Chers finalistes, préparez-vous pour le grand jour avec nos contenus !

Des items de toutes les options taillés sur mesure pour que vous prépariez mieux vos épreuves

Start learning
Relations fondamentales de la dynamique.
Matériel didactique : Tableau noir,craies blanches
Objectif opérationnel : A l’issue de la leçon, les élèves seront capables de calculer la force.

Revision

Qu’appel-t-on poids et masse d’un corps ?

Révision

Le poids c’est la force d’un corps variable.

- La masse étant la quantité de la matière invariable.

Motivation

Comment s’appelle la force qui permet de mettre un corps en mouvement soit au repos ?

Motivation

C’est l'inertie.

Annonce du sujet

Quelle est la leçon du jour?

Annonce du sujet

Relations fondamentales de la dynamique.

- Que vous rappelle l’équation de la vitesse en m.R.V ?

- Qu’appelle-t-on inertie ?

- Donnez l’équation de la force ?

 

Relations fondamentales de la dynamique

Principe de l’inertie : un corps matériel en M.R.U ne peut de lui-même modifier son état de mouvement.

Le corps s’oppose à toute variation de la vitesse qu’on veut lui communiquer : qui est doué de l’inertie.

Mais sous l’influence d’une force, le corps en mouvement se met au repos, soit un corps au repos modifie son état, changement de vitesse, direction et s’arrête.

Donc tout corps non soumis à l’action d’une force conserve indéfiniment son état de repos ou de M.R.U.

2. Principe de la force constante

Appliquons sur un corps au repos une force constante, après une séance d’action de la force, ce corps a acquis une vitesse v=a.t

Donc une force constante en intensité, en direction communique à un corps mobile en M.R.U.A.

1ère Relation de la dynamique

Si on soumet le corps de masse m à une force particulière : son poids P, il prend un mouvement vertical de haut en bas et uniformément accéléré. L’Accélération est alors l’accélération de la pesanteur : f.

 

Applications numériques

                                   m     en kg

                                   g      en m/s2

Ex : 1) Un corps pèse 180 kg 1kgf=9,81N soumis a une accélération constante.

Quelle force faut-il lui communiquer dans ces mêmes conditions.

8.1.28PHP Version194msRequest Duration6MBMemory UsageGET lessons/{id}/{slug}Route
    • Booting (38.87ms)
    • Application (155ms)
    • 1 x Application (79.9%)
      154.99ms
      1 x Booting (20.04%)
      38.87ms
      7 templates were rendered
      • public.lessons.show (resources/views/public/lessons/show.blade.php)2bladefile
        Params
        0
        lesson
        1
        lessons
      • components.banner-page (resources/views/components/banner-page.blade.php)7bladefile
        Params
        0
        property
        1
        firstTitle
        2
        secondTitle
        3
        src
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.ad-card-lesson-long (resources/views/components/ad-card-lesson-long.blade.php)7bladefile
        Params
        0
        summary
        1
        title
        2
        actionLink
        3
        actionText
        4
        attributes
        5
        slot
        6
        __laravel_slots
      • components.button-link (resources/views/components/button-link.blade.php)6bladefile
        Params
        0
        class
        1
        title
        2
        href
        3
        attributes
        4
        slot
        5
        __laravel_slots
      • layouts.public (resources/views/layouts/public.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      • layouts.include.public.header (resources/views/layouts/include/public/header.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      • layouts.include.public.footer (resources/views/layouts/include/public/footer.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        lesson
        4
        lessons
        5
        component
        6
        __currentLoopData
        7
        lesson_
        8
        loop
        9
        section
      uri
      GET lessons/{id}/{slug}
      middleware
      web
      controller
      App\Http\Controllers\Public\LessonController@show
      as
      public.lesson.show
      namespace
      prefix
      /lessons
      where
      file
      app/Http/Controllers/Public/LessonController.php:86-138
      36 statements were executed97.76ms
      • select * from `oldt_posts` where (`id` = '1667' and `slug` = 'relations-fondamentales-de-la-dynamique') and exists (select * from `oldt_material_sheets` where `oldt_posts`.`material_sheet_id` = `oldt_material_sheets`.`id`) limit 1
        3.41ms/app/Http/Controllers/Public/LessonController.php:92schoolap
        Metadata
        Bindings
        • 0. 1667
        • 1. relations-fondamentales-de-la-dynamique
        Backtrace
        • 15. /app/Http/Controllers/Public/LessonController.php:92
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `lessons` where `lessons`.`id` = '1667' and `lessons`.`deleted_at` is null limit 1
        1.23ms/app/Repositories/LessonRepository.php:41schoolap
        Metadata
        Bindings
        • 0. 1667
        Backtrace
        • 19. /app/Repositories/LessonRepository.php:41
        • 20. /app/Http/Controllers/Public/LessonController.php:95
        • 21. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 22. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 23. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `lessons` where `lessons`.`deleted_at` is null order by RAND() limit 4
        46.85ms/app/Http/Controllers/Public/LessonController.php:96schoolap
        Metadata
        Backtrace
        • 14. /app/Http/Controllers/Public/LessonController.php:96
        • 15. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 16. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • update `lessons` set `count_view` = `count_view` + 1, `lessons`.`updated_at` = '2025-05-02 09:20:06' where `id` = 1667 and `lessons`.`deleted_at` is null
        22.43ms/app/Http/Controllers/Public/LessonController.php:98schoolap
        Metadata
        Bindings
        • 0. 2025-05-02 09:20:06
        • 1. 1667
        Backtrace
        • 16. /app/Http/Controllers/Public/LessonController.php:98
        • 17. /vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. /vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. /vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `chapters` where `chapters`.`id` = 521 and `chapters`.`deleted_at` is null limit 1
        1.21msview::public.lessons.show:10schoolap
        Metadata
        Bindings
        • 0. 521
        Backtrace
        • 20. view::public.lessons.show:10
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `course_classes` where `course_classes`.`id` = 188 and `course_classes`.`deleted_at` is null limit 1
        1.49msview::public.lessons.show:10schoolap
        Metadata
        Bindings
        • 0. 188
        Backtrace
        • 20. view::public.lessons.show:10
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `classes` where `classes`.`id` in (101) and `classes`.`deleted_at` is null
        890μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 25. view::public.lessons.show:10
        • 27. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 29. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 30. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `cycle_levels` where `cycle_levels`.`id` in (70)
        850μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 30. view::public.lessons.show:10
        • 32. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 35. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `cycles` where `cycles`.`id` in (11)
        970μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 35. view::public.lessons.show:10
        • 37. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 38. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 39. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 40. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `levels` where `levels`.`id` in (28)
        650μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 35. view::public.lessons.show:10
        • 37. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 38. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 39. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 40. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `courses` where `courses`.`id` in (103) and `courses`.`deleted_at` is null
        730μsview::public.lessons.show:10schoolap
        Metadata
        Backtrace
        • 25. view::public.lessons.show:10
        • 27. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 28. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 29. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 30. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_sections` where `lesson_sections`.`lesson_id` = 1667 and `lesson_sections`.`lesson_id` is not null
        1.81msview::public.lessons.show:116schoolap
        Metadata
        Bindings
        • 0. 1667
        Backtrace
        • 19. view::public.lessons.show:116
        • 21. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 22. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 24. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14066 and `lesson_contents`.`deleted_at` is null limit 1
        1.36msview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14066
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13849 and `content_texts`.`deleted_at` is null limit 1
        1.39msview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13849
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14067 and `lesson_contents`.`deleted_at` is null limit 1
        660μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14067
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13850 and `content_texts`.`deleted_at` is null limit 1
        740μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13850
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14068 and `lesson_contents`.`deleted_at` is null limit 1
        680μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14068
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13851 and `content_texts`.`deleted_at` is null limit 1
        590μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13851
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14069 and `lesson_contents`.`deleted_at` is null limit 1
        660μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14069
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13852 and `content_texts`.`deleted_at` is null limit 1
        540μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13852
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14070 and `lesson_contents`.`deleted_at` is null limit 1
        530μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14070
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13853 and `content_texts`.`deleted_at` is null limit 1
        730μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13853
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14071 and `lesson_contents`.`deleted_at` is null limit 1
        640μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14071
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13854 and `content_texts`.`deleted_at` is null limit 1
        440μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13854
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14072 and `lesson_contents`.`deleted_at` is null limit 1
        590μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14072
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13855 and `content_texts`.`deleted_at` is null limit 1
        470μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13855
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14073 and `lesson_contents`.`deleted_at` is null limit 1
        370μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14073
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13856 and `content_texts`.`deleted_at` is null limit 1
        410μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13856
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14074 and `lesson_contents`.`deleted_at` is null limit 1
        420μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14074
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13857 and `content_texts`.`deleted_at` is null limit 1
        450μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13857
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14075 and `lesson_contents`.`deleted_at` is null limit 1
        470μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14075
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13858 and `content_texts`.`deleted_at` is null limit 1
        460μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13858
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14076 and `lesson_contents`.`deleted_at` is null limit 1
        480μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14076
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13859 and `content_texts`.`deleted_at` is null limit 1
        580μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13859
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `lesson_contents` where `lesson_contents`.`id` = 14077 and `lesson_contents`.`deleted_at` is null limit 1
        750μsview::public.lessons.show:117schoolap
        Metadata
        Bindings
        • 0. 14077
        Backtrace
        • 20. view::public.lessons.show:117
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      • select * from `content_texts` where `content_texts`.`id` = 13860 and `content_texts`.`deleted_at` is null limit 1
        830μsview::public.lessons.show:133schoolap
        Metadata
        Bindings
        • 0. 13860
        Backtrace
        • 20. view::public.lessons.show:133
        • 22. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 23. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 24. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
        • 25. /vendor/laravel/framework/src/Illuminate/View/View.php:195
      App\Models\ContentText
      12
      App\Models\Lesson\LessonContent
      12
      App\Models\Lesson\LessonSection
      12
      App\Models\Course\Course
      1
      App\Models\Level
      1
      App\Models\Cycle
      1
      App\Models\CycleLevel
      1
      App\Models\Classe
      1
      App\Models\Course\CourseClass
      1
      App\Models\Chapter
      1
      App\Models\Lesson\Lesson
      5
        _token
        lhwhuPMCi5jwUvSDZYSguoExMekY9Rz53c1OICwY
        applocale
        en
        _previous
        array:1 [ "url" => "https://s8.schoolap.com/lessons/1667/relations-fondamentales-de-la-dynamique" ...
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /lessons/1667/relations-fondamentales-de-la-dynamique
        status_code
        200
        
        status_text
        OK
        format
        html
        content_type
        text/html; charset=UTF-8
        request_query
        []
        
        request_request
        []
        
        request_headers
        0 of 0
        array:17 [ "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "connection" => array:1 [ 0 => "keep-alive" ] "host" => array:1 [ 0 => "s8.schoolap.com" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
        request_server
        0 of 0
        array:41 [ "USER" => "www-data" "HOME" => "/var/www" "HTTP_ACCEPT_ENCODING" => "gzip, deflate, br, zstd" "HTTP_SEC_FETCH_DEST" => "document" "HTTP_SEC_FETCH_USER" => "?1" "HTTP_SEC_FETCH_MODE" => "navigate" "HTTP_SEC_FETCH_SITE" => "none" "HTTP_ACCEPT" => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" "HTTP_USER_AGENT" => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" "HTTP_UPGRADE_INSECURE_REQUESTS" => "1" "HTTP_SEC_CH_UA_PLATFORM" => ""Windows"" "HTTP_SEC_CH_UA_MOBILE" => "?0" "HTTP_SEC_CH_UA" => ""Chromium";v="130", "HeadlessChrome";v="130", "Not?A_Brand";v="99"" "HTTP_CACHE_CONTROL" => "no-cache" "HTTP_PRAGMA" => "no-cache" "HTTP_CONNECTION" => "keep-alive" "HTTP_HOST" => "s8.schoolap.com" "REDIRECT_STATUS" => "200" "SERVER_NAME" => "s8.schoolap.com" "SERVER_PORT" => "443" "SERVER_ADDR" => "188.166.147.66" "REMOTE_PORT" => "31035" "REMOTE_ADDR" => "3.21.190.123" "SERVER_SOFTWARE" => "nginx/1.18.0" "GATEWAY_INTERFACE" => "CGI/1.1" "HTTPS" => "on" "REQUEST_SCHEME" => "https" "SERVER_PROTOCOL" => "HTTP/1.1" "DOCUMENT_ROOT" => "/var/www/s8.schoolap.com/public" "DOCUMENT_URI" => "/index.php" "REQUEST_URI" => "/lessons/1667/relations-fondamentales-de-la-dynamique" "SCRIPT_NAME" => "/index.php" "CONTENT_LENGTH" => "" "CONTENT_TYPE" => "" "REQUEST_METHOD" => "GET" "QUERY_STRING" => "" "SCRIPT_FILENAME" => "/var/www/s8.schoolap.com/public/index.php" "FCGI_ROLE" => "RESPONDER" "PHP_SELF" => "/index.php" "REQUEST_TIME_FLOAT" => 1746177606.7789 "REQUEST_TIME" => 1746177606 ]
        request_cookies
        []
        
        response_headers
        0 of 0
        array:5 [ "content-type" => array:1 [ 0 => "text/html; charset=UTF-8" ] "cache-control" => array:1 [ 0 => "no-cache, private" ] "date" => array:1 [ 0 => "Fri, 02 May 2025 09:20:06 GMT" ] "set-cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6IlRzdVIrSjkrRm0zcXg2eUxXdWlES1E9PSIsInZhbHVlIjoidGxZKy9HWGZzeGtmcGVXZjZRSW0vVEN6YTdSWjdyVUM3RnZma1o4QmR3S2lQVWUxQTF1NC95RlZlMDF1aXFpMSIsIm1hYyI6IjU0N2Q5ZTJkYmRlNzlhYTg5ZDY1ZGI5ODRiYjUyOWY1YWMwYzllZjQxODdlMWVlZDI5NjVhODFjNGJhNDI3OWEiLCJ0YWciOiIifQ%3D%3D; expires=Fri, 09 May 2025 08:00:06 GMT; Max-Age=600000; path=/; httponly; samesite=laxlang_schoolap=eyJpdiI6IlRzdVIrSjkrRm0zcXg2eUxXdWlES1E9PSIsInZhbHVlIjoidGxZKy9HWGZzeGtmcGVXZjZRSW0vVEN6YTdSWjdyVUM3RnZma1o4QmR3S2lQVWUxQTF1NC95RlZlMDF1aXFpMSIsIm" 1 => "XSRF-TOKEN=eyJpdiI6IjVkYTNOOHp4azBlSVNMZENoQVNNYVE9PSIsInZhbHVlIjoiZkFJUmVFeG5DRGVnSlVWVHhTMjh6TUhLaW9Fd0JtQ2J3dmRHUFBkampLWXB6b05odlhHcFpMWFhMTWtDYXhTNU4xZGwyTzFGYlFxN096eWRoeGdVeWxPekthRkpSUE5yNUxsTGJIUTJHaGlHazV4RlpYMS95aWpldmxINmtaQkIiLCJtYWMiOiI2NzFkNDRlZDYzNzU0ZTFkZDQ2MDNiZmE4ZmI0Y2M0MzA2YThlZDZmZWQ1YTc5MGVhOWI3NmI1M2NlYjQ1NGFiIiwidGFnIjoiIn0%3D; expires=Fri, 02 May 2025 11:20:06 GMT; Max-Age=7200; path=/; samesite=laxXSRF-TOKEN=eyJpdiI6IjVkYTNOOHp4azBlSVNMZENoQVNNYVE9PSIsInZhbHVlIjoiZkFJUmVFeG5DRGVnSlVWVHhTMjh6TUhLaW9Fd0JtQ2J3dmRHUFBkampLWXB6b05odlhHcFpMWFhMTWtDYXhTNU4xZGwyT" 2 => "schoolap_session=eyJpdiI6IkxKYnA1Zk5FNVVNMUk0RXNYZFlQYVE9PSIsInZhbHVlIjoicWVnTnFhY25BWUFXTlR6dytQcDgyellBd2dSWkNOL3lEVkxnQllOeVFNQXZVeDYwdFZpK2txdTB1ODM2OEtSMFdUa0puLzlNT1JCbkp2MDcvbnV2UXRMWVliT2lZOEo0Uzd1V0FkdFU3ZURUZkUrbGptY2sxb3pRb29ycjh0N1giLCJtYWMiOiI2MjE4NzYxNjE3MWUzOTY1Y2JjNjliMDEwNjVkN2Y1MGQ3YjE2ZDFhYjU0YjhmZDVkZmU2MGQxMTBmMmM5NTYwIiwidGFnIjoiIn0%3D; expires=Fri, 02 May 2025 11:20:06 GMT; Max-Age=7200; path=/; httponly; samesite=laxschoolap_session=eyJpdiI6IkxKYnA1Zk5FNVVNMUk0RXNYZFlQYVE9PSIsInZhbHVlIjoicWVnTnFhY25BWUFXTlR6dytQcDgyellBd2dSWkNOL3lEVkxnQllOeVFNQXZVeDYwdFZpK2txdTB1ODM2OEtSMFd" ] "Set-Cookie" => array:3 [ 0 => "lang_schoolap=eyJpdiI6IlRzdVIrSjkrRm0zcXg2eUxXdWlES1E9PSIsInZhbHVlIjoidGxZKy9HWGZzeGtmcGVXZjZRSW0vVEN6YTdSWjdyVUM3RnZma1o4QmR3S2lQVWUxQTF1NC95RlZlMDF1aXFpMSIsIm1hYyI6IjU0N2Q5ZTJkYmRlNzlhYTg5ZDY1ZGI5ODRiYjUyOWY1YWMwYzllZjQxODdlMWVlZDI5NjVhODFjNGJhNDI3OWEiLCJ0YWciOiIifQ%3D%3D; expires=Fri, 09-May-2025 08:00:06 GMT; path=/; httponlylang_schoolap=eyJpdiI6IlRzdVIrSjkrRm0zcXg2eUxXdWlES1E9PSIsInZhbHVlIjoidGxZKy9HWGZzeGtmcGVXZjZRSW0vVEN6YTdSWjdyVUM3RnZma1o4QmR3S2lQVWUxQTF1NC95RlZlMDF1aXFpMSIsIm" 1 => "XSRF-TOKEN=eyJpdiI6IjVkYTNOOHp4azBlSVNMZENoQVNNYVE9PSIsInZhbHVlIjoiZkFJUmVFeG5DRGVnSlVWVHhTMjh6TUhLaW9Fd0JtQ2J3dmRHUFBkampLWXB6b05odlhHcFpMWFhMTWtDYXhTNU4xZGwyTzFGYlFxN096eWRoeGdVeWxPekthRkpSUE5yNUxsTGJIUTJHaGlHazV4RlpYMS95aWpldmxINmtaQkIiLCJtYWMiOiI2NzFkNDRlZDYzNzU0ZTFkZDQ2MDNiZmE4ZmI0Y2M0MzA2YThlZDZmZWQ1YTc5MGVhOWI3NmI1M2NlYjQ1NGFiIiwidGFnIjoiIn0%3D; expires=Fri, 02-May-2025 11:20:06 GMT; path=/XSRF-TOKEN=eyJpdiI6IjVkYTNOOHp4azBlSVNMZENoQVNNYVE9PSIsInZhbHVlIjoiZkFJUmVFeG5DRGVnSlVWVHhTMjh6TUhLaW9Fd0JtQ2J3dmRHUFBkampLWXB6b05odlhHcFpMWFhMTWtDYXhTNU4xZGwyT" 2 => "schoolap_session=eyJpdiI6IkxKYnA1Zk5FNVVNMUk0RXNYZFlQYVE9PSIsInZhbHVlIjoicWVnTnFhY25BWUFXTlR6dytQcDgyellBd2dSWkNOL3lEVkxnQllOeVFNQXZVeDYwdFZpK2txdTB1ODM2OEtSMFdUa0puLzlNT1JCbkp2MDcvbnV2UXRMWVliT2lZOEo0Uzd1V0FkdFU3ZURUZkUrbGptY2sxb3pRb29ycjh0N1giLCJtYWMiOiI2MjE4NzYxNjE3MWUzOTY1Y2JjNjliMDEwNjVkN2Y1MGQ3YjE2ZDFhYjU0YjhmZDVkZmU2MGQxMTBmMmM5NTYwIiwidGFnIjoiIn0%3D; expires=Fri, 02-May-2025 11:20:06 GMT; path=/; httponlyschoolap_session=eyJpdiI6IkxKYnA1Zk5FNVVNMUk0RXNYZFlQYVE9PSIsInZhbHVlIjoicWVnTnFhY25BWUFXTlR6dytQcDgyellBd2dSWkNOL3lEVkxnQllOeVFNQXZVeDYwdFZpK2txdTB1ODM2OEtSMFd" ] ]
        session_attributes
        0 of 0
        array:5 [ "_token" => "lhwhuPMCi5jwUvSDZYSguoExMekY9Rz53c1OICwY" "applocale" => "en" "_previous" => array:1 [ "url" => "https://s8.schoolap.com/lessons/1667/relations-fondamentales-de-la-dynamique" ] "_flash" => array:2 [ "old" => [] "new" => [] ] "PHPDEBUGBAR_STACK_DATA" => [] ]