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Номер 314, страница 99 - 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
8 класс. Работа и мощность тока. Закон Джоуля-Ленца - номер 314, страница 99.
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" => 1425608 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-314" "field_display_title" => "314" "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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "59" "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 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ …1] #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 [ …4] ] "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 [ …1] #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 [ …4] ] "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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "59" "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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "59" "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" => 1424779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_page_start" => "59" "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" => 1424790 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа и мощность тока. Закон Джоуля-Ленца" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "95" "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" => 1424790 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Работа и мощность тока. Закон Джоуля-Ленца" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "95" "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" => 1678141 "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 [ …1] #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" => "1425608" "type" => "task" ] "text" => "<p><strong>314.</strong> Электрочайник закипает через 15 мин после включения в сеть. Нагревательный элемент намотан из проволоки длиной 6 м. Какой длины должна быть проволока нагревательного элемента, чтобы тот же чайник закипел через 10 мин?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "314-1.jpg" "alt" => null "width" => "2528" "height" => 650 "path" => "/media/fizika_07/moskovkina-sz/0-8/314-1.webp?ts=1758885775" ] ] ] #original: array:7 [ "id" => 1678141 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1091} "task" => array:2 [ "refs" => "1425608" "type" => "task" ] "text" => "<p><strong>314.</strong> Электрочайник закипает через 15 мин после включения в сеть. Нагревательный элемент намотан из проволоки длиной 6 м. Какой длины должна быть проволока нагревательного элемента, чтобы тот же чайник закипел через 10 мин?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "314-1.jpg" "alt" => null "width" => "2528" "height" => 650 "path" => "/media/fizika_07/moskovkina-sz/0-8/314-1.webp?ts=1758885775" ] ] ] #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" => 1781989 "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 [ …1] #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" => "1425608" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$t_1 = 15 \text{ мин} = 15 \cdot 60 \text{ с} = 900 \text{ с}$</p><p>$l_1 = 6 \text{ м}$</p><p>$t_2 = 10 \text{ мин} = 10 \cdot 60 \text{ с} = 600 \text{ с}$</p><p><strong>Найти:</strong></p><p>$l_2$ - ?</p><p><strong>Решение:</strong></p><p>Количество теплоты $\text{Q}$, необходимое для того, чтобы вскипятить воду в чайнике, в обоих случаях одинаково, так как по условию задачи "тот же чайник" (предполагаем, что масса воды, ее начальная температура и тепловые потери одинаковы).</p><p>Количество теплоты, выделяемое нагревательным элементом, можно найти по закону Джоуля-Ленца:</p><p>$Q = P \cdot t$</p><p>где $\text{P}$ — это мощность нагревателя, а $\text{t}$ — время нагрева.</p><p>Мощность нагревательного элемента, подключенного к сети с постоянным напряжением $\text{U}$, зависит от его сопротивления $\text{R}$ следующим образом:</p><p>$P = \frac{U^2}{R}$</p><p>Сопротивление $\text{R}$ проволоки прямо пропорционально ее длине $\text{l}$ и обратно пропорционально площади поперечного сечения $\text{S}$:</p><p>$R = \\rho\frac{l}{S}$</p><p>где $\rho$ — удельное сопротивление материала проволоки. Так как материал и толщина проволоки не меняются, $\rho$ и $\text{S}$ являются постоянными величинами.</p><p>Подставим выражения для мощности и сопротивления в формулу для количества теплоты:</p><p>$Q = \frac{U^2}{R} t = \frac{U^2}{(\\rho\frac{l}{S})} t = \frac{U^2 S}{\\rhol} t$</p><p>Запишем это уравнение для первого и второго случаев:</p><p>Для первого случая: $Q_1 = \frac{U^2 S}{\\rhol_1} t_1$</p><p>Для второго случая: $Q_2 = \frac{U^2 S}{\\rhol_2} t_2$</p><p>Поскольку количество теплоты, необходимое для закипания, одинаково ($Q_1 = Q_2$), мы можем приравнять правые части этих уравнений:</p><p>$\frac{U^2 S}{\\rhol_1} t_1 = \frac{U^2 S}{\\rhol_2} t_2$</p><p>Так как напряжение сети $\text{U}$, удельное сопротивление $\rho$ и площадь сечения $\text{S}$ не меняются, мы можем сократить постоянный множитель $\frac{U^2 S}{\rho}$:</p><p>$\frac{t_1}{l_1} = \frac{t_2}{l_2}$</p><p>Из этого соотношения выразим искомую длину проволоки $l_2$:</p><p>$l_2 = l_1 \cdot \frac{t_2}{t_1}$</p><p>Подставим известные значения. Обратите внимание, что время можно подставлять в минутах, так как единицы измерения в дроби сократятся:</p><p>$l_2 = 6 \text{ м} \cdot \frac{10 \text{ мин}}{15 \text{ мин}} = 6 \cdot \frac{2}{3} = 4 \text{ м}$</p><p>Чтобы чайник закипал быстрее, его мощность должна быть больше. Мощность $P = U^2/R$ обратно пропорциональна сопротивлению $\text{R}$. Сопротивление $\text{R}$, в свою очередь, прямо пропорционально длине проволоки $\text{l}$. Таким образом, для увеличения мощности нужно уменьшить длину проволоки, что и подтверждает наш расчет.</p><p><strong>Ответ:</strong> чтобы тот же чайник закипел через 10 минут, длина проволоки нагревательного элемента должна быть 4 м.</p>" ] #original: array:6 [ "id" => 1781989 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1425608" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$t_1 = 15 \text{ мин} = 15 \cdot 60 \text{ с} = 900 \text{ с}$</p><p>$l_1 = 6 \text{ м}$</p><p>$t_2 = 10 \text{ мин} = 10 \cdot 60 \text{ с} = 600 \text{ с}$</p><p><strong>Найти:</strong></p><p>$l_2$ - ?</p><p><strong>Решение:</strong></p><p>Количество теплоты $\text{Q}$, необходимое для того, чтобы вскипятить воду в чайнике, в обоих случаях одинаково, так как по условию задачи "тот же чайник" (предполагаем, что масса воды, ее начальная температура и тепловые потери одинаковы).</p><p>Количество теплоты, выделяемое нагревательным элементом, можно найти по закону Джоуля-Ленца:</p><p>$Q = P \cdot t$</p><p>где $\text{P}$ — это мощность нагревателя, а $\text{t}$ — время нагрева.</p><p>Мощность нагревательного элемента, подключенного к сети с постоянным напряжением $\text{U}$, зависит от его сопротивления $\text{R}$ следующим образом:</p><p>$P = \frac{U^2}{R}$</p><p>Сопротивление $\text{R}$ проволоки прямо пропорционально ее длине $\text{l}$ и обратно пропорционально площади поперечного сечения $\text{S}$:</p><p>$R = \\rho\frac{l}{S}$</p><p>где $\rho$ — удельное сопротивление материала проволоки. Так как материал и толщина проволоки не меняются, $\rho$ и $\text{S}$ являются постоянными величинами.</p><p>Подставим выражения для мощности и сопротивления в формулу для количества теплоты:</p><p>$Q = \frac{U^2}{R} t = \frac{U^2}{(\\rho\frac{l}{S})} t = \frac{U^2 S}{\\rhol} t$</p><p>Запишем это уравнение для первого и второго случаев:</p><p>Для первого случая: $Q_1 = \frac{U^2 S}{\\rhol_1} t_1$</p><p>Для второго случая: $Q_2 = \frac{U^2 S}{\\rhol_2} t_2$</p><p>Поскольку количество теплоты, необходимое для закипания, одинаково ($Q_1 = Q_2$), мы можем приравнять правые части этих уравнений:</p><p>$\frac{U^2 S}{\\rhol_1} t_1 = \frac{U^2 S}{\\rhol_2} t_2$</p><p>Так как напряжение сети $\text{U}$, удельное сопротивление $\rho$ и площадь сечения $\text{S}$ не меняются, мы можем сократить постоянный множитель $\frac{U^2 S}{\rho}$:</p><p>$\frac{t_1}{l_1} = \frac{t_2}{l_2}$</p><p>Из этого соотношения выразим искомую длину проволоки $l_2$:</p><p>$l_2 = l_1 \cdot \frac{t_2}{t_1}$</p><p>Подставим известные значения. Обратите внимание, что время можно подставлять в минутах, так как единицы измерения в дроби сократятся:</p><p>$l_2 = 6 \text{ м} \cdot \frac{10 \text{ мин}}{15 \text{ мин}} = 6 \cdot \frac{2}{3} = 4 \text{ м}$</p><p>Чтобы чайник закипал быстрее, его мощность должна быть больше. Мощность $P = U^2/R$ обратно пропорциональна сопротивлению $\text{R}$. Сопротивление $\text{R}$, в свою очередь, прямо пропорционально длине проволоки $\text{l}$. Таким образом, для увеличения мощности нужно уменьшить длину проволоки, что и подтверждает наш расчет.</p><p><strong>Ответ:</strong> чтобы тот же чайник закипел через 10 минут, длина проволоки нагревательного элемента должна быть 4 м.</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" => "1425609" "type" => "task" ] "previous" => array:2 [ "refs" => "1425607" "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" => 1426202 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-99" "field_display_title" => "99" "field_folder" => "1" "field_image_name" => "99" "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" => 1678734 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1678734 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109} "book_page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1426203" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426201" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:7 [ 0 => App\Models\Task {#1256 #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" => 1425606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => "99" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-312" "field_display_title" => "312" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1258 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425607" "type" => "task" ] "previous" => array:2 [ "refs" => "1425605" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426201" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "98" "field_page_end" => "99" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-312" "field_display_title" => "312" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1257} "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 {#1258} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260} "content" => Illuminate\Database\Eloquent\Collection {#1262} "next" => array:2 [ "refs" => "1425607" "type" => "task" ] "previous" => array:2 [ "refs" => "1425605" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1268} "page" => array:2 [ "refs" => "1426201" "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 {#1263 #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" => 1425607 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-313" "field_display_title" => "313" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1270 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425608" "type" => "task" ] "previous" => array:2 [ "refs" => "1425606" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425607 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-313" "field_display_title" => "313" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261} "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 {#1270} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264} "content" => Illuminate\Database\Eloquent\Collection {#1265} "next" => array:2 [ "refs" => "1425608" "type" => "task" ] "previous" => array:2 [ "refs" => "1425606" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1280} "page" => array:2 [ "refs" => "1426202" "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 {#1275 #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" => 1425608 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-314" "field_display_title" => "314" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1282 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425609" "type" => "task" ] "previous" => array:2 [ "refs" => "1425607" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425608 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-314" "field_display_title" => "314" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267} "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 {#1282} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1278} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276} "content" => Illuminate\Database\Eloquent\Collection {#1279} "next" => array:2 [ "refs" => "1425609" "type" => "task" ] "previous" => array:2 [ "refs" => "1425607" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1277} "page" => array:2 [ "refs" => "1426202" "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 {#1287 #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" => 1425609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-315" "field_display_title" => "315" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1289 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1291 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425610" "type" => "task" ] "previous" => array:2 [ "refs" => "1425608" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-315" "field_display_title" => "315" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1288} "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 {#1289} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1290} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1291} "content" => Illuminate\Database\Eloquent\Collection {#1293} "next" => array:2 [ "refs" => "1425610" "type" => "task" ] "previous" => array:2 [ "refs" => "1425608" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1299} "page" => array:2 [ "refs" => "1426202" "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 => "*" ] } 4 => App\Models\Task {#1294 #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" => 1425610 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-316" "field_display_title" => "316" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1375 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1376 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425611" "type" => "task" ] "previous" => array:2 [ "refs" => "1425609" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1383 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425610 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-316" "field_display_title" => "316" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1292} "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 {#1301} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1297} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1375} "content" => Illuminate\Database\Eloquent\Collection {#1376} "next" => array:2 [ "refs" => "1425611" "type" => "task" ] "previous" => array:2 [ "refs" => "1425609" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1383} "page" => array:2 [ "refs" => "1426202" "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 => "*" ] } 5 => App\Models\Task {#1378 #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" => 1425611 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-317" "field_display_title" => "317" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1377 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1385 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1379 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1380 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1425612" "type" => "task" ] "previous" => array:2 [ "refs" => "1425610" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1395 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1426202" "type" => "book_page" ] ] #original: array:24 [ "id" => 1425611 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-317" "field_display_title" => "317" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1377} "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 {#1385} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1379} "content" => Illuminate\Database\Eloquent\Collection {#1380} "next" => array:2 [ "refs" => "1425612" …1 ] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1395} "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 {#1390 #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" => 1425612 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => "100" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-318" "field_display_title" => "318" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1382 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1397 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1393 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1391 …2} "content" => Illuminate\Database\Eloquent\Collection {#1392 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1407 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1425612 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => "100" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-318" "field_display_title" => "318" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1382 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1397 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1393 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1391 …2} "content" => Illuminate\Database\Eloquent\Collection {#1392 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1407 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1426202 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/page-99" "field_display_title" => "99" "field_folder" => "1" "field_image_name" => "99" "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" => "1426203" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1426201" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1242} ] #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" => 1425608 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "99" "field_page_end" => null "field_url" => "/7-klass/fizika/moskovkina-sbornik-zadach/8-314" "field_display_title" => "314" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1071} "next" => array:2 [ "refs" => "1425609" "type" => "task" ] "previous" => array:2 [ "refs" => "1425607" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1102} "page" => array:2 [ "refs" => "1426202" "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 => "*" ] }
№314 (с. 99)
Условие. №314 (с. 99)
скриншот условия
314. Электрочайник закипает через 15 мин после включения в сеть. Нагревательный элемент намотан из проволоки длиной 6 м. Какой длины должна быть проволока нагревательного элемента, чтобы тот же чайник закипел через 10 мин?
Решение. №314 (с. 99)
Дано:
$t_1 = 15 \text{ мин} = 15 \cdot 60 \text{ с} = 900 \text{ с}$
$l_1 = 6 \text{ м}$
$t_2 = 10 \text{ мин} = 10 \cdot 60 \text{ с} = 600 \text{ с}$
Найти:
$l_2$ - ?
Решение:
Количество теплоты $\text{Q}$, необходимое для того, чтобы вскипятить воду в чайнике, в обоих случаях одинаково, так как по условию задачи "тот же чайник" (предполагаем, что масса воды, ее начальная температура и тепловые потери одинаковы).
Количество теплоты, выделяемое нагревательным элементом, можно найти по закону Джоуля-Ленца:
$Q = P \cdot t$
где $\text{P}$ — это мощность нагревателя, а $\text{t}$ — время нагрева.
Мощность нагревательного элемента, подключенного к сети с постоянным напряжением $\text{U}$, зависит от его сопротивления $\text{R}$ следующим образом:
$P = \frac{U^2}{R}$
Сопротивление $\text{R}$ проволоки прямо пропорционально ее длине $\text{l}$ и обратно пропорционально площади поперечного сечения $\text{S}$:
$R = \\rho\frac{l}{S}$
где $\rho$ — удельное сопротивление материала проволоки. Так как материал и толщина проволоки не меняются, $\rho$ и $\text{S}$ являются постоянными величинами.
Подставим выражения для мощности и сопротивления в формулу для количества теплоты:
$Q = \frac{U^2}{R} t = \frac{U^2}{(\\rho\frac{l}{S})} t = \frac{U^2 S}{\\rhol} t$
Запишем это уравнение для первого и второго случаев:
Для первого случая: $Q_1 = \frac{U^2 S}{\\rhol_1} t_1$
Для второго случая: $Q_2 = \frac{U^2 S}{\\rhol_2} t_2$
Поскольку количество теплоты, необходимое для закипания, одинаково ($Q_1 = Q_2$), мы можем приравнять правые части этих уравнений:
$\frac{U^2 S}{\\rhol_1} t_1 = \frac{U^2 S}{\\rhol_2} t_2$
Так как напряжение сети $\text{U}$, удельное сопротивление $\rho$ и площадь сечения $\text{S}$ не меняются, мы можем сократить постоянный множитель $\frac{U^2 S}{\rho}$:
$\frac{t_1}{l_1} = \frac{t_2}{l_2}$
Из этого соотношения выразим искомую длину проволоки $l_2$:
$l_2 = l_1 \cdot \frac{t_2}{t_1}$
Подставим известные значения. Обратите внимание, что время можно подставлять в минутах, так как единицы измерения в дроби сократятся:
$l_2 = 6 \text{ м} \cdot \frac{10 \text{ мин}}{15 \text{ мин}} = 6 \cdot \frac{2}{3} = 4 \text{ м}$
Чтобы чайник закипал быстрее, его мощность должна быть больше. Мощность $P = U^2/R$ обратно пропорциональна сопротивлению $\text{R}$. Сопротивление $\text{R}$, в свою очередь, прямо пропорционально длине проволоки $\text{l}$. Таким образом, для увеличения мощности нужно уменьшить длину проволоки, что и подтверждает наш расчет.
Ответ: чтобы тот же чайник закипел через 10 минут, длина проволоки нагревательного элемента должна быть 4 м.
Другие задания:
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