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Номер 247, страница 30 - гдз по физике 7-9 класс сборник задач Московкина, Волков
Авторы: Московкина Е. Г., Волков В. А.
Тип: Сборник задач
Издательство: ВАКО
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-408-00459-1
Популярные ГДЗ в 7 классе
7 класс. Сообщающиеся сосуды - номер 247, страница 30.
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" => 1425058 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-247" "field_display_title" => "247" "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 {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #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" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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" => 4994 "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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #connection: "mysql" …29 } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:3 [ 0 => App\Models\Term {#1044 …30} 1 => App\Models\Term {#1045 …30} 2 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:2 [ 0 => App\Models\Term {#1050 …30} 1 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #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" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047} "field_author" => Illuminate\Database\Eloquent\Collection {#1049} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #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 {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "4" "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 {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1108 #items: array:2 [ 0 => App\Models\Branch {#1116 #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" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "4" "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 {#1150 #items: array:1 [ 0 => App\Models\Book {#1118 #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" => 4994 "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 {#1120 #items: array:1 [ 0 => App\Models\Term {#1119 #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 {#1121 #items: array:3 [ 0 => App\Models\Term {#1122 #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" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "field_translit" => "sedmoj" ] #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 {#1123 #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 => "*" ] } 2 => App\Models\Term {#1124 #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 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #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" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #original: array:6 [ "id" => 5227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ВАКО" "field_cases" => null "field_translit" => "vako" ] #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 {#1127 #items: array:2 [ 0 => App\Models\Term {#1128 #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" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5285 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Московкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Елена" "field_patronymic" => "Геннадьевна" "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 {#1129 #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" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4026 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Волков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "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 {#1130 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Term {#1132 #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" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #original: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "сборник задач" "field_creative_case" => "сборником задач" "field_dative_case" => "сборнику задач" "field_genitive_case" => "сборника задач" "field_nominative_case" => "сборник задач" "field_prepositional_case" => "сборнике задач" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #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 {#1133 #items: array:1 [ 0 => App\Models\Term {#1134 #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 {#1135 #items: array:1 [ 0 => App\Models\Term {#1136 #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 {#1137 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1147 #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" => 378 "subject" => 556 "class_subject" => 491 ] ] #original: array:50 [ "id" => 4994 "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 {#1120} "field_class" => Illuminate\Database\Eloquent\Collection {#1121} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1130} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1131} "field_country" => Illuminate\Database\Eloquent\Collection {#1133} "field_city" => Illuminate\Database\Eloquent\Collection {#1135} "field_series" => Illuminate\Database\Eloquent\Collection {#1137} "field_umk" => Illuminate\Database\Eloquent\Collection {#1138} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1141} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => null "field_default_folder" => "/fizika_07/moskovkina-sz/" "field_isbn" => "978-5-408-00459-1" "field_cover" => array:1 [ 0 => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_07/moskovkina-sz/covers/cover1.webp?ts=1758729953" "alt" => "" "width" => "1466" "height" => "2407" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 556 "class_subject" => 491 ] ] #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 {#1148 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424761 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "7 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_page_start" => "4" "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 {#1150} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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 {#1149 #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" => 1424770 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сообщающиеся сосуды" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "29" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424770 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сообщающиеся сосуды" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "29" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #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 {#1071 #items: array:2 [ 0 => 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:7 [ "id" => 1677591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Edition {#1098 #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" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Term {#1097 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6044 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "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" => "1425058" "type" => "task" ] "text" => "<p><strong>247.</strong> В U-образную трубку с вертикальными прямыми коленами налиты керосин и вода (см. рисунок). На рисунке $x = 10 \text{ см}$, $H = 30 \text{ см}$. Определите высоту $\text{h}$ столба воды в левом колене.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "247-1.jpg" "alt" => null "width" => "2621" "height" => 1507 "path" => "/media/fizika_07/moskovkina-sz/0-7/247-1.webp?ts=1758885515" ] ] ] #original: array:7 [ "id" => 1677591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1425058" "type" => "task" ] "text" => "<p><strong>247.</strong> В U-образную трубку с вертикальными прямыми коленами налиты керосин и вода (см. рисунок). На рисунке $x = 10 \text{ см}$, $H = 30 \text{ см}$. Определите высоту $\text{h}$ столба воды в левом колене.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "247-1.jpg" "alt" => null "width" => "2621" "height" => 1507 "path" => "/media/fizika_07/moskovkina-sz/0-7/247-1.webp?ts=1758885515" ] ] ] #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 {#1093 #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" => 1781439 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1088 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1087} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086} "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" => "1425058" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$x = 10 \text{ см} = 0.1 \text{ м}$</p><p>$H = 30 \text{ см} = 0.3 \text{ м}$</p><p>Плотность воды: ${\rho_в} = 1000 \text{ кг/м}^3$</p><p>Плотность керосина: ${\rho_к} = 800 \text{ кг/м}^3$</p><p><strong>Найти:</strong></p><p>$\text{h}$ - ?</p><p><strong>Решение:</strong></p><p>В U-образной трубке находятся две несмешивающиеся жидкости в равновесии. Это задача на закон сообщающихся сосудов. Согласно этому закону, давление на любом горизонтальном уровне в покоящейся жидкости одинаково.</p><p>Выберем в качестве уровня для сравнения давлений горизонтальную линию, проходящую через границу раздела воды и керосина. Эта граница находится в правом колене трубки.</p><p>Давление $p_1$ на этом уровне в левом колене создается столбом воды высотой $(h - x)$ и атмосферным давлением $p_a$ над ним:</p><p>$p_1 = p_a + {\rho_в} g (h - x)$</p><p>Давление $p_2$ на этом же уровне в правом колене создается столбом керосина высотой $(H - x)$ и атмосферным давлением $p_a$:</p><p>$p_2 = p_a + {\rho_к} g (H - x)$</p><p>Поскольку система находится в равновесии, давления на одном и том же горизонтальном уровне должны быть равны:</p><p>$p_1 = p_2$</p><p>$p_a + {\rho_в} g (h - x) = p_a + {\rho_к} g (H - x)$</p><p>Сократим в обеих частях уравнения атмосферное давление $p_a$ и ускорение свободного падения $\text{g}$:</p><p>${\rho_в} (h - x) = {\rho_к} (H - x)$</p><p>Из этого равенства выразим искомую высоту $\text{h}$:</p><p>$h - x = \frac{{\rho_к}}{{\rho_в}} (H - x)$</p><p>$h = x + \frac{{\rho_к}}{{\rho_в}} (H - x)$</p><p>Теперь подставим числовые значения, переведенные в систему СИ:</p><p>$h = 0.1 \text{ м} + \frac{800 \text{ кг/м}^3}{1000 \text{ кг/м}^3} (0.3 \text{ м} - 0.1 \text{ м})$</p><p>$h = 0.1 + 0.8 \cdot 0.2$</p><p>$h = 0.1 + 0.16$</p><p>$h = 0.26 \text{ м}$</p><p>Переведем полученное значение обратно в сантиметры:</p><p>$h = 26 \text{ см}$</p><p><strong>Ответ:</strong> высота столба воды в левом колене $h = 26 \text{ см}$.</p>" ] #original: array:6 [ "id" => 1781439 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1425058" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$x = 10 \text{ см} = 0.1 \text{ м}$</p><p>$H = 30 \text{ см} = 0.3 \text{ м}$</p><p>Плотность воды: ${\rho_в} = 1000 \text{ кг/м}^3$</p><p>Плотность керосина: ${\rho_к} = 800 \text{ кг/м}^3$</p><p><strong>Найти:</strong></p><p>$\text{h}$ - ?</p><p><strong>Решение:</strong></p><p>В U-образной трубке находятся две несмешивающиеся жидкости в равновесии. Это задача на закон сообщающихся сосудов. Согласно этому закону, давление на любом горизонтальном уровне в покоящейся жидкости одинаково.</p><p>Выберем в качестве уровня для сравнения давлений горизонтальную линию, проходящую через границу раздела воды и керосина. Эта граница находится в правом колене трубки.</p><p>Давление $p_1$ на этом уровне в левом колене создается столбом воды высотой $(h - x)$ и атмосферным давлением $p_a$ над ним:</p><p>$p_1 = p_a + {\rho_в} g (h - x)$</p><p>Давление $p_2$ на этом же уровне в правом колене создается столбом керосина высотой $(H - x)$ и атмосферным давлением $p_a$:</p><p>$p_2 = p_a + {\rho_к} g (H - x)$</p><p>Поскольку система находится в равновесии, давления на одном и том же горизонтальном уровне должны быть равны:</p><p>$p_1 = p_2$</p><p>$p_a + {\rho_в} g (h - x) = p_a + {\rho_к} g (H - x)$</p><p>Сократим в обеих частях уравнения атмосферное давление $p_a$ и ускорение свободного падения $\text{g}$:</p><p>${\rho_в} (h - x) = {\rho_к} (H - x)$</p><p>Из этого равенства выразим искомую высоту $\text{h}$:</p><p>$h - x = \frac{{\rho_к}}{{\rho_в}} (H - x)$</p><p>$h = x + \frac{{\rho_к}}{{\rho_в}} (H - x)$</p><p>Теперь подставим числовые значения, переведенные в систему СИ:</p><p>$h = 0.1 \text{ м} + \frac{800 \text{ кг/м}^3}{1000 \text{ кг/м}^3} (0.3 \text{ м} - 0.1 \text{ м})$</p><p>$h = 0.1 + 0.8 \cdot 0.2$</p><p>$h = 0.1 + 0.16$</p><p>$h = 0.26 \text{ м}$</p><p>Переведем полученное значение обратно в сантиметры:</p><p>$h = 26 \text{ см}$</p><p><strong>Ответ:</strong> высота столба воды в левом колене $h = 26 \text{ см}$.</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" => "1425059" "type" => "task" ] "previous" => array:2 [ "refs" => "1425057" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\BookPage {#1104 #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" => 1426133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-30" "field_display_title" => "30" "field_folder" => "1" "field_image_name" => "30" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1118} ] #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 {#1078 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Element {#1115 #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" => 1678665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Edition {#1098} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1426133" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "30-1.jpg" "alt" => null "width" => "2962" "height" => 4897 "path" => "/media/fizika_07/moskovkina-sz/0-1/30-1.webp?ts=1758886608" ] ] ] #original: array:6 [ "id" => 1678665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109} "book_page" => array:2 [ "refs" => "1426133" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "30-1.jpg" "alt" => null "width" => "2962" "height" => 4897 "path" => "/media/fizika_07/moskovkina-sz/0-1/30-1.webp?ts=1758886608" ] ] ] #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" => "1426134" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426132" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:6 [ 0 => App\Models\Task {#1255 #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" => 1425054 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-243" "field_display_title" => "243" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1257 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:2 [ 0 => App\Models\Element {#1270 …30} 1 => App\Models\Element {#1272 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425055" "type" => "task" ] "previous" => array:2 [ "refs" => "1425053" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426133" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425054 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-243" "field_display_title" => "243" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256} "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 {#1257} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259} "content" => Illuminate\Database\Eloquent\Collection {#1261} "next" => array:2 [ "refs" => "1425055" "type" => "task" ] "previous" => array:2 [ "refs" => "1425053" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267} "page" => array:2 [ "refs" => "1426133" "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 {#1262 #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" => 1425055 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-244" "field_display_title" => "244" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1269 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:2 [ 0 => App\Models\Element {#1282 …30} 1 => App\Models\Element {#1284 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425056" "type" => "task" ] "previous" => array:2 [ "refs" => "1425054" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426133" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425055 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-244" "field_display_title" => "244" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260} "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 {#1269} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263} "content" => Illuminate\Database\Eloquent\Collection {#1264} "next" => array:2 [ "refs" => "1425056" "type" => "task" ] "previous" => array:2 [ "refs" => "1425054" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279} "page" => array:2 [ "refs" => "1426133" "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 {#1274 #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" => 1425056 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-245" "field_display_title" => "245" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1281 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:2 [ 0 => App\Models\Element {#1294 …30} 1 => App\Models\Element {#1296 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425057" "type" => "task" ] "previous" => array:2 [ "refs" => "1425055" "type" => "task" ] 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Illuminate\Database\Eloquent\Collection {#1276} "next" => array:2 [ "refs" => "1425057" "type" => "task" ] "previous" => array:2 [ "refs" => "1425055" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1291} "page" => array:2 [ "refs" => "1426133" "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 {#1286 #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" => 1425057 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => 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#items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1302 #items: array:2 [ 0 => App\Models\Element {#1099} 1 => App\Models\Element {#1093} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425059" "type" => "task" ] "previous" => array:2 [ "refs" => "1425057" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426133" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425058 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-247" "field_display_title" => "247" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290} "field_metatags_title" => 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=> "/7-klass/fizika/moskovkina-sbornik-zadach/7-248" "field_display_title" => "248" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1311} "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 {#1312} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1313} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1314} "content" => Illuminate\Database\Eloquent\Collection {#1316} "next" => array:2 [ "refs" => "1425060" "type" => "task" ] "previous" => array:2 [ "refs" => "1425058" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1322} "page" => array:2 [ "refs" => "1426133" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1426133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-30" "field_display_title" => "30" "field_folder" => "1" "field_image_name" => "30" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1085} "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 {#1078} "content" => Illuminate\Database\Eloquent\Collection {#1111} "next" => array:2 [ "refs" => "1426134" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426132" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243} ] #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" => 1425058 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-247" "field_display_title" => "247" "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" => [] 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№247 (с. 30)
Условие. №247 (с. 30)
скриншот условия
247. В U-образную трубку с вертикальными прямыми коленами налиты керосин и вода (см. рисунок). На рисунке $x = 10 \text{ см}$, $H = 30 \text{ см}$. Определите высоту $\text{h}$ столба воды в левом колене.
Решение. №247 (с. 30)
Дано:
$x = 10 \text{ см} = 0.1 \text{ м}$
$H = 30 \text{ см} = 0.3 \text{ м}$
Плотность воды: ${\rho_в} = 1000 \text{ кг/м}^3$
Плотность керосина: ${\rho_к} = 800 \text{ кг/м}^3$
Найти:
$\text{h}$ - ?
Решение:
В U-образной трубке находятся две несмешивающиеся жидкости в равновесии. Это задача на закон сообщающихся сосудов. Согласно этому закону, давление на любом горизонтальном уровне в покоящейся жидкости одинаково.
Выберем в качестве уровня для сравнения давлений горизонтальную линию, проходящую через границу раздела воды и керосина. Эта граница находится в правом колене трубки.
Давление $p_1$ на этом уровне в левом колене создается столбом воды высотой $(h - x)$ и атмосферным давлением $p_a$ над ним:
$p_1 = p_a + {\rho_в} g (h - x)$
Давление $p_2$ на этом же уровне в правом колене создается столбом керосина высотой $(H - x)$ и атмосферным давлением $p_a$:
$p_2 = p_a + {\rho_к} g (H - x)$
Поскольку система находится в равновесии, давления на одном и том же горизонтальном уровне должны быть равны:
$p_1 = p_2$
$p_a + {\rho_в} g (h - x) = p_a + {\rho_к} g (H - x)$
Сократим в обеих частях уравнения атмосферное давление $p_a$ и ускорение свободного падения $\text{g}$:
${\rho_в} (h - x) = {\rho_к} (H - x)$
Из этого равенства выразим искомую высоту $\text{h}$:
$h - x = \frac{{\rho_к}}{{\rho_в}} (H - x)$
$h = x + \frac{{\rho_к}}{{\rho_в}} (H - x)$
Теперь подставим числовые значения, переведенные в систему СИ:
$h = 0.1 \text{ м} + \frac{800 \text{ кг/м}^3}{1000 \text{ кг/м}^3} (0.3 \text{ м} - 0.1 \text{ м})$
$h = 0.1 + 0.8 \cdot 0.2$
$h = 0.1 + 0.16$
$h = 0.26 \text{ м}$
Переведем полученное значение обратно в сантиметры:
$h = 26 \text{ см}$
Ответ: высота столба воды в левом колене $h = 26 \text{ см}$.
Другие задания:
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