gdz.top
Номер 6.6, страница 34 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Механика. 6. Гидростатика и аэростатика - номер 6.6, страница 34.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288123 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1048 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:4 [ 0 => App\Models\Term {#1052 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1054 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" …1 ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:3 [ 0 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, zadachnik" ] #original: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Term {#1066 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Term {#1068 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #original: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1056} "field_author" => Illuminate\Database\Eloquent\Collection {#1058} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1062} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_country" => Illuminate\Database\Eloquent\Collection {#1065} "field_city" => Illuminate\Database\Eloquent\Collection {#1067} "field_series" => Illuminate\Database\Eloquent\Collection {#1069} "field_umk" => Illuminate\Database\Eloquent\Collection {#1070} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:3 [ 0 => App\Models\Branch {#1198 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1199 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1199} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1200} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1202 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1203} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1204} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1205} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1206 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287873 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "6. Гидростатика и аэростатика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1207 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "34" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1285 #items: array:1 [ 0 => App\Models\Branch {#1209 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1210 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1210} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1245} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287873 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "6. Гидростатика и аэростатика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1207} "field_page_start" => "34" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1208} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1285} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:3 [ 0 => App\Models\Element {#1181 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1477898 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Edition {#1180 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1179 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1177 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1175 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1179} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1177} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1175} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "text" => "<p><strong>6.6**.</strong> Как изменятся уровни жидкостей после открывания крана (см. задачу 6.5), если спирт заменить керосином? Керосин имеет ту же плотность, что и спирт, но, в отличие от него, не смешивается с водой. Капиллярные эффекты не учитывайте.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1461" "height" => 284 "path" => "/media/fizika_08/gelfgat-u/0-06/6-1.webp?ts=1756049756" ] ] ] #original: array:7 [ "id" => 1477898 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173} "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "text" => "<p><strong>6.6**.</strong> Как изменятся уровни жидкостей после открывания крана (см. задачу 6.5), если спирт заменить керосином? Керосин имеет ту же плотность, что и спирт, но, в отличие от него, не смешивается с водой. Капиллярные эффекты не учитывайте.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1461" "height" => 284 "path" => "/media/fizika_08/gelfgat-u/0-06/6-1.webp?ts=1756049756" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1174 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1478389 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:1 [ 0 => App\Models\Edition {#1172 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1168 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1171} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1168} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1438" "height" => 996 "path" => "/media/fizika_08/gelfgat-u/1-06/6-1.webp?ts=1756049818" ] ] ] #original: array:6 [ "id" => 1478389 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1165} "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1438" "height" => 996 "path" => "/media/fizika_08/gelfgat-u/1-06/6-1.webp?ts=1756049818" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1163 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1737816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Edition {#1166 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1162 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1161} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1162} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1156} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1160} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "text" => "<p>В данной задаче рассматривается система сообщающихся сосудов, в одном из которых находится вода, а в другом — керосин. Плотность керосина ($ \rho_к $) меньше плотности воды ($ \rho_в $), и эти жидкости не смешиваются. Проанализируем, как изменятся уровни жидкостей после открытия крана, соединяющего сосуды.</p><p><strong>Дано:</strong></p><p>Начальная высота столба воды: $ h_в = H $<br>Начальная высота столба керосина: $ h_к = H $<br>Плотность воды: $ \rho_в $<br>Плотность керосина: $ \rho_к $<br>Из условия известно, что $ \rho_к < \rho_в $. Сосуды имеют одинаковую площадь поперечного сечения $ S $.</p><p><strong>Найти:</strong></p><p>Изменение уровней воды $ \Delta h_в $ и керосина $ \Delta h_к $.</p><p><strong>Решение:</strong><br>В начальном состоянии жидкости разделены краном, и их уровни в обоих сосудах одинаковы и равны $ H $.</p><p>После открытия крана система придет в состояние равновесия. Так как керосин имеет меньшую плотность, он окажется наверху, а более плотная вода — внизу. Поскольку жидкости не смешиваются, они разделятся: вода займет нижнюю часть обоих сосудов и соединительную трубку, а весь керосин соберется в одном из сосудов поверх воды.</p><p>Для расчета конечных уровней введем систему координат. Пусть ось $ y $ направлена вертикально вверх, а начало отсчета $ y=0 $ находится на уровне дна сосудов. Будем считать, что керосин собрался в левом сосуде.</p><p>Обозначим: </p><ul><li>$ y_{гр} $ — высота границы раздела воды и керосина в левом сосуде.</li><li>$ y_в $ — конечная высота уровня воды в правом сосуде.</li><li>$ y_к $ — конечная высота уровня керосина в левом сосуде.</li></ul><p></p><p>Условие гидростатического равновесия заключается в равенстве давлений на любом горизонтальном уровне. Запишем это условие для уровня границы раздела жидкостей $ y_{гр} $: $ P_{атм} + \rho_к g (y_к - y_{гр}) = P_{атм} + \rho_в g (y_в - y_{гр}) $ $ \rho_к (y_к - y_{гр}) = \rho_в (y_в - y_{гр}) $ (1)</p><p>Теперь используем закон сохранения объема для каждой жидкости. Начальный объем керосина был $ V_к = S \cdot H $. В конечном состоянии он занимает объем в левом сосуде от $ y_{гр} $ до $ y_к $: $ S \cdot H = S \cdot (y_к - y_{гр}) \implies y_к - y_{гр} = H $ (2)</p><p>Начальный объем воды был $ V_в = S \cdot H $. В конечном состоянии вода занимает объем в левом сосуде до уровня $ y_{гр} $ и в правом сосуде до уровня $ y_в $: $ S \cdot H = S \cdot y_{гр} + S \cdot y_в \implies H = y_{гр} + y_в $ (3)</p><p>Получили систему из трех уравнений. Подставим (2) в (1): $ \rho_к H = \rho_в (y_в - y_{гр}) $</p><p>Из уравнения (3) выразим $ y_в = H - y_{гр} $ и подставим в предыдущее выражение: $ \rho_к H = \rho_в ( (H - y_{гр}) - y_{гр} ) $ $ \rho_к H = \rho_в (H - 2y_{гр}) $</p><p>Выразим отсюда высоту границы раздела $ y_{гр} $: $ \frac{\rho_к}{\rho_в} H = H - 2y_{гр} $ $ 2y_{гр} = H - H \frac{\rho_к}{\rho_в} $ $ y_{гр} = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $</p><p>Теперь найдем конечные уровни жидкостей. Конечный уровень воды в правом сосуде: $ y_в = H - y_{гр} = H - \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 - \frac{1}{2} + \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) $</p><p>Конечный уровень керосина в левом сосуде: $ y_к = H + y_{гр} = H + \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 + \frac{1}{2} - \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) $</p><p>Сравним конечные уровни с начальным уровнем $ H $. Изменение уровня воды: $ \Delta h_в = y_в - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(\frac{\rho_к}{\rho_в} - 1\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_в < 0 $. Уровень воды понизится.</p><p>Изменение уровня керосина: $ \Delta h_к = y_к - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_к > 0 $. Уровень керосина повысится.</p><p><strong>Ответ:</strong><br>После открытия крана уровень воды в одном сосуде понизится, а уровень керосина в другом сосуде повысится. Уровень воды опустится на величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, а уровень керосина поднимется на ту же величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, где $ H $ — начальная высота столбов жидкостей, $ \rho_в $ — плотность воды, $ \rho_к $ — плотность керосина.</p>" ] #original: array:6 [ "id" => 1737816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1157} "task" => array:2 [ "refs" => "1288123" "type" => "task" ] "text" => "<p>В данной задаче рассматривается система сообщающихся сосудов, в одном из которых находится вода, а в другом — керосин. Плотность керосина ($ \rho_к $) меньше плотности воды ($ \rho_в $), и эти жидкости не смешиваются. Проанализируем, как изменятся уровни жидкостей после открытия крана, соединяющего сосуды.</p><p><strong>Дано:</strong></p><p>Начальная высота столба воды: $ h_в = H $<br>Начальная высота столба керосина: $ h_к = H $<br>Плотность воды: $ \rho_в $<br>Плотность керосина: $ \rho_к $<br>Из условия известно, что $ \rho_к < \rho_в $. Сосуды имеют одинаковую площадь поперечного сечения $ S $.</p><p><strong>Найти:</strong></p><p>Изменение уровней воды $ \Delta h_в $ и керосина $ \Delta h_к $.</p><p><strong>Решение:</strong><br>В начальном состоянии жидкости разделены краном, и их уровни в обоих сосудах одинаковы и равны $ H $.</p><p>После открытия крана система придет в состояние равновесия. Так как керосин имеет меньшую плотность, он окажется наверху, а более плотная вода — внизу. Поскольку жидкости не смешиваются, они разделятся: вода займет нижнюю часть обоих сосудов и соединительную трубку, а весь керосин соберется в одном из сосудов поверх воды.</p><p>Для расчета конечных уровней введем систему координат. Пусть ось $ y $ направлена вертикально вверх, а начало отсчета $ y=0 $ находится на уровне дна сосудов. Будем считать, что керосин собрался в левом сосуде.</p><p>Обозначим: </p><ul><li>$ y_{гр} $ — высота границы раздела воды и керосина в левом сосуде.</li><li>$ y_в $ — конечная высота уровня воды в правом сосуде.</li><li>$ y_к $ — конечная высота уровня керосина в левом сосуде.</li></ul><p></p><p>Условие гидростатического равновесия заключается в равенстве давлений на любом горизонтальном уровне. Запишем это условие для уровня границы раздела жидкостей $ y_{гр} $: $ P_{атм} + \rho_к g (y_к - y_{гр}) = P_{атм} + \rho_в g (y_в - y_{гр}) $ $ \rho_к (y_к - y_{гр}) = \rho_в (y_в - y_{гр}) $ (1)</p><p>Теперь используем закон сохранения объема для каждой жидкости. Начальный объем керосина был $ V_к = S \cdot H $. В конечном состоянии он занимает объем в левом сосуде от $ y_{гр} $ до $ y_к $: $ S \cdot H = S \cdot (y_к - y_{гр}) \implies y_к - y_{гр} = H $ (2)</p><p>Начальный объем воды был $ V_в = S \cdot H $. В конечном состоянии вода занимает объем в левом сосуде до уровня $ y_{гр} $ и в правом сосуде до уровня $ y_в $: $ S \cdot H = S \cdot y_{гр} + S \cdot y_в \implies H = y_{гр} + y_в $ (3)</p><p>Получили систему из трех уравнений. Подставим (2) в (1): $ \rho_к H = \rho_в (y_в - y_{гр}) $</p><p>Из уравнения (3) выразим $ y_в = H - y_{гр} $ и подставим в предыдущее выражение: $ \rho_к H = \rho_в ( (H - y_{гр}) - y_{гр} ) $ $ \rho_к H = \rho_в (H - 2y_{гр}) $</p><p>Выразим отсюда высоту границы раздела $ y_{гр} $: $ \frac{\rho_к}{\rho_в} H = H - 2y_{гр} $ $ 2y_{гр} = H - H \frac{\rho_к}{\rho_в} $ $ y_{гр} = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $</p><p>Теперь найдем конечные уровни жидкостей. Конечный уровень воды в правом сосуде: $ y_в = H - y_{гр} = H - \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 - \frac{1}{2} + \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) $</p><p>Конечный уровень керосина в левом сосуде: $ y_к = H + y_{гр} = H + \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 + \frac{1}{2} - \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) $</p><p>Сравним конечные уровни с начальным уровнем $ H $. Изменение уровня воды: $ \Delta h_в = y_в - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(\frac{\rho_к}{\rho_в} - 1\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_в < 0 $. Уровень воды понизится.</p><p>Изменение уровня керосина: $ \Delta h_к = y_к - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_к > 0 $. Уровень керосина повысится.</p><p><strong>Ответ:</strong><br>После открытия крана уровень воды в одном сосуде понизится, а уровень керосина в другом сосуде повысится. Уровень воды опустится на величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, а уровень керосина поднимется на ту же величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, где $ H $ — начальная высота столбов жидкостей, $ \rho_в $ — плотность воды, $ \rho_к $ — плотность керосина.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1288124" "type" => "task" ] "previous" => array:2 [ "refs" => "1288122" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\BookPage {#1150 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1340385 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-34" "field_display_title" => "34" "field_folder" => "1" "field_image_name" => "34" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1186 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1159 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Element {#1145 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1518506 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1143 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1518506 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1143 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1340386" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340384" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1362 #items: array:6 [ 0 => App\Models\Task {#1374 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288118 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-1" "field_display_title" => "6.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1375 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1376 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1377 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1378 …2} "content" => Illuminate\Database\Eloquent\Collection {#1381 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1387 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288118 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-1" "field_display_title" => "6.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1375 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1376 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1377 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1378 …2} "content" => Illuminate\Database\Eloquent\Collection {#1381 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1387 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1380 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288119 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-2" "field_display_title" => "6.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1386 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1384 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1401 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288119 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-2" "field_display_title" => "6.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1386 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1384 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1401 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1385 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288120 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-3" "field_display_title" => "6.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1382 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1400 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1402 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1398 …2} "content" => Illuminate\Database\Eloquent\Collection {#1397 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1415 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288120 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-3" "field_display_title" => "6.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1382 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1400 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1402 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1398 …2} "content" => Illuminate\Database\Eloquent\Collection {#1397 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1415 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1399 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288121 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-4" "field_display_title" => "6.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1396 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1414 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1412 …2} "content" => Illuminate\Database\Eloquent\Collection {#1411 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1429 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288121 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-4" "field_display_title" => "6.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1396 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1414 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1416 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1412 …2} "content" => Illuminate\Database\Eloquent\Collection {#1411 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1429 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1413 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-5" "field_display_title" => "6.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1410 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1428 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1430 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1426 …2} "content" => Illuminate\Database\Eloquent\Collection {#1425 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1443 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-5" "field_display_title" => "6.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1410 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1428 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1430 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1426 …2} "content" => Illuminate\Database\Eloquent\Collection {#1425 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1443 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1427 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288123 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1424 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1442 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1444 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1440 …2} "content" => Illuminate\Database\Eloquent\Collection {#1438 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1441 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288123 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1424 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1442 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1444 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1440 …2} "content" => Illuminate\Database\Eloquent\Collection {#1438 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1441 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1340385 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-34" "field_display_title" => "34" "field_folder" => "1" "field_image_name" => "34" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1186} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1159} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158} "content" => Illuminate\Database\Eloquent\Collection {#1144} "next" => array:2 [ "refs" => "1340386" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340384" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1362} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1288123 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "34" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188} "content" => Illuminate\Database\Eloquent\Collection {#1149} "next" => array:2 [ "refs" => "1288124" "type" => "task" ] "previous" => array:2 [ "refs" => "1288122" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1185} "page" => array:2 [ "refs" => "1340385" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№6.6 (с. 34)
Условие. №6.6 (с. 34)
скриншот условия
6.6**. Как изменятся уровни жидкостей после открывания крана (см. задачу 6.5), если спирт заменить керосином? Керосин имеет ту же плотность, что и спирт, но, в отличие от него, не смешивается с водой. Капиллярные эффекты не учитывайте.
Решение. №6.6 (с. 34)
Решение 2. №6.6 (с. 34)
В данной задаче рассматривается система сообщающихся сосудов, в одном из которых находится вода, а в другом — керосин. Плотность керосина ($ \rho_к $) меньше плотности воды ($ \rho_в $), и эти жидкости не смешиваются. Проанализируем, как изменятся уровни жидкостей после открытия крана, соединяющего сосуды.
Дано:
Начальная высота столба воды: $ h_в = H $
Начальная высота столба керосина: $ h_к = H $
Плотность воды: $ \rho_в $
Плотность керосина: $ \rho_к $
Из условия известно, что $ \rho_к < \rho_в $. Сосуды имеют одинаковую площадь поперечного сечения $ S $.
Найти:
Изменение уровней воды $ \Delta h_в $ и керосина $ \Delta h_к $.
Решение:
В начальном состоянии жидкости разделены краном, и их уровни в обоих сосудах одинаковы и равны $ H $.
После открытия крана система придет в состояние равновесия. Так как керосин имеет меньшую плотность, он окажется наверху, а более плотная вода — внизу. Поскольку жидкости не смешиваются, они разделятся: вода займет нижнюю часть обоих сосудов и соединительную трубку, а весь керосин соберется в одном из сосудов поверх воды.
Для расчета конечных уровней введем систему координат. Пусть ось $ y $ направлена вертикально вверх, а начало отсчета $ y=0 $ находится на уровне дна сосудов. Будем считать, что керосин собрался в левом сосуде.
Обозначим:
- $ y_{гр} $ — высота границы раздела воды и керосина в левом сосуде.
- $ y_в $ — конечная высота уровня воды в правом сосуде.
- $ y_к $ — конечная высота уровня керосина в левом сосуде.
Условие гидростатического равновесия заключается в равенстве давлений на любом горизонтальном уровне. Запишем это условие для уровня границы раздела жидкостей $ y_{гр} $: $ P_{атм} + \rho_к g (y_к - y_{гр}) = P_{атм} + \rho_в g (y_в - y_{гр}) $ $ \rho_к (y_к - y_{гр}) = \rho_в (y_в - y_{гр}) $ (1)
Теперь используем закон сохранения объема для каждой жидкости. Начальный объем керосина был $ V_к = S \cdot H $. В конечном состоянии он занимает объем в левом сосуде от $ y_{гр} $ до $ y_к $: $ S \cdot H = S \cdot (y_к - y_{гр}) \implies y_к - y_{гр} = H $ (2)
Начальный объем воды был $ V_в = S \cdot H $. В конечном состоянии вода занимает объем в левом сосуде до уровня $ y_{гр} $ и в правом сосуде до уровня $ y_в $: $ S \cdot H = S \cdot y_{гр} + S \cdot y_в \implies H = y_{гр} + y_в $ (3)
Получили систему из трех уравнений. Подставим (2) в (1): $ \rho_к H = \rho_в (y_в - y_{гр}) $
Из уравнения (3) выразим $ y_в = H - y_{гр} $ и подставим в предыдущее выражение: $ \rho_к H = \rho_в ( (H - y_{гр}) - y_{гр} ) $ $ \rho_к H = \rho_в (H - 2y_{гр}) $
Выразим отсюда высоту границы раздела $ y_{гр} $: $ \frac{\rho_к}{\rho_в} H = H - 2y_{гр} $ $ 2y_{гр} = H - H \frac{\rho_к}{\rho_в} $ $ y_{гр} = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $
Теперь найдем конечные уровни жидкостей. Конечный уровень воды в правом сосуде: $ y_в = H - y_{гр} = H - \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 - \frac{1}{2} + \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) $
Конечный уровень керосина в левом сосуде: $ y_к = H + y_{гр} = H + \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) = H \left(1 + \frac{1}{2} - \frac{\rho_к}{2\rho_в}\right) = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) $
Сравним конечные уровни с начальным уровнем $ H $. Изменение уровня воды: $ \Delta h_в = y_в - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(1 + \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(\frac{\rho_к}{\rho_в} - 1\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_в < 0 $. Уровень воды понизится.
Изменение уровня керосина: $ \Delta h_к = y_к - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в}\right) - H = \frac{H}{2} \left(3 - \frac{\rho_к}{\rho_в} - 2\right) = \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $ Так как $ \rho_к < \rho_в $, то $ \frac{\rho_к}{\rho_в} < 1 $, следовательно, $ \Delta h_к > 0 $. Уровень керосина повысится.
Ответ:
После открытия крана уровень воды в одном сосуде понизится, а уровень керосина в другом сосуде повысится. Уровень воды опустится на величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, а уровень керосина поднимется на ту же величину $ \frac{H}{2} \left(1 - \frac{\rho_к}{\rho_в}\right) $, где $ H $ — начальная высота столбов жидкостей, $ \rho_в $ — плотность воды, $ \rho_к $ — плотность керосина.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 8-11 класс, для упражнения номер 6.6 расположенного на странице 34 к учебнику, задачнику 2005 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №6.6 (с. 34), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), учебного пособия издательства Илекса.