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Номер 320, страница 40 - 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. Архимедова сила. Плавание судов. Воздухоплавание - номер 320, страница 40.
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" => 1425131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-320" "field_display_title" => "320" "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 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "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 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "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 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "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 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#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 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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" => 1424773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Архимедова сила. Плавание судов. Воздухоплавание" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "38" "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" => 1424773 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Архимедова сила. Плавание судов. Воздухоплавание" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "38" "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" => 1677664 "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 …2} "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 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "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 …2} "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 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "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" => "1425131" "type" => "task" ] "text" => "<p><strong>320.</strong> Полый железный шар плавает в воде, полностью в нее погрузившись. Чему равна масса шара, если объем полости $20\text{ см}^3$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "320-1.jpg" "alt" => null "width" => "2621" "height" => 460 "path" => "/media/fizika_07/moskovkina-sz/0-7/320-1.webp?ts=1758885550" ] ] ] #original: array:7 [ "id" => 1677664 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1425131" "type" => "task" ] "text" => "<p><strong>320.</strong> Полый железный шар плавает в воде, полностью в нее погрузившись. Чему равна масса шара, если объем полости $20\text{ см}^3$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "320-1.jpg" "alt" => null "width" => "2621" "height" => 460 "path" => "/media/fizika_07/moskovkina-sz/0-7/320-1.webp?ts=1758885550" ] ] ] #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" => 1781512 "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 …2} "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 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "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 …2} "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 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "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" => "1425131" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$V_{полости} = 20 \text{ см}^3$</p><p>Шар плавает в воде, полностью погрузившись.</p><p>Плотность воды: $ρ_{в} = 1000 \text{ кг/м}^3$</p><p>Плотность железа: $ρ_{ж} = 7800 \text{ кг/м}^3$</p><p>$V_{полости} = 20 \text{ см}^3 = 20 \cdot (10^{-2} \text{ м})^3 = 20 \cdot 10^{-6} \text{ м}^3 = 2 \cdot 10^{-5} \text{ м}^3$</p><p><strong>Найти:</strong></p><p>$m_{ш}$ - ?</p><p><strong>Решение:</strong></p><p>По условию задачи, полый железный шар плавает в воде, полностью в нее погрузившись. Это означает, что он находится в состоянии равновесия. Условие плавания тела, полностью погруженного в жидкость, заключается в том, что действующая на него сила тяжести $F_т$ уравновешивается выталкивающей силой (силой Архимеда) $F_А$.</p><p>$F_т = F_А$</p><p>Сила тяжести определяется массой шара $m_{ш}$ и ускорением свободного падения $\text{g}$:</p><p>$F_т = m_{ш} \cdot g$</p><p>Сила Архимеда равна весу вытесненной жидкости. Так как шар погружен полностью, объем вытесненной воды $V_{в}$ равен полному внешнему объему шара $V_{ш}$.</p><p>$F_А = ρ_{в} \cdot g \cdot V_{ш}$</p><p>Приравнивая силы, получаем:</p><p>$m_{ш} \cdot g = ρ_{в} \cdot g \cdot V_{ш}$</p><p>Сократив $\text{g}$, получим выражение для массы шара:</p><p>$m_{ш} = ρ_{в} \cdot V_{ш}$</p><p>Полный объем шара $V_{ш}$ складывается из объема железа $V_{ж}$ и объема внутренней полости $V_{полости}$.</p><p>$V_{ш} = V_{ж} + V_{полости}$</p><p>Масса шара $m_{ш}$ — это масса железа, из которого он сделан. Ее можно выразить через плотность железа $ρ_{ж}$ и объем железа $V_{ж}$:</p><p>$m_{ш} = ρ_{ж} \cdot V_{ж}$, откуда $V_{ж} = \frac{m_{ш}}{ρ_{ж}}$</p><p>Подставим выражения для $V_{ш}$ и $V_{ж}$ в формулу для массы шара:</p><p>$m_{ш} = ρ_{в} \cdot (V_{ж} + V_{полости})$</p><p>$m_{ш} = ρ_{в} \cdot (\frac{m_{ш}}{ρ_{ж}} + V_{полости})$</p><p>Теперь решим это уравнение относительно $m_{ш}$:</p><p>$m_{ш} = \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} + ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} - \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} = ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} \cdot (1 - \frac{ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} \cdot (\frac{ρ_{ж} - ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$</p><p>Отсюда находим итоговую формулу для массы шара:</p><p>$m_{ш} = \frac{ρ_{в} \cdot V_{полости} \cdot ρ_{ж}}{ρ_{ж} - ρ_{в}}$</p><p>Подставим числовые значения в системе СИ:</p><p>$m_{ш} = \frac{1000 \frac{\text{кг}}{\text{м}^3} \cdot 2 \cdot 10^{-5} \text{ м}^3 \cdot 7800 \frac{\text{кг}}{\text{м}^3}}{7800 \frac{\text{кг}}{\text{м}^3} - 1000 \frac{\text{кг}}{\text{м}^3}} = \frac{1000 \cdot 2 \cdot 10^{-5} \cdot 7800}{6800} \text{ кг}$</p><p>$m_{ш} = \frac{156}{6800} \text{ кг} \approx 0.02294 \text{ кг}$</p><p>Переведем массу в граммы:</p><p>$0.02294 \text{ кг} \approx 22.94 \text{ г}$</p><p>Округляя до целых, получаем 23 г.</p><p><strong>Ответ:</strong> масса шара равна примерно 23 г.</p>" ] #original: array:6 [ "id" => 1781512 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1425131" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$V_{полости} = 20 \text{ см}^3$</p><p>Шар плавает в воде, полностью погрузившись.</p><p>Плотность воды: $ρ_{в} = 1000 \text{ кг/м}^3$</p><p>Плотность железа: $ρ_{ж} = 7800 \text{ кг/м}^3$</p><p>$V_{полости} = 20 \text{ см}^3 = 20 \cdot (10^{-2} \text{ м})^3 = 20 \cdot 10^{-6} \text{ м}^3 = 2 \cdot 10^{-5} \text{ м}^3$</p><p><strong>Найти:</strong></p><p>$m_{ш}$ - ?</p><p><strong>Решение:</strong></p><p>По условию задачи, полый железный шар плавает в воде, полностью в нее погрузившись. Это означает, что он находится в состоянии равновесия. Условие плавания тела, полностью погруженного в жидкость, заключается в том, что действующая на него сила тяжести $F_т$ уравновешивается выталкивающей силой (силой Архимеда) $F_А$.</p><p>$F_т = F_А$</p><p>Сила тяжести определяется массой шара $m_{ш}$ и ускорением свободного падения $\text{g}$:</p><p>$F_т = m_{ш} \cdot g$</p><p>Сила Архимеда равна весу вытесненной жидкости. Так как шар погружен полностью, объем вытесненной воды $V_{в}$ равен полному внешнему объему шара $V_{ш}$.</p><p>$F_А = ρ_{в} \cdot g \cdot V_{ш}$</p><p>Приравнивая силы, получаем:</p><p>$m_{ш} \cdot g = ρ_{в} \cdot g \cdot V_{ш}$</p><p>Сократив $\text{g}$, получим выражение для массы шара:</p><p>$m_{ш} = ρ_{в} \cdot V_{ш}$</p><p>Полный объем шара $V_{ш}$ складывается из объема железа $V_{ж}$ и объема внутренней полости $V_{полости}$.</p><p>$V_{ш} = V_{ж} + V_{полости}$</p><p>Масса шара $m_{ш}$ — это масса железа, из которого он сделан. Ее можно выразить через плотность железа $ρ_{ж}$ и объем железа $V_{ж}$:</p><p>$m_{ш} = ρ_{ж} \cdot V_{ж}$, откуда $V_{ж} = \frac{m_{ш}}{ρ_{ж}}$</p><p>Подставим выражения для $V_{ш}$ и $V_{ж}$ в формулу для массы шара:</p><p>$m_{ш} = ρ_{в} \cdot (V_{ж} + V_{полости})$</p><p>$m_{ш} = ρ_{в} \cdot (\frac{m_{ш}}{ρ_{ж}} + V_{полости})$</p><p>Теперь решим это уравнение относительно $m_{ш}$:</p><p>$m_{ш} = \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} + ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} - \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} = ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} \cdot (1 - \frac{ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$</p><p>$m_{ш} \cdot (\frac{ρ_{ж} - ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$</p><p>Отсюда находим итоговую формулу для массы шара:</p><p>$m_{ш} = \frac{ρ_{в} \cdot V_{полости} \cdot ρ_{ж}}{ρ_{ж} - ρ_{в}}$</p><p>Подставим числовые значения в системе СИ:</p><p>$m_{ш} = \frac{1000 \frac{\text{кг}}{\text{м}^3} \cdot 2 \cdot 10^{-5} \text{ м}^3 \cdot 7800 \frac{\text{кг}}{\text{м}^3}}{7800 \frac{\text{кг}}{\text{м}^3} - 1000 \frac{\text{кг}}{\text{м}^3}} = \frac{1000 \cdot 2 \cdot 10^{-5} \cdot 7800}{6800} \text{ кг}$</p><p>$m_{ш} = \frac{156}{6800} \text{ кг} \approx 0.02294 \text{ кг}$</p><p>Переведем массу в граммы:</p><p>$0.02294 \text{ кг} \approx 22.94 \text{ г}$</p><p>Округляя до целых, получаем 23 г.</p><p><strong>Ответ:</strong> масса шара равна примерно 23 г.</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" => "1425132" "type" => "task" ] "previous" => array:2 [ "refs" => "1425130" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => 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"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" => 1678675 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1678675 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1426144" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426142" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:11 [ 0 => App\Models\Task {#1260 #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" => 1425130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-319" "field_display_title" => "319" "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 {#1262 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2} "content" => Illuminate\Database\Eloquent\Collection {#1266 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1272 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-319" "field_display_title" => "319" "field_outside_task" => null 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#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" => 1425131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-320" "field_display_title" => "320" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1265 …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 {#1274 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1270 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => Illuminate\Database\Eloquent\Collection {#1271 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-320" "field_display_title" => "320" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1265 …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 {#1274 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1270 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268 …2} "content" => 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null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1280 …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 {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1282 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283 …2} "content" => Illuminate\Database\Eloquent\Collection {#1285 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1291 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425132 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-321" "field_display_title" => "321" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1280 …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 {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1282 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283 …2} "content" => Illuminate\Database\Eloquent\Collection {#1285 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1291 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#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" => 1425133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-322" "field_display_title" => "322" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1284 …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 {#1293 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1287 …2} "content" => Illuminate\Database\Eloquent\Collection {#1288 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425133 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-322" "field_display_title" => "322" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1284 …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 {#1293 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1287 …2} "content" => Illuminate\Database\Eloquent\Collection {#1288 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …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 {#1298 #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" => 1425134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-323" "field_display_title" => "323" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 …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 {#1305 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299 …2} "content" => Illuminate\Database\Eloquent\Collection {#1300 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1315 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425134 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-323" "field_display_title" => "323" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1290 …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 {#1305 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1301 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1299 …2} "content" => Illuminate\Database\Eloquent\Collection {#1300 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1315 …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 {#1310 #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" => 1425135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-324" "field_display_title" => "324" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1302 …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 {#1317 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1313 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1311 …2} "content" => Illuminate\Database\Eloquent\Collection {#1312 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1327 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425135 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-324" "field_display_title" => "324" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1302 …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 {#1317 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1313 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1311 …2} "content" => Illuminate\Database\Eloquent\Collection {#1312 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1327 …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 => "*" ] } 6 => App\Models\Task {#1322 #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" => 1425136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-325" "field_display_title" => "325" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1314 …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 {#1329 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1325 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1323 …2} "content" => Illuminate\Database\Eloquent\Collection {#1342 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1347 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425136 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-325" "field_display_title" => "325" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1314 …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 {#1329 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1325 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1323 …2} "content" => Illuminate\Database\Eloquent\Collection {#1342 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1347 …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 => "*" ] } 7 => App\Models\Task {#1326 #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" => 1425137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-326" "field_display_title" => "326" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1334 …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 {#1324 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1339 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1338 …2} "content" => Illuminate\Database\Eloquent\Collection {#1354 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1359 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-326" "field_display_title" => "326" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1334 …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 {#1324 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1339 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1338 …2} "content" => Illuminate\Database\Eloquent\Collection {#1354 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1359 …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 => "*" ] } 8 => App\Models\Task {#1337 #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" => 1425138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-327" "field_display_title" => "327" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1336 …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 {#1335 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1343 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1345 …2} "content" => Illuminate\Database\Eloquent\Collection {#1366 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1371 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-327" "field_display_title" => "327" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1336 …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 {#1335 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1343 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1345 …2} "content" => Illuminate\Database\Eloquent\Collection {#1366 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1371 …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 => "*" ] } 9 => App\Models\Task {#1349 #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" => 1425139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-328" "field_display_title" => "328" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1340 …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 {#1341 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1355 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1357 …2} "content" => Illuminate\Database\Eloquent\Collection {#1378 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1383 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-328" "field_display_title" => "328" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1340 …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 {#1341 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1355 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1357 …2} "content" => Illuminate\Database\Eloquent\Collection {#1378 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1383 …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 => "*" ] } 10 => App\Models\Task {#1361 #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" => 1425140 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => "41" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-329" "field_display_title" => "329" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1346 …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 {#1344 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1367 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1369 …2} "content" => Illuminate\Database\Eloquent\Collection {#1390 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1395 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425140 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_page_end" => "41" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/7-329" "field_display_title" => "329" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1346 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null …12 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1426143 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "40" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-40" "field_display_title" => "40" "field_folder" => "1" "field_image_name" => "40" "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 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№320 (с. 40)
Условие. №320 (с. 40)
скриншот условия
320. Полый железный шар плавает в воде, полностью в нее погрузившись. Чему равна масса шара, если объем полости $20\text{ см}^3$?
Решение. №320 (с. 40)
Дано:
$V_{полости} = 20 \text{ см}^3$
Шар плавает в воде, полностью погрузившись.
Плотность воды: $ρ_{в} = 1000 \text{ кг/м}^3$
Плотность железа: $ρ_{ж} = 7800 \text{ кг/м}^3$
$V_{полости} = 20 \text{ см}^3 = 20 \cdot (10^{-2} \text{ м})^3 = 20 \cdot 10^{-6} \text{ м}^3 = 2 \cdot 10^{-5} \text{ м}^3$
Найти:
$m_{ш}$ - ?
Решение:
По условию задачи, полый железный шар плавает в воде, полностью в нее погрузившись. Это означает, что он находится в состоянии равновесия. Условие плавания тела, полностью погруженного в жидкость, заключается в том, что действующая на него сила тяжести $F_т$ уравновешивается выталкивающей силой (силой Архимеда) $F_А$.
$F_т = F_А$
Сила тяжести определяется массой шара $m_{ш}$ и ускорением свободного падения $\text{g}$:
$F_т = m_{ш} \cdot g$
Сила Архимеда равна весу вытесненной жидкости. Так как шар погружен полностью, объем вытесненной воды $V_{в}$ равен полному внешнему объему шара $V_{ш}$.
$F_А = ρ_{в} \cdot g \cdot V_{ш}$
Приравнивая силы, получаем:
$m_{ш} \cdot g = ρ_{в} \cdot g \cdot V_{ш}$
Сократив $\text{g}$, получим выражение для массы шара:
$m_{ш} = ρ_{в} \cdot V_{ш}$
Полный объем шара $V_{ш}$ складывается из объема железа $V_{ж}$ и объема внутренней полости $V_{полости}$.
$V_{ш} = V_{ж} + V_{полости}$
Масса шара $m_{ш}$ — это масса железа, из которого он сделан. Ее можно выразить через плотность железа $ρ_{ж}$ и объем железа $V_{ж}$:
$m_{ш} = ρ_{ж} \cdot V_{ж}$, откуда $V_{ж} = \frac{m_{ш}}{ρ_{ж}}$
Подставим выражения для $V_{ш}$ и $V_{ж}$ в формулу для массы шара:
$m_{ш} = ρ_{в} \cdot (V_{ж} + V_{полости})$
$m_{ш} = ρ_{в} \cdot (\frac{m_{ш}}{ρ_{ж}} + V_{полости})$
Теперь решим это уравнение относительно $m_{ш}$:
$m_{ш} = \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} + ρ_{в} \cdot V_{полости}$
$m_{ш} - \frac{ρ_{в} \cdot m_{ш}}{ρ_{ж}} = ρ_{в} \cdot V_{полости}$
$m_{ш} \cdot (1 - \frac{ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$
$m_{ш} \cdot (\frac{ρ_{ж} - ρ_{в}}{ρ_{ж}}) = ρ_{в} \cdot V_{полости}$
Отсюда находим итоговую формулу для массы шара:
$m_{ш} = \frac{ρ_{в} \cdot V_{полости} \cdot ρ_{ж}}{ρ_{ж} - ρ_{в}}$
Подставим числовые значения в системе СИ:
$m_{ш} = \frac{1000 \frac{\text{кг}}{\text{м}^3} \cdot 2 \cdot 10^{-5} \text{ м}^3 \cdot 7800 \frac{\text{кг}}{\text{м}^3}}{7800 \frac{\text{кг}}{\text{м}^3} - 1000 \frac{\text{кг}}{\text{м}^3}} = \frac{1000 \cdot 2 \cdot 10^{-5} \cdot 7800}{6800} \text{ кг}$
$m_{ш} = \frac{156}{6800} \text{ кг} \approx 0.02294 \text{ кг}$
Переведем массу в граммы:
$0.02294 \text{ кг} \approx 22.94 \text{ г}$
Округляя до целых, получаем 23 г.
Ответ: масса шара равна примерно 23 г.
Другие задания:
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