec{a}$), nous tournons dans le sens des aiguilles d'une montre, le résultat ($-\vec{c}$) s'enfonce (descend) dans le plan $ab$. @@ -483,7 +483,7 @@ Que donne la multiplication d'un vecteur par un autre vecteur (non co-linéaire) \subsection*{Question 11} \vspace{-0.4cm} \begin{minipage}{.49\linewidth} - Dessiner : + Calculer et dessiner : \begin{itemize} \item $ 2\vec{u} + \vec{v}$ \item $ \vec{u} - 3\vec{v}$ @@ -525,7 +525,7 @@ Quel effet de la force est exprimé par son moment ? \item Une rotation \item Une variation de l'accélération du corps \item Une variation de sa vitesse (accélération) - \item l'énergie fournie par cette force lorsque son point d'application se déplace (l'objet subissant la force se déplace ou se déforme) + \item L'énergie fournie par cette force lorsque son point d'application se déplace (l'objet subissant la force se déplace ou se déforme) \end{enumerate} \subsection*{Question 15} @@ -535,7 +535,7 @@ Comment optimiser l'effet de rotation d'une force de faible intensité ? \item Appliquer la force perpendiculairement au mouvement \item Appliquer la force perpendiculairement au mouvement et loin de l'axe de rotation \item Appliquer un couple de forces - \item Appliquer la force que un corps le plus grand possible + \item Appliquer la force sur un corps le plus grand possible \end{enumerate} \subsection*{Question 16} diff --git a/Syllabus/chap_statique.tex b/Syllabus/chap_statique.tex index 0ebca3c..791b153 100644 --- a/Syllabus/chap_statique.tex +++ b/Syllabus/chap_statique.tex @@ -9,7 +9,7 @@ \end{definition} \begin{minipage}[l]{.55\linewidth} - En d'autre termes, le polygone de sustentation est le plus petit polygone convexe reliant l’ensemble des points par lesquels un corps repose sur une surface. + En d'autres termes, le polygone de sustentation est le plus petit polygone convexe reliant l’ensemble des points par lesquels un corps repose sur une surface. \bigskip \par @@ -30,7 +30,7 @@ La notion d'\textit{équilibre} implique souvent une notion de repos (aucun mouv C'est d'autant plus le cas ici, en \textit{équilibre statique}. \bigskip -La définition de l'équilibre statique implique donc que la résultante des forces qui s'exercent sur le corps soit nulle mais aussi que les moments de forces soient nuls. +La définition de l'équilibre statique implique donc que la résultante des forces qui s'exercent sur le corps soit nulle mais aussi que la résultante des moments de forces soit nulle. Mis en formule, cela donne : \[\mybox{\sum_i \vec{F}_i = 0 ~et~ \sum_i \overrightarrow{\mathcal{L}(\vec{F}_i)} = 0}\] @@ -80,12 +80,12 @@ C'est le rapport de ces deux facteurs l'un par rapport à l'autre qui détermine \end{minipage} Un équilibre en suspension est plus stable qu’un équilibre au-dessus de ses appuis. -Un corps restera plus facilement en équilibre s’il présente la forme d’un pendule (suspendu) que s’il présente la forme d’un cône inversé en appui sur sa pointe. +Un corps restera plus facilement en équilibre s’il présente la forme d’un pendule (i.e. objet suspendu) que s’il présente la forme d’un cône inversé en appui sur sa pointe (e.g. gymnaste dans une toile de trampoline). \medskip Plus la projection du centre de gravité est proche du centre du polygone de sustentation, plus l'équilibre est stable. % : le corps est en suspension. -Cela signifie que le corps reviendra à sa position initiale s'il est (modérément) perturbé. +Cela signifie que le corps reviendra à sa position initiale s'il est modérément perturbé. \medskip \begin{minipage}[l]{.49\linewidth} @@ -103,10 +103,10 @@ Cela signifie que le corps reviendra à sa position initiale s'il est (modérém \includegraphics[scale=0.35]{../Img/stabilite.png} \end{minipage} -A l'opposé, plus le centre de gravité est proche de la limite (le bord) du polygone de sustentation, plus l'équilibre est instable : le corps a d'autant plus de risque de quitter sa position initiale s'il est perturbé que le centre de gravité est proche de la limite. +A l'opposé, plus le centre de gravité est proche de la limite du polygone de sustentation, plus l'équilibre est instable : le corps a d'autant plus de risque de quitter sa position initiale s'il est perturbé que le centre de gravité est proche de la limite. \bigskip -Si la projection du centre de gravité est en dehors de la surface de sustentation, le corps est en déséquilibre et le mouvement (chute) est inévitable. +Si la projection du centre de gravité est en dehors de la surface de sustentation, le corps est en déséquilibre et le mouvement, une chute, est inévitable. \newpage @@ -202,7 +202,7 @@ Classer les polygones de sustentation de la Question 3 par ordre de stabilité r \end{enumerate} \subsection*{Question 5} -D'après la définition, un cors est en équilibre statique quand\ldots +D'après la définition, un corps est en équilibre statique quand\ldots \begin{enumerate} \item Les forces et moments de forces qui agissent sur lui se neutralisent. \item Il n'y a pas de force qui agissent sur lui. @@ -212,7 +212,7 @@ D'après la définition, un cors est en équilibre statique quand\ldots \subsection*{Question 6} \vspace{-0.2cm} -D'après les définitions d'équilibre statique et de corps isolé, une corps isolé est-il en équilibre ? +D'après les définitions d'équilibre statique et de corps isolé, un corps isolé est-il en équilibre ? \begin{enumerate} \item Oui \item Non @@ -220,14 +220,14 @@ D'après les définitions d'équilibre statique et de corps isolé, une corps is \subsection*{Question 7} \vspace{-0.2cm} -D'après les définitions d'équilibre statique et de corps pseudo-isolé, une corps pseudo-isolé est-il en équilibre ? +D'après les définitions d'équilibre statique et de corps pseudo-isolé, un corps pseudo-isolé est-il en équilibre ? \begin{enumerate} \item Oui \item Non \end{enumerate} \subsection*{Question 8} -Qu'est ce que la stabilité d'un corps ? +Qu'est-ce que la stabilité d'un corps ? \begin{enumerate} \item Sa capacité à résister à un déplacement. \item Sa capacité à maintenir son état d'équilibre. % A REVOIR @@ -248,16 +248,16 @@ La stabilité d'un corps dépend de deux facteurs. Lesquels ? Quels sont les types de dépendance de ces deux facteurs ci-dessous pour la stabilité ? \begin{enumerate} \item Proportionnelle au polygone de sustentation et proportionnelle à la hauteur de centre de gravité. - \item Proportionnelle au polygone de sustentation et inversément proportionnelle à la hauteur de centre de gravité. - \item Inversément proportionnelle au polygone de sustentation et proportionnelle à la hauteur de centre de gravité. - \item Inversément proportionnelle au polygone de sustentation et inversément proportionnelle à la hauteur de centre de gravité. + \item Proportionnelle au polygone de sustentation et inversement proportionnelle à la hauteur de centre de gravité. + \item Inversement proportionnelle au polygone de sustentation et proportionnelle à la hauteur de centre de gravité. + \item Inversement proportionnelle au polygone de sustentation et inversément proportionnelle à la hauteur de centre de gravité. \end{enumerate} \subsection*{Question 11} A partir de quand il y a-t-il un déséquilibre ? \begin{enumerate} \item A partir du moment où la projection du centre de gravité est sur une arête du polygone de sustentation. - \item Tant que la projection du centre de gravité est proche du "centre" du polygone de sustentation. + \item Tant que la projection du centre de gravité est proche du centre du polygone de sustentation. \item Une fois que la projection du centre de gravité sort du polygone de sustentation. \item Dès que le corps est soumis à une force extérieure. \end{enumerate} \ No newline at end of file diff --git a/Syllabus/layout_syllabus_ffg b/Syllabus/layout_syllabus_ffg index 232457c..0f0879e 160000 --- a/Syllabus/layout_syllabus_ffg +++ b/Syllabus/layout_syllabus_ffg @@ -1 +1 @@ -Subproject commit 232457cd7b8100ca6c4cee709f020c9b6f7f6dc6 +Subproject commit 0f0879ecdcdf76ab53851f640c8f0675f3248e62