Sign in
Login

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
Les grandeurs et leurs unités
Domaine Science Sous domaine Physique, Technologie et TIC
Section Technique Option Mécanique
Discipline Mecanique Classe 4ème
Matériel didactique Tableau noir,craies blanches Auteur SCHOOLAP.COM
Objectif opérationnel A l’issus de la leçon, les élevés seront capable de connaitre les grandeurs et leur unité correspondant
Réference R. THUBAUT, A. TOURNAY MECANIQUE GENERALE
Activité initiale

Rappel

Quel sont les systèmes d’unités que nous allons  utiliser en 4ème MG ?

Rappel

En 4ème MG, nous allons utiliser 2 systèmes d’unités qui sont : MKSA et MKPS

Motivation

Pourquoi connaitre les unités  ou pourquoi faire l’étude des unités ?

Motivation

Parce que il fallait connaître les unités de ces divers systèmes et faire les conversions entre les unités.

Annonce du sujet

Qu'allons nous étudier aujourd'hui

Annonce du sujet

Nous  allons étudier les unités, parce que chaque grandeur qui existe  à toujours  son unité de passe ou son unité principale.
Activité principale

En quelle unité s’exprime la puissance

La puissance s’exprime en Watts (w) ou en Nm/s

LES GRANDEURS ET LEURS UNITES

  1. Les unités de  base  (principale)
  • Longueur         : le mètre (m)
  • La masse         : le kilogramme (kg)
  • Le temps         : la seconde (sec)
  • L’intensité du courant électrique, l’ampère (A) 
  1. Les grandeurs secondaires
  • La surface  S (m2)
  • Le volume  V (m2)
  • La vitesse V (m/s)
  • L’énergie (Nm, J, kgtm)
  • La puissance P (W,Nm/s kgfm/s)
  • L’espace  e (m)
  • L’accélération  a ( m/s)
  • La force   F (  N,kgf)
  • La pression p (N/m2 )

NB :

  • 1kgm = 9,81 Nm
  • 1Cv= 75 kgfm/s = 736w
  • IN = 1 kgm /S2

Les multiple et sous multiples des unités

Chaque grandeur à son unité principale admise par le système international (s.i), les multiples et les sous-multiples des grandeurs sont formés par certains préfixes.

  1. Les préfixes multiples

 
  1. Les préfixes sous-multiples
  • Déca (da) : 101
  • Hecto (h) 102
  • Kilo (k) : 103
  • Méga (m) 106
  • Giga (G) 109
  • Déci (d) : 10-1
  • Centi  ( c) 102
  • Milli (m) 10-3
  • Micro (m) 10-6
  • Nano (n) 10-9
  • Picro ( p) 1012
Synthèse

Qu'est ce que nous retenons sur les grandeurs et leurs unités 

Nous retenons que chaque grandeur a son unité de base et a des multiples et des sous multiples.
MessagesTimelineExceptionsViews7RouteQueries14Models18GateSessionRequest
8.1.28PHP Version226msRequest Duration5MBMemory UsageGET fiches/{id}/{slug}Route
    • Booting (33.9ms)
    • Application (192ms)
    • 1 x Application (84.96%)
      192.06ms
      1 x Booting (14.99%)
      33.90ms
      7 templates were rendered
      • public.fiches.show (resources/views/public/fiches/show.blade.php)2bladefile
        Params
        0
        post
        1
        posts
      • 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
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      • layouts.include.public.header (resources/views/layouts/include/public/header.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      • layouts.include.public.footer (resources/views/layouts/include/public/footer.blade.php)10bladefile
        Params
        0
        __env
        1
        app
        2
        errors
        3
        post
        4
        posts
        5
        component
        6
        __currentLoopData
        7
        post_
        8
        loop
        9
        content
      uri
      GET fiches/{id}/{slug}
      middleware
      web
      controller
      App\Http\Controllers\Public\FicheController@show
      as
      public.fiche.show
      namespace
      prefix
      /fiches
      where
      file
      app/Http/Controllers/Public/FicheController.php:46-73
      14 statements were executed164ms
      schoolap
      • select * from `oldt_posts` where `oldt_posts`.`id` = '846' limit 1
        1.93ms/app/Repositories/PostRepository.php:39schoolap
        Metadata
        Bindings
        • 0. 846
        Backtrace
        • 19. /app/Repositories/PostRepository.php:39
        • 20. /app/Http/Controllers/Public/FicheController.php:48
        • 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 (`post_id` = 846) and `lessons`.`deleted_at` is null limit 1
        710μs/app/Http/Controllers/Public/FicheController.php:52schoolap
        Metadata
        Bindings
        • 0. 846
        Backtrace
        • 15. /app/Http/Controllers/Public/FicheController.php:52
        • 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
      • update `lessons` set `count_view` = `count_view` + 1, `lessons`.`updated_at` = '2025-05-05 04:56:56' where `id` = 1291 and `lessons`.`deleted_at` is null
        3.71ms/app/Http/Controllers/Public/FicheController.php:55schoolap
        Metadata
        Bindings
        • 0. 2025-05-05 04:56:56
        • 1. 1291
        Backtrace
        • 16. /app/Http/Controllers/Public/FicheController.php:55
        • 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 `oldt_posts` where `published` = 1 order by RAND() limit 4
        48.95ms/app/Http/Controllers/Public/FicheController.php:61schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 14. /app/Http/Controllers/Public/FicheController.php:61
        • 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
      • select * from `oldt_material_sheets` where `oldt_material_sheets`.`id` = 424 limit 1
        1.07msview::public.fiches.show:7schoolap
        Metadata
        Bindings
        • 0. 424
        Backtrace
        • 20. view::public.fiches.show:7
        • 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 `oldt_grades` where `oldt_grades`.`id` = 4 and `oldt_grades`.`id` is not null limit 1
        710μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 4
        Backtrace
        • 20. view::public.fiches.show:15
        • 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 `oldt_options` where `oldt_options`.`id` = 12 limit 1
        610μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 12
        Backtrace
        • 20. view::public.fiches.show:15
        • 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 `oldt_disciplines` where `oldt_disciplines`.`id` = 43 limit 1
        660μsview::public.fiches.show:15schoolap
        Metadata
        Bindings
        • 0. 43
        Backtrace
        • 20. view::public.fiches.show:15
        • 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 `oldt_sub_domains` where `oldt_sub_domains`.`id` = 3 and `oldt_sub_domains`.`id` is not null limit 1
        960μsview::public.fiches.show:120schoolap
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 20. view::public.fiches.show:120
        • 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 `oldt_domains` where `oldt_domains`.`id` = 1 and `oldt_domains`.`id` is not null limit 1
        560μsview::public.fiches.show:120schoolap
        Metadata
        Bindings
        • 0. 1
        Backtrace
        • 20. view::public.fiches.show:120
        • 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 `oldt_sections` where `oldt_sections`.`id` = 3 limit 1
        450μsview::public.fiches.show:136schoolap
        Metadata
        Bindings
        • 0. 3
        Backtrace
        • 20. view::public.fiches.show:136
        • 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 `oldt_material_sheet_contents` where `material_sheet_id` = 424 and `activity` = 0
        34.98ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 424
        • 1. 0
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:191
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `oldt_material_sheet_contents` where `material_sheet_id` = 424 and `activity` = 1
        35.52ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 424
        • 1. 1
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:203
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `oldt_material_sheet_contents` where `material_sheet_id` = 424 and `activity` = 2
        32.77ms/app/Models/Old/MaterialSheet.php:73schoolap
        Metadata
        Bindings
        • 0. 424
        • 1. 2
        Backtrace
        • 14. /app/Models/Old/MaterialSheet.php:73
        • 15. view::public.fiches.show:214
        • 17. /vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 18. /vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 19. /vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      App\Models\Old\MaterialSheetContent
      5
      App\Models\Old\Section
      1
      App\Models\Old\Domain
      1
      App\Models\Old\SubDomain
      1
      App\Models\Old\Discipline
      1
      App\Models\Old\Option
      1
      App\Models\Old\Grade
      1
      App\Models\Old\MaterialSheet
      1
      App\Models\Lesson\Lesson
      1
      App\Models\Old\Post
      5
        _token
        gnRbGUBeEcPjP3lpcMXq8H5z3VzX75hFrXSceuA9
        applocale
        en
        _previous
        array:1 [ "url" => "https://s8.schoolap.com/fiches/846/les-grandeurs-et-leurs-unites" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /fiches/846/les-grandeurs-et-leurs-unites
        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" => "8440"
  "REMOTE_ADDR" => "3.138.151.162"
  "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" => "/fiches/846/les-grandeurs-et-leurs-unites"
  "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" => 1746421016.2764
  "REQUEST_TIME" => 1746421016
]
        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 => "Mon, 05 May 2025 04:56:56 GMT"
  ]
  "set-cookie" => array:3 [▶
    0 => "lang_schoolap=eyJpdiI6IkdyMDFxM3R0bjZ3MFdYZThVeDcweGc9PSIsInZhbHVlIjoiZ0t1QThpSkljcDdDYzRxc1ZjNm0vT1FVTHRtejJETVVhTUd4RjFvdGh5M05ySDBDM0h3a2Y4N3dGc0w2U0lDZSIsIm1hYyI6IjQ1MjM5YzdjN2Y4NGNiNzRlNzJkMjM3ODZjOTEzMWY2ZDEwMzZiMzE3NTdhZjY5MGVjZmY4MWRlYmIzZDliOGQiLCJ0YWciOiIifQ%3D%3D; expires=Mon, 12 May 2025 03:36:56 GMT; Max-Age=600000; path=/; httponly; samesite=lax ◀lang_schoolap=eyJpdiI6IkdyMDFxM3R0bjZ3MFdYZThVeDcweGc9PSIsInZhbHVlIjoiZ0t1QThpSkljcDdDYzRxc1ZjNm0vT1FVTHRtejJETVVhTUd4RjFvdGh5M05ySDBDM0h3a2Y4N3dGc0w2U0lDZSIsIm ▶"
    1 => "XSRF-TOKEN=eyJpdiI6IklEWUtlVlZjQnZSNXVHQTFkWHhCR1E9PSIsInZhbHVlIjoidmxBaVVxTXNoRFlZenFQWFBqZGZ2dHk1cm9WQlJVR250SGJYZHlUVm90TGJNUVNLT2c4RU10NVBUcDdvMDRpOFZsc01NVFdJTlQ3aC9qeDFtREFDM3MrR2VlMW5UcGU5bWdGSGJMOEgvcGpmNWcvMlRmN1E3cVlvUzFVaHRwd3YiLCJtYWMiOiJkNGZhNWY4ODJkMGMwZjMwMjgwMDdlYjdlYmMwZGIwNWZhNDkzNjExM2MwNGIzOTFhY2Q0OTZjOWU2OTU3OWViIiwidGFnIjoiIn0%3D; expires=Mon, 05 May 2025 06:56:56 GMT; Max-Age=7200; path=/; samesite=lax ◀XSRF-TOKEN=eyJpdiI6IklEWUtlVlZjQnZSNXVHQTFkWHhCR1E9PSIsInZhbHVlIjoidmxBaVVxTXNoRFlZenFQWFBqZGZ2dHk1cm9WQlJVR250SGJYZHlUVm90TGJNUVNLT2c4RU10NVBUcDdvMDRpOFZsc01NV ▶"
    2 => "schoolap_session=eyJpdiI6IkJZaWMwS3JXMzBzbjAxQVp4UGV2R3c9PSIsInZhbHVlIjoiWElTR3Q2WityN1diWjBrUXB0N21qMVQ3NWk0RG5Fc3pCaGdOWW14Z1JtcStjWUIra3JiNGd5QWpzbHZHb1B5MUJZM0g3OHpVN1BXdXExM01QZFVBTE12RGg4R29LNi9OV1BQdTY0TStnN005TVB4SlJMRDVQZlp1T1p2dUFTU1ciLCJtYWMiOiIyM2E0NTIwNTY3NTFhOGI0MGNkMjY4Y2FlNTdhNjNmYTU2YWU4MmJkMTJiZDZiNTg5MGUxYzMyZWZmMGE2ODM0IiwidGFnIjoiIn0%3D; expires=Mon, 05 May 2025 06:56:56 GMT; Max-Age=7200; path=/; httponly; samesite=lax ◀schoolap_session=eyJpdiI6IkJZaWMwS3JXMzBzbjAxQVp4UGV2R3c9PSIsInZhbHVlIjoiWElTR3Q2WityN1diWjBrUXB0N21qMVQ3NWk0RG5Fc3pCaGdOWW14Z1JtcStjWUIra3JiNGd5QWpzbHZHb1B5MUJ ▶"
  ]
  "Set-Cookie" => array:3 [▶
    0 => "lang_schoolap=eyJpdiI6IkdyMDFxM3R0bjZ3MFdYZThVeDcweGc9PSIsInZhbHVlIjoiZ0t1QThpSkljcDdDYzRxc1ZjNm0vT1FVTHRtejJETVVhTUd4RjFvdGh5M05ySDBDM0h3a2Y4N3dGc0w2U0lDZSIsIm1hYyI6IjQ1MjM5YzdjN2Y4NGNiNzRlNzJkMjM3ODZjOTEzMWY2ZDEwMzZiMzE3NTdhZjY5MGVjZmY4MWRlYmIzZDliOGQiLCJ0YWciOiIifQ%3D%3D; expires=Mon, 12-May-2025 03:36:56 GMT; path=/; httponly ◀lang_schoolap=eyJpdiI6IkdyMDFxM3R0bjZ3MFdYZThVeDcweGc9PSIsInZhbHVlIjoiZ0t1QThpSkljcDdDYzRxc1ZjNm0vT1FVTHRtejJETVVhTUd4RjFvdGh5M05ySDBDM0h3a2Y4N3dGc0w2U0lDZSIsIm ▶"
    1 => "XSRF-TOKEN=eyJpdiI6IklEWUtlVlZjQnZSNXVHQTFkWHhCR1E9PSIsInZhbHVlIjoidmxBaVVxTXNoRFlZenFQWFBqZGZ2dHk1cm9WQlJVR250SGJYZHlUVm90TGJNUVNLT2c4RU10NVBUcDdvMDRpOFZsc01NVFdJTlQ3aC9qeDFtREFDM3MrR2VlMW5UcGU5bWdGSGJMOEgvcGpmNWcvMlRmN1E3cVlvUzFVaHRwd3YiLCJtYWMiOiJkNGZhNWY4ODJkMGMwZjMwMjgwMDdlYjdlYmMwZGIwNWZhNDkzNjExM2MwNGIzOTFhY2Q0OTZjOWU2OTU3OWViIiwidGFnIjoiIn0%3D; expires=Mon, 05-May-2025 06:56:56 GMT; path=/ ◀XSRF-TOKEN=eyJpdiI6IklEWUtlVlZjQnZSNXVHQTFkWHhCR1E9PSIsInZhbHVlIjoidmxBaVVxTXNoRFlZenFQWFBqZGZ2dHk1cm9WQlJVR250SGJYZHlUVm90TGJNUVNLT2c4RU10NVBUcDdvMDRpOFZsc01NV ▶"
    2 => "schoolap_session=eyJpdiI6IkJZaWMwS3JXMzBzbjAxQVp4UGV2R3c9PSIsInZhbHVlIjoiWElTR3Q2WityN1diWjBrUXB0N21qMVQ3NWk0RG5Fc3pCaGdOWW14Z1JtcStjWUIra3JiNGd5QWpzbHZHb1B5MUJZM0g3OHpVN1BXdXExM01QZFVBTE12RGg4R29LNi9OV1BQdTY0TStnN005TVB4SlJMRDVQZlp1T1p2dUFTU1ciLCJtYWMiOiIyM2E0NTIwNTY3NTFhOGI0MGNkMjY4Y2FlNTdhNjNmYTU2YWU4MmJkMTJiZDZiNTg5MGUxYzMyZWZmMGE2ODM0IiwidGFnIjoiIn0%3D; expires=Mon, 05-May-2025 06:56:56 GMT; path=/; httponly ◀schoolap_session=eyJpdiI6IkJZaWMwS3JXMzBzbjAxQVp4UGV2R3c9PSIsInZhbHVlIjoiWElTR3Q2WityN1diWjBrUXB0N21qMVQ3NWk0RG5Fc3pCaGdOWW14Z1JtcStjWUIra3JiNGd5QWpzbHZHb1B5MUJ ▶"
  ]
]
        session_attributes
          0 of 0   
        array:5 [▼
  "_token" => "gnRbGUBeEcPjP3lpcMXq8H5z3VzX75hFrXSceuA9"
  "applocale" => "en"
  "_previous" => array:1 [▶
    "url" => "https://s8.schoolap.com/fiches/846/les-grandeurs-et-leurs-unites"
  ]
  "_flash" => array:2 [▶
    "old" => []
    "new" => []
  ]
  "PHPDEBUGBAR_STACK_DATA" => []
]