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Номер 3.8, страница 142 - 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
Тесты. Третий уровень - номер 3.8, страница 142.
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" => 1288891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-8" "field_display_title" => "3.8" "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" => 1287894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тесты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "136" "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" "field_prepositional_case" => "десятом" ] "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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 [ "field_accusative_case" => "учебник, задачник" "field_creative_case" => "учебником, задачником" "field_dative_case" => "учебнику, задачнику" "field_genitive_case" => "учебника, задачника" "field_nominative_case" => "учебник, задачник" "field_prepositional_case" => "учебнике, задачнике" ] "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 [ "field_accusative_case" => "учебник, задачник" "field_creative_case" => "учебником, задачником" "field_dative_case" => "учебнику, задачнику" "field_genitive_case" => "учебника, задачника" "field_nominative_case" => "учебник, задачник" "field_prepositional_case" => "учебнике, задачнике" ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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" => 1287894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тесты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "136" "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 {#1115 #items: array:2 [ 0 => App\Models\Branch {#1123 #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" => 1287894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тесты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "136" "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 {#1125 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тесты" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124} "field_page_start" => "136" "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 {#1125} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126} ] #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 {#1127 #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" => 1287897 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Третий уровень" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "141" "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 {#1129 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287897 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Третий уровень" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_page_start" => "141" "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 {#1129} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1112 #items: array:3 [ 0 => App\Models\Element {#1104 #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" => 1479423 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Edition {#1105 #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 {#1102 #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 {#1101 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1098 #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 {#1102} "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 {#1101} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1098} "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" => "1288891" "type" => "task" ] "text" => "<p><strong>Т 3.8.</strong> На рисунке показано положение столбика ртути длиной 10 см в вертикально расположенной трубке длиной 90 см. Трубка герметично закрыта с обоих концов. Если ее расположить горизонтально, столбик ртути переместится в середину трубки. Каким станет при этом давление в трубке? Температуру считайте постоянной.</p><p><strong>А.</strong> 23 см рт. ст.</p><p><strong>Б.</strong> 38 см рт. ст.</p><p><strong>В.</strong> 10 см рт. ст.</p><p><strong>Г.</strong> 19 см рт. ст.</p><p><strong>Д.</strong> Среди ответов А-Г нет правильного.</p><p>К месту 3.8</p>" "img" => array:2 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1156" "height" => 506 "path" => "/media/fizika_08/gelfgat-u/0-test3/8-1.webp?ts=1756050204" ] 1 => array:5 [ "name" => "8-2.jpg" "alt" => null "width" => "276" "height" => 797 "path" => "/media/fizika_08/gelfgat-u/0-test3/8-2.webp?ts=1756050204" ] ] ] #original: array:7 [ "id" => 1479423 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1097} "task" => array:2 [ "refs" => "1288891" "type" => "task" ] "text" => "<p><strong>Т 3.8.</strong> На рисунке показано положение столбика ртути длиной 10 см в вертикально расположенной трубке длиной 90 см. Трубка герметично закрыта с обоих концов. Если ее расположить горизонтально, столбик ртути переместится в середину трубки. Каким станет при этом давление в трубке? Температуру считайте постоянной.</p><p><strong>А.</strong> 23 см рт. ст.</p><p><strong>Б.</strong> 38 см рт. ст.</p><p><strong>В.</strong> 10 см рт. ст.</p><p><strong>Г.</strong> 19 см рт. ст.</p><p><strong>Д.</strong> Среди ответов А-Г нет правильного.</p><p>К месту 3.8</p>" "img" => array:2 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1156" "height" => 506 "path" => "/media/fizika_08/gelfgat-u/0-test3/8-1.webp?ts=1756050204" ] 1 => array:5 [ "name" => "8-2.jpg" "alt" => null "width" => "276" "height" => 797 "path" => "/media/fizika_08/gelfgat-u/0-test3/8-2.webp?ts=1756050204" ] ] ] #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 {#1099 #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" => 1479667 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Edition {#1096 #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 {#1095 #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 {#1093 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #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 {#1095} "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 {#1093} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "1288891" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "447" "height" => 114 "path" => "/media/fizika_08/gelfgat-u/1-test3/8-1.webp?ts=1756050274" ] ] ] #original: array:6 [ "id" => 1479667 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1087} "task" => array:2 [ "refs" => "1288891" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "447" "height" => 114 "path" => "/media/fizika_08/gelfgat-u/1-test3/8-1.webp?ts=1756050274" ] ] ] #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 {#1091 #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" => 1738584 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Edition {#1090 #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 {#1041 #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 {#1086 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #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 {#1041} "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 {#1086} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "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" => "1288891" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина столбика ртути $h_{рт} = 10$ см</p><p>Общая длина трубки $L = 90$ см</p><p>Начальная длина нижнего столбика воздуха $L_1 = 30$ см</p><p>Начальная длина верхнего столбика воздуха $L_2 = 50$ см</p><p>$T = \text{const}$ (процесс изотермический)</p><p>Перевод данных в систему СИ:</p><p>$h_{рт} = 10 \text{ см} = 0.1 \text{ м}$</p><p>$L = 90 \text{ см} = 0.9 \text{ м}$</p><p>$L_1 = 30 \text{ см} = 0.3 \text{ м}$</p><p>$L_2 = 50 \text{ см} = 0.5 \text{ м}$</p><p><strong>Найти:</strong></p><p>$P'$ — давление в трубке в горизонтальном положении.</p><p><strong>Решение:</strong></p><p>Поскольку ответы даны в сантиметрах ртутного столба (см рт. ст.), для удобства все вычисления будем производить в этих единицах, используя длины в сантиметрах.</p><p>В начальном (вертикальном) положении столбик ртути находится в равновесии. Это означает, что давление нижнего столбика воздуха $P_1$ уравновешивает давление верхнего столбика воздуха $P_2$ и давление самого столбика ртути $P_{рт}$.</p><p>Давление столбика ртути равно его высоте: $P_{рт} = h_{рт} = 10$ см рт. ст.</p><p>Условие равновесия имеет вид: $P_1 = P_2 + P_{рт}$, или</p><p>$P_1 = P_2 + 10$ (1)</p><p>Когда трубку располагают горизонтально, столбик ртути перемещается в середину. Общая длина, доступная для воздуха, составляет $L_{воздуха} = L - h_{рт} = 90 - 10 = 80$ см. Так как столбик ртути находится посередине, длина каждого столбика воздуха становится одинаковой:</p><p>$L'_1 = L'_2 = L' = \frac{80}{2} = 40$ см.</p><p>В горизонтальном положении вес ртути не создаёт разности давлений между столбиками воздуха, поэтому их давления становятся равными: $P'_1 = P'_2 = P'$.</p><p>Процесс происходит при постоянной температуре, поэтому для каждого столбика воздуха можно применить закон Бойля-Мариотта ($PV = \text{const}$). Так как площадь поперечного сечения трубки $\text{S}$ постоянна ($V = S \cdot L_{воздуха}$), закон можно записать в виде $P \cdot L_{воздуха} = \text{const}$.</p><p>Для первого (изначально нижнего) столбика воздуха:</p><p>$P_1 L_1 = P' L'$</p><p>$P_1 \cdot 30 = P' \cdot 40$ (2)</p><p>Для второго (изначально верхнего) столбика воздуха:</p><p>$P_2 L_2 = P' L'$</p><p>$P_2 \cdot 50 = P' \cdot 40$ (3)</p><p>Теперь решим систему из трех уравнений (1), (2), (3) для нахождения $P'$.</p><p>Из уравнений (2) и (3) выразим $P_1$ и $P_2$ через $P'$:</p><p>$P_1 = \frac{40}{30} P' = \frac{4}{3} P'$</p><p>$P_2 = \frac{40}{50} P' = \frac{4}{5} P'$</p><p>Подставим эти выражения в уравнение (1):</p><p>$\frac{4}{3} P' = \frac{4}{5} P' + 10$</p><p>Перенесем слагаемые с $P'$ в левую часть:</p><p>$\frac{4}{3} P' - \frac{4}{5} P' = 10$</p><p>Приведем к общему знаменателю:</p><p>$(\frac{20}{15} - \frac{12}{15}) P' = 10$</p><p>$\frac{8}{15} P' = 10$</p><p>$P' = 10 \cdot \frac{15}{8} = \frac{150}{8} = \frac{75}{4} = 18.75$ см рт. ст.</p><p>Полученное значение $18.75$ см рт. ст. наиболее близко к варианту ответа Г (19 см рт. ст.).</p><p><strong>Ответ:</strong></p><p>Давление в трубке станет $18.75$ см рт. ст. Среди предложенных вариантов наиболее близким является Г (19 см рт. ст.).</p>" ] #original: array:6 [ "id" => 1738584 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1043} "task" => array:2 [ "refs" => "1288891" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина столбика ртути $h_{рт} = 10$ см</p><p>Общая длина трубки $L = 90$ см</p><p>Начальная длина нижнего столбика воздуха $L_1 = 30$ см</p><p>Начальная длина верхнего столбика воздуха $L_2 = 50$ см</p><p>$T = \text{const}$ (процесс изотермический)</p><p>Перевод данных в систему СИ:</p><p>$h_{рт} = 10 \text{ см} = 0.1 \text{ м}$</p><p>$L = 90 \text{ см} = 0.9 \text{ м}$</p><p>$L_1 = 30 \text{ см} = 0.3 \text{ м}$</p><p>$L_2 = 50 \text{ см} = 0.5 \text{ м}$</p><p><strong>Найти:</strong></p><p>$P'$ — давление в трубке в горизонтальном положении.</p><p><strong>Решение:</strong></p><p>Поскольку ответы даны в сантиметрах ртутного столба (см рт. ст.), для удобства все вычисления будем производить в этих единицах, используя длины в сантиметрах.</p><p>В начальном (вертикальном) положении столбик ртути находится в равновесии. Это означает, что давление нижнего столбика воздуха $P_1$ уравновешивает давление верхнего столбика воздуха $P_2$ и давление самого столбика ртути $P_{рт}$.</p><p>Давление столбика ртути равно его высоте: $P_{рт} = h_{рт} = 10$ см рт. ст.</p><p>Условие равновесия имеет вид: $P_1 = P_2 + P_{рт}$, или</p><p>$P_1 = P_2 + 10$ (1)</p><p>Когда трубку располагают горизонтально, столбик ртути перемещается в середину. Общая длина, доступная для воздуха, составляет $L_{воздуха} = L - h_{рт} = 90 - 10 = 80$ см. Так как столбик ртути находится посередине, длина каждого столбика воздуха становится одинаковой:</p><p>$L'_1 = L'_2 = L' = \frac{80}{2} = 40$ см.</p><p>В горизонтальном положении вес ртути не создаёт разности давлений между столбиками воздуха, поэтому их давления становятся равными: $P'_1 = P'_2 = P'$.</p><p>Процесс происходит при постоянной температуре, поэтому для каждого столбика воздуха можно применить закон Бойля-Мариотта ($PV = \text{const}$). Так как площадь поперечного сечения трубки $\text{S}$ постоянна ($V = S \cdot L_{воздуха}$), закон можно записать в виде $P \cdot L_{воздуха} = \text{const}$.</p><p>Для первого (изначально нижнего) столбика воздуха:</p><p>$P_1 L_1 = P' L'$</p><p>$P_1 \cdot 30 = P' \cdot 40$ (2)</p><p>Для второго (изначально верхнего) столбика воздуха:</p><p>$P_2 L_2 = P' L'$</p><p>$P_2 \cdot 50 = P' \cdot 40$ (3)</p><p>Теперь решим систему из трех уравнений (1), (2), (3) для нахождения $P'$.</p><p>Из уравнений (2) и (3) выразим $P_1$ и $P_2$ через $P'$:</p><p>$P_1 = \frac{40}{30} P' = \frac{4}{3} P'$</p><p>$P_2 = \frac{40}{50} P' = \frac{4}{5} P'$</p><p>Подставим эти выражения в уравнение (1):</p><p>$\frac{4}{3} P' = \frac{4}{5} P' + 10$</p><p>Перенесем слагаемые с $P'$ в левую часть:</p><p>$\frac{4}{3} P' - \frac{4}{5} P' = 10$</p><p>Приведем к общему знаменателю:</p><p>$(\frac{20}{15} - \frac{12}{15}) P' = 10$</p><p>$\frac{8}{15} P' = 10$</p><p>$P' = 10 \cdot \frac{15}{8} = \frac{150}{8} = \frac{75}{4} = 18.75$ см рт. ст.</p><p>Полученное значение $18.75$ см рт. ст. наиболее близко к варианту ответа Г (19 см рт. ст.).</p><p><strong>Ответ:</strong></p><p>Давление в трубке станет $18.75$ см рт. ст. Среди предложенных вариантов наиболее близким является Г (19 см рт. ст.).</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" => "1288892" "type" => "task" ] "previous" => array:2 [ "refs" => "1288890" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\BookPage {#1039 #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" => 1340493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-142" "field_display_title" => "142" "field_folder" => "1" "field_image_name" => "142" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #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 {#1040 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Element {#1131 #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" => 1518614 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1340493" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1518614 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1133} "book_page" => array:2 [ "refs" => "1340493" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1340494" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340492" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:6 [ 0 => App\Models\Task {#1218 #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" => 1288889 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-6" "field_display_title" => "3.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ …1] #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 {#1220 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1288890" "type" => "task" ] "previous" => array:2 [ "refs" => "1288888" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1340493" "type" => "book_page" ] ] #original: array:24 [ "id" => 1288889 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-6" "field_display_title" => "3.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219} "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 {#1220} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1222} "content" => Illuminate\Database\Eloquent\Collection {#1225} "next" => array:2 [ "refs" => "1288890" "type" => "task" ] "previous" => array:2 [ "refs" => "1288888" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1231} "page" => array:2 [ "refs" => "1340493" "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 => "*" ] } 1 => App\Models\Task {#1224 #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" => 1288890 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-7" "field_display_title" => "3.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ …1] #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 {#1230 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1288891" "type" => "task" ] "previous" => array:2 [ "refs" => "1288889" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1340493" "type" => "book_page" ] ] #original: array:24 [ "id" => 1288890 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-7" "field_display_title" => "3.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1223} "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 {#1230} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228} "content" => Illuminate\Database\Eloquent\Collection {#1227} "next" => array:2 [ "refs" => "1288891" "type" => "task" ] "previous" => array:2 [ "refs" => "1288889" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1245} "page" => array:2 [ "refs" => "1340493" "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 => "*" ] } 2 => App\Models\Task {#1229 #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" => 1288891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-8" "field_display_title" => "3.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ …1] #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 {#1244 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:3 [ …3] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1288892" "type" => "task" ] "previous" => array:2 [ "refs" => "1288890" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1340493" "type" => "book_page" ] ] #original: array:24 [ "id" => 1288891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-8" "field_display_title" => "3.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226} "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 {#1244} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242} "content" => Illuminate\Database\Eloquent\Collection {#1240} "next" => array:2 [ "refs" => "1288892" "type" => "task" ] "previous" => array:2 [ "refs" => "1288890" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1243} "page" => array:2 [ "refs" => "1340493" "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 => "*" ] } 3 => App\Models\Task {#1241 #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" => 1288892 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-9" "field_display_title" => "3.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:1 [ …1] #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 {#1255 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1256 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257 …2} "content" => Illuminate\Database\Eloquent\Collection {#1260 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1266 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288892 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-9" "field_display_title" => "3.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1254} "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 {#1255 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1256 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257 …2} "content" => Illuminate\Database\Eloquent\Collection {#1260 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1266 …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 {#1259 #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" => 1288893 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-10" "field_display_title" => "3.10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …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 {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 …2} "content" => Illuminate\Database\Eloquent\Collection {#1262 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1280 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288893 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-10" "field_display_title" => "3.10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …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 {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 …2} "content" => Illuminate\Database\Eloquent\Collection {#1262 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1280 …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 {#1264 #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" => 1288894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-11" "field_display_title" => "3.11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1279 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1281 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1276 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1294 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-11" "field_display_title" => "3.11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1279 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1281 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 …2} "content" => Illuminate\Database\Eloquent\Collection {#1276 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1294 …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" => 1340493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-142" "field_display_title" => "142" "field_folder" => "1" "field_image_name" => "142" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1042} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082} "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 {#1040} "content" => Illuminate\Database\Eloquent\Collection {#1132} "next" => array:2 [ "refs" => "1340494" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340492" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1206} ] #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" => 1288891 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "142" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/test3-8" "field_display_title" => "3.8" "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 {#1115} "content" => Illuminate\Database\Eloquent\Collection {#1112} "next" => array:2 [ "refs" => "1288892" "type" => "task" ] "previous" => array:2 [ "refs" => "1288890" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1108} "page" => array:2 [ "refs" => "1340493" "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 => "*" ] }
№3.8 (с. 142)
Условие. №3.8 (с. 142)
скриншот условия
Т 3.8. На рисунке показано положение столбика ртути длиной 10 см в вертикально расположенной трубке длиной 90 см. Трубка герметично закрыта с обоих концов. Если ее расположить горизонтально, столбик ртути переместится в середину трубки. Каким станет при этом давление в трубке? Температуру считайте постоянной.
А. 23 см рт. ст.
Б. 38 см рт. ст.
В. 10 см рт. ст.
Г. 19 см рт. ст.
Д. Среди ответов А-Г нет правильного.
К месту 3.8
Решение. №3.8 (с. 142)
Решение 2. №3.8 (с. 142)
Дано:
Длина столбика ртути $h_{рт} = 10$ см
Общая длина трубки $L = 90$ см
Начальная длина нижнего столбика воздуха $L_1 = 30$ см
Начальная длина верхнего столбика воздуха $L_2 = 50$ см
$T = \text{const}$ (процесс изотермический)
Перевод данных в систему СИ:
$h_{рт} = 10 \text{ см} = 0.1 \text{ м}$
$L = 90 \text{ см} = 0.9 \text{ м}$
$L_1 = 30 \text{ см} = 0.3 \text{ м}$
$L_2 = 50 \text{ см} = 0.5 \text{ м}$
Найти:
$P'$ — давление в трубке в горизонтальном положении.
Решение:
Поскольку ответы даны в сантиметрах ртутного столба (см рт. ст.), для удобства все вычисления будем производить в этих единицах, используя длины в сантиметрах.
В начальном (вертикальном) положении столбик ртути находится в равновесии. Это означает, что давление нижнего столбика воздуха $P_1$ уравновешивает давление верхнего столбика воздуха $P_2$ и давление самого столбика ртути $P_{рт}$.
Давление столбика ртути равно его высоте: $P_{рт} = h_{рт} = 10$ см рт. ст.
Условие равновесия имеет вид: $P_1 = P_2 + P_{рт}$, или
$P_1 = P_2 + 10$ (1)
Когда трубку располагают горизонтально, столбик ртути перемещается в середину. Общая длина, доступная для воздуха, составляет $L_{воздуха} = L - h_{рт} = 90 - 10 = 80$ см. Так как столбик ртути находится посередине, длина каждого столбика воздуха становится одинаковой:
$L'_1 = L'_2 = L' = \frac{80}{2} = 40$ см.
В горизонтальном положении вес ртути не создаёт разности давлений между столбиками воздуха, поэтому их давления становятся равными: $P'_1 = P'_2 = P'$.
Процесс происходит при постоянной температуре, поэтому для каждого столбика воздуха можно применить закон Бойля-Мариотта ($PV = \text{const}$). Так как площадь поперечного сечения трубки $\text{S}$ постоянна ($V = S \cdot L_{воздуха}$), закон можно записать в виде $P \cdot L_{воздуха} = \text{const}$.
Для первого (изначально нижнего) столбика воздуха:
$P_1 L_1 = P' L'$
$P_1 \cdot 30 = P' \cdot 40$ (2)
Для второго (изначально верхнего) столбика воздуха:
$P_2 L_2 = P' L'$
$P_2 \cdot 50 = P' \cdot 40$ (3)
Теперь решим систему из трех уравнений (1), (2), (3) для нахождения $P'$.
Из уравнений (2) и (3) выразим $P_1$ и $P_2$ через $P'$:
$P_1 = \frac{40}{30} P' = \frac{4}{3} P'$
$P_2 = \frac{40}{50} P' = \frac{4}{5} P'$
Подставим эти выражения в уравнение (1):
$\frac{4}{3} P' = \frac{4}{5} P' + 10$
Перенесем слагаемые с $P'$ в левую часть:
$\frac{4}{3} P' - \frac{4}{5} P' = 10$
Приведем к общему знаменателю:
$(\frac{20}{15} - \frac{12}{15}) P' = 10$
$\frac{8}{15} P' = 10$
$P' = 10 \cdot \frac{15}{8} = \frac{150}{8} = \frac{75}{4} = 18.75$ см рт. ст.
Полученное значение $18.75$ см рт. ст. наиболее близко к варианту ответа Г (19 см рт. ст.).
Ответ:
Давление в трубке станет $18.75$ см рт. ст. Среди предложенных вариантов наиболее близким является Г (19 см рт. ст.).
Другие задания:
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