gdz.top
Номер 2, страница 78 - гдз по физике 8 класс учебник Пёрышкин
Авторы: Пёрышкин И. М.
Тип: Учебник
Издательство: Просвещение
Год издания: 2023 - 2026
Уровень обучения: базовый
Цвет обложки: белый с градусником
ISBN: 978-5-09-102555-2
Допущено Министерством просвещения Российской Федерации
Популярные ГДЗ в 8 классе
Глава 1. Тепловые явления. Параграф 20. Влажность воздуха. Способы определения влажности воздуха. Задание 13 - номер 2, страница 78.
App\Models\Task {#1024 // 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" => 599013 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "78" "field_page_end" => null "field_url" => "/8-klass/fizika/peryshkin-uchebnik/20-4-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "3" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 51 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1061 …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" => 51 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1061 …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 {#1063 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "3" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1063} ] #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 {#1064 #items: array:3 [ 0 => App\Models\Branch {#1065 #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" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "3" "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 {#1068 #items: array:1 [ 0 => App\Models\Book {#1069 #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" => 51 "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 {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #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 {#1072 #items: array:1 [ 0 => App\Models\Term {#1073 #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 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Term {#1075 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #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" => 6884 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Пёрышкин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "И" "field_patronymic" => "М" "field_surname_rp" => null ] #original: array:12 [ "id" => 6884 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Пёрышкин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "И" "field_patronymic" => "М" "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 {#1078 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #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 {#1081 #items: array:1 [ 0 => App\Models\Term {#1082 #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 {#1083 #items: array:1 [ 0 => App\Models\Term {#1084 #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 …3 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Term {#1088 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1090 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Term {#1092 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" "alt" => "" "width" => "1350" "height" => "1772" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Term {#1098 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: 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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 51 "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 {#1070} "field_class" => Illuminate\Database\Eloquent\Collection {#1072} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074} "field_author" => Illuminate\Database\Eloquent\Collection {#1076} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1078} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1079} "field_country" => Illuminate\Database\Eloquent\Collection {#1081} "field_city" => Illuminate\Database\Eloquent\Collection {#1083} "field_series" => Illuminate\Database\Eloquent\Collection {#1085} "field_umk" => Illuminate\Database\Eloquent\Collection {#1086} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1087} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1089} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1091} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1093} "field_under_the_edition_degree" => null "field_cover_description" => "с градусником" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => null "field_allowed" => "Допущено Министерством просвещения Российской Федерации" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "706" "field_priority" => "2" "field_default_folder" => "/fizika_08/Peryshkin-u23/" "field_isbn" => "978-5-09-102555-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825" "alt" => "" "width" => "1350" "height" => "1772" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1094} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1095} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_url" => "/8-klass/fizika/peryshkin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1097} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598563 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1066} "field_page_start" => "3" "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 {#1068} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1099} ] #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 {#1100 #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" => 598635 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Влажность воздуха. Способы определения влажности воздуха" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1101 #items: array:1 [ 0 => App\Models\Term {#1102 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "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_page_start" => "73" "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 {#1103 #items: array:1 [ 0 => App\Models\Book {#1069} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Branch {#1023} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 598635 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Влажность воздуха. Способы определения влажности воздуха" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1101} "field_page_start" => "73" "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 {#1103} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1104} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1105 #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" => 598639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 13" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "78" "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 {#1107 #items: array:1 [ 0 => App\Models\Book {#1069} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Branch {#1109 #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" => 598635 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Влажность воздуха. Способы определения влажности воздуха" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_page_start" => "73" "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 {#1111 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1112 …2} ] #original: array:24 [ "id" => 598635 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Влажность воздуха. Способы определения влажности воздуха" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_page_start" => "73" "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 {#1111 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1112 …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:24 [ "id" => 598639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задание 13" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1106} "field_page_start" => "78" "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 {#1107} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1108} ] #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 {#1113 #items: array:4 [ 0 => App\Models\Element {#1114 #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" => 745462 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Edition {#1116 #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" => 1636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1121 …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" => "599013" "type" => "task" ] "text" => """ <p><strong>2</strong>. Придумайте несколько задач, используя данные таблиц 5 и 6. Обменяйтесь с товарищем условиями задач и решите их.</p><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-20-4/2.webp?ts=1743615324" alt="Придумать несколько задач, используя данные таблиц 5 и 6" loading="lazy" width="1649" height="667">\n </figure>\n <figcaption> </figcaption></figure><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-20-4/2_0.webp?ts=1743615324" alt="Придумать несколько задач, используя данные таблиц 5 и 6" loading="lazy" width="1646" height="1283">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "733" "height" => 97 "path" => "/media/fizika_08/Peryshkin-u23/0-20-4/2-1.webp?ts=1738080879" ] ] ] #original: array:7 [ "id" => 745462 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1115} "task" => array:2 [ "refs" => "599013" "type" => "task" ] "text" => """ <p><strong>2</strong>. Придумайте несколько задач, используя данные таблиц 5 и 6. Обменяйтесь с товарищем условиями задач и решите их.</p><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-20-4/2.webp?ts=1743615324" alt="Придумать несколько задач, используя данные таблиц 5 и 6" loading="lazy" width="1649" height="667">\n </figure>\n <figcaption> </figcaption></figure><figure><figure class="align-center">\n <img src="/media/fizika_08/Peryshkin-u23/0-20-4/2_0.webp?ts=1743615324" alt="Придумать несколько задач, используя данные таблиц 5 и 6" loading="lazy" width="1646" height="1283">\n </figure>\n <figcaption> </figcaption></figure> """ "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "733" "height" => 97 "path" => "/media/fizika_08/Peryshkin-u23/0-20-4/2-1.webp?ts=1738080879" ] ] ] #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 {#1122 #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" => 745623 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Edition {#1124 #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" => 1637 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Колесникович" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1637 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 1" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => 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745623 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123} "task" => array:2 [ "refs" => "599013" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "2064" "height" => 2255 "path" => "/media/fizika_08/Peryshkin-u23/1-20-4/2-1.webp?ts=1738080915" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1130 #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" => 746981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Edition {#1132 #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" => 1639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …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" => "599013" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "831" "height" => 349 "path" => "/media/fizika_08/Peryshkin-u23/2-20-4/2-1.webp?ts=1738081024" ] ] ] #original: array:6 [ "id" => 746981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131} "task" => array:2 [ "refs" => "599013" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "2-1.png" "alt" => null "width" => "831" "height" => 349 "path" => "/media/fizika_08/Peryshkin-u23/2-20-4/2-1.webp?ts=1738081024" ] ] ] #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\Element {#1138 #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" => 1466818 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Edition {#1140 #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" => 5406 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5406 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4" "field_order" => "5" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …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" => "599013" "type" => "task" ] "text" => "<p>Поскольку в задании не предоставлены таблицы 5 и 6, в качестве примера создадим их и на их основе составим и решим две задачи.</p><p><strong>Таблица 5. Плотность некоторых веществ (при н.у.)</strong></p><table border="1" style="border-collapse: collapse; width: 100%;"><thead><tr style="background-color: #f2f2f2;"><th style="padding: 8px; text-align: left;">Вещество</th><th style="padding: 8px; text-align: left;">Плотность, $ \text{кг/м}^3 $</th></tr></thead><tbody><tr><td style="padding: 8px;">Алюминий</td><td style="padding: 8px;">2700</td></tr><tr><td style="padding: 8px;">Сталь</td><td style="padding: 8px;">7800</td></tr><tr><td style="padding: 8px;">Медь</td><td style="padding: 8px;">8900</td></tr><tr><td style="padding: 8px;">Вода</td><td style="padding: 8px;">1000</td></tr><tr><td style="padding: 8px;">Дерево (сосна)</td><td style="padding: 8px;">400</td></tr></tbody></table><p><strong>Таблица 6. Удельное электрическое сопротивление (при 20 °C)</strong></p><table border="1" style="border-collapse: collapse; width: 100%;"><thead><tr style="background-color: #f2f2f2;"><th style="padding: 8px; text-align: left;">Вещество</th><th style="padding: 8px; text-align: left;">Удельное сопротивление, $ \text{Ом} \cdot \text{м} $</th></tr></thead><tbody><tr><td style="padding: 8px;">Медь</td><td style="padding: 8px;">$ 1.7 \cdot 10^{-8} $</td></tr><tr><td style="padding: 8px;">Алюминий</td><td style="padding: 8px;">$ 2.8 \cdot 10^{-8} $</td></tr><tr><td style="padding: 8px;">Сталь</td><td style="padding: 8px;">$ 1.2 \cdot 10^{-7} $</td></tr><tr><td style="padding: 8px;">Нихром</td><td style="padding: 8px;">$ 1.1 \cdot 10^{-6} $</td></tr></tbody></table><br><p><strong>Задача 1.</strong></p><p>Стальной шар имеет массу 3.9 кг. Какой объем имеет этот шар? Сравните его массу с массой алюминиевого шара такого же объема.</p><p><strong>Дано:</strong></p><p>$m_{ст} = 3.9 \text{ кг}$<br>$\rho_{ст} = 7800 \text{ кг/м³}$ (из таблицы 5)<br>$\rho_{ал} = 2700 \text{ кг/м³}$ (из таблицы 5)</p><p>Все данные уже представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>$V_{ст}$ - ?<br>$m_{ал}$ - ?</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Плотность, масса и объем тела связаны формулой $ \rho = m/V $. Отсюда можно выразить объем: $ V = m/\rho $.<br>Найдем объем стального шара, используя его массу и плотность стали из таблицы 5:<br>$V_{ст} = m_{ст} / \rho_{ст} = 3.9 \text{ кг} / 7800 \text{ кг/м³} = 0.0005 \text{ м³}$.</p><p><strong>2.</strong> По условию задачи, объем алюминиевого шара равен объему стального: $ V_{ал} = V_{ст} = 0.0005 \text{ м³} $.<br>Найдем массу алюминиевого шара, используя его объем и плотность алюминия из таблицы 5:<br>$m_{ал} = \rho_{ал} \cdot V_{ал} = 2700 \text{ кг/м³} \cdot 0.0005 \text{ м³} = 1.35 \text{ кг}$.</p><p><strong>3.</strong> Сравним массы шаров:<br>$m_{ст} / m_{ал} = 3.9 \text{ кг} / 1.35 \text{ кг} \approx 2.89$.<br>Масса стального шара почти в 2.9 раза больше массы алюминиевого шара того же объема.</p><p><strong>Ответ:</strong> объем стального шара равен $0.0005 \text{ м³}$; масса алюминиевого шара такого же объема составляет $1.35 \text{ кг}$; масса стального шара больше массы алюминиевого шара примерно в 2.89 раза.</p><br><p><strong>Задача 2.</strong></p><p>Определите сопротивление медного провода длиной 100 м и площадью поперечного сечения 0.5 мм². Какой длины должен быть алюминиевый провод с такой же площадью поперечного сечения, чтобы иметь такое же сопротивление?</p><p><strong>Дано:</strong></p><p>$l_м = 100 \text{ м}$<br>$S = 0.5 \text{ мм²}$<br>$\rho_{э, м} = 1.7 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)<br>$\rho_{э, ал} = 2.8 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)<br>$R_{ал} = R_м$</p><p>Переведем площадь сечения в систему СИ (м²):<br>$S = 0.5 \text{ мм²} = 0.5 \cdot (10^{-3} \text{ м})^2 = 0.5 \cdot 10^{-6} \text{ м²}$.</p><p><strong>Найти:</strong></p><p>$R_м$ - ?<br>$l_{ал}$ - ?</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сопротивление проводника вычисляется по формуле $ R = \rho_э \cdot (l/S) $, где $ \rho_э $ – удельное электрическое сопротивление, $ l $ – длина, $ S $ – площадь поперечного сечения.<br>Найдем сопротивление медного провода, используя данные из условия и таблицы 6:<br>$ R_м = \rho_{э, м} \cdot (l_м / S) = (1.7 \cdot 10^{-8} \text{ Ом·м} \cdot 100 \text{ м}) / (0.5 \cdot 10^{-6} \text{ м²}) = 3.4 \text{ Ом}$.</p><p><strong>2.</strong> По условию, сопротивление алюминиевого провода должно быть таким же: $ R_{ал} = R_м = 3.4 \text{ Ом} $.<br>Из формулы сопротивления $ R_{ал} = \rho_{э, ал} \cdot (l_{ал} / S) $ выразим длину алюминиевого провода $ l_{ал} $:<br>$ l_{ал} = (R_{ал} \cdot S) / \rho_{э, ал} $.<br>Подставим числовые значения:<br>$ l_{ал} = (3.4 \text{ Ом} \cdot 0.5 \cdot 10^{-6} \text{ м²}) / (2.8 \cdot 10^{-8} \text{ Ом·м}) \approx 60.7 \text{ м}$.</p><p><strong>Ответ:</strong> сопротивление медного провода равно $3.4 \text{ Ом}$; чтобы иметь такое же сопротивление, алюминиевый провод с такой же площадью поперечного сечения должен иметь длину примерно $60.7 \text{ м}$.</p>" ] #original: array:6 [ "id" => 1466818 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139} "task" => array:2 [ "refs" => "599013" "type" => "task" ] "text" => "<p>Поскольку в задании не предоставлены таблицы 5 и 6, в качестве примера создадим их и на их основе составим и решим две задачи.</p><p><strong>Таблица 5. Плотность некоторых веществ (при н.у.)</strong></p><table border="1" style="border-collapse: collapse; width: 100%;"><thead><tr style="background-color: #f2f2f2;"><th style="padding: 8px; text-align: left;">Вещество</th><th style="padding: 8px; text-align: left;">Плотность, $ \text{кг/м}^3 $</th></tr></thead><tbody><tr><td style="padding: 8px;">Алюминий</td><td style="padding: 8px;">2700</td></tr><tr><td style="padding: 8px;">Сталь</td><td style="padding: 8px;">7800</td></tr><tr><td style="padding: 8px;">Медь</td><td style="padding: 8px;">8900</td></tr><tr><td style="padding: 8px;">Вода</td><td style="padding: 8px;">1000</td></tr><tr><td style="padding: 8px;">Дерево (сосна)</td><td style="padding: 8px;">400</td></tr></tbody></table><p><strong>Таблица 6. Удельное электрическое сопротивление (при 20 °C)</strong></p><table border="1" style="border-collapse: collapse; width: 100%;"><thead><tr style="background-color: #f2f2f2;"><th style="padding: 8px; text-align: left;">Вещество</th><th style="padding: 8px; text-align: left;">Удельное сопротивление, $ \text{Ом} \cdot \text{м} $</th></tr></thead><tbody><tr><td style="padding: 8px;">Медь</td><td style="padding: 8px;">$ 1.7 \cdot 10^{-8} $</td></tr><tr><td style="padding: 8px;">Алюминий</td><td style="padding: 8px;">$ 2.8 \cdot 10^{-8} $</td></tr><tr><td style="padding: 8px;">Сталь</td><td style="padding: 8px;">$ 1.2 \cdot 10^{-7} $</td></tr><tr><td style="padding: 8px;">Нихром</td><td style="padding: 8px;">$ 1.1 \cdot 10^{-6} $</td></tr></tbody></table><br><p><strong>Задача 1.</strong></p><p>Стальной шар имеет массу 3.9 кг. Какой объем имеет этот шар? Сравните его массу с массой алюминиевого шара такого же объема.</p><p><strong>Дано:</strong></p><p>$m_{ст} = 3.9 \text{ кг}$<br>$\rho_{ст} = 7800 \text{ кг/м³}$ (из таблицы 5)<br>$\rho_{ал} = 2700 \text{ кг/м³}$ (из таблицы 5)</p><p>Все данные уже представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>$V_{ст}$ - ?<br>$m_{ал}$ - ?</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Плотность, масса и объем тела связаны формулой $ \rho = m/V $. Отсюда можно выразить объем: $ V = m/\rho $.<br>Найдем объем стального шара, используя его массу и плотность стали из таблицы 5:<br>$V_{ст} = m_{ст} / \rho_{ст} = 3.9 \text{ кг} / 7800 \text{ кг/м³} = 0.0005 \text{ м³}$.</p><p><strong>2.</strong> По условию задачи, объем алюминиевого шара равен объему стального: $ V_{ал} = V_{ст} = 0.0005 \text{ м³} $.<br>Найдем массу алюминиевого шара, используя его объем и плотность алюминия из таблицы 5:<br>$m_{ал} = \rho_{ал} \cdot V_{ал} = 2700 \text{ кг/м³} \cdot 0.0005 \text{ м³} = 1.35 \text{ кг}$.</p><p><strong>3.</strong> Сравним массы шаров:<br>$m_{ст} / m_{ал} = 3.9 \text{ кг} / 1.35 \text{ кг} \approx 2.89$.<br>Масса стального шара почти в 2.9 раза больше массы алюминиевого шара того же объема.</p><p><strong>Ответ:</strong> объем стального шара равен $0.0005 \text{ м³}$; масса алюминиевого шара такого же объема составляет $1.35 \text{ кг}$; масса стального шара больше массы алюминиевого шара примерно в 2.89 раза.</p><br><p><strong>Задача 2.</strong></p><p>Определите сопротивление медного провода длиной 100 м и площадью поперечного сечения 0.5 мм². Какой длины должен быть алюминиевый провод с такой же площадью поперечного сечения, чтобы иметь такое же сопротивление?</p><p><strong>Дано:</strong></p><p>$l_м = 100 \text{ м}$<br>$S = 0.5 \text{ мм²}$<br>$\rho_{э, м} = 1.7 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)<br>$\rho_{э, ал} = 2.8 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)<br>$R_{ал} = R_м$</p><p>Переведем площадь сечения в систему СИ (м²):<br>$S = 0.5 \text{ мм²} = 0.5 \cdot (10^{-3} \text{ м})^2 = 0.5 \cdot 10^{-6} \text{ м²}$.</p><p><strong>Найти:</strong></p><p>$R_м$ - ?<br>$l_{ал}$ - ?</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сопротивление проводника вычисляется по формуле $ R = \rho_э \cdot (l/S) $, где $ \rho_э $ – удельное электрическое сопротивление, $ l $ – длина, $ S $ – площадь поперечного сечения.<br>Найдем сопротивление медного провода, используя данные из условия и таблицы 6:<br>$ R_м = \rho_{э, м} \cdot (l_м / S) = (1.7 \cdot 10^{-8} \text{ Ом·м} \cdot 100 \text{ м}) / (0.5 \cdot 10^{-6} \text{ м²}) = 3.4 \text{ Ом}$.</p><p><strong>2.</strong> По условию, сопротивление алюминиевого провода должно быть таким же: $ R_{ал} = R_м = 3.4 \text{ Ом} $.<br>Из формулы сопротивления $ R_{ал} = \rho_{э, ал} \cdot (l_{ал} / S) $ выразим длину алюминиевого провода $ l_{ал} $:<br>$ l_{ал} = (R_{ал} \cdot S) / \rho_{э, ал} $.<br>Подставим числовые значения:<br>$ l_{ал} = (3.4 \text{ Ом} \cdot 0.5 \cdot 10^{-6} \text{ м²}) / (2.8 \cdot 10^{-8} \text{ Ом·м}) \approx 60.7 \text{ м}$.</p><p><strong>Ответ:</strong> сопротивление медного провода равно $3.4 \text{ Ом}$; чтобы иметь такое же сопротивление, алюминиевый провод с такой же площадью поперечного сечения должен иметь длину примерно $60.7 \text{ м}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] 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№2 (с. 78)
Условие. №2 (с. 78)
скриншот условия
2. Придумайте несколько задач, используя данные таблиц 5 и 6. Обменяйтесь с товарищем условиями задач и решите их.
Решение 1. №2 (с. 78)
Решение 3. №2 (с. 78)
Решение 4. №2 (с. 78)
Поскольку в задании не предоставлены таблицы 5 и 6, в качестве примера создадим их и на их основе составим и решим две задачи.
Таблица 5. Плотность некоторых веществ (при н.у.)
| Вещество | Плотность, $ \text{кг/м}^3 $ |
|---|---|
| Алюминий | 2700 |
| Сталь | 7800 |
| Медь | 8900 |
| Вода | 1000 |
| Дерево (сосна) | 400 |
Таблица 6. Удельное электрическое сопротивление (при 20 °C)
| Вещество | Удельное сопротивление, $ \text{Ом} \cdot \text{м} $ |
|---|---|
| Медь | $ 1.7 \cdot 10^{-8} $ |
| Алюминий | $ 2.8 \cdot 10^{-8} $ |
| Сталь | $ 1.2 \cdot 10^{-7} $ |
| Нихром | $ 1.1 \cdot 10^{-6} $ |
Задача 1.
Стальной шар имеет массу 3.9 кг. Какой объем имеет этот шар? Сравните его массу с массой алюминиевого шара такого же объема.
Дано:
$m_{ст} = 3.9 \text{ кг}$
$\rho_{ст} = 7800 \text{ кг/м³}$ (из таблицы 5)
$\rho_{ал} = 2700 \text{ кг/м³}$ (из таблицы 5)
Все данные уже представлены в системе СИ.
Найти:
$V_{ст}$ - ?
$m_{ал}$ - ?
Решение:
1. Плотность, масса и объем тела связаны формулой $ \rho = m/V $. Отсюда можно выразить объем: $ V = m/\rho $.
Найдем объем стального шара, используя его массу и плотность стали из таблицы 5:
$V_{ст} = m_{ст} / \rho_{ст} = 3.9 \text{ кг} / 7800 \text{ кг/м³} = 0.0005 \text{ м³}$.
2. По условию задачи, объем алюминиевого шара равен объему стального: $ V_{ал} = V_{ст} = 0.0005 \text{ м³} $.
Найдем массу алюминиевого шара, используя его объем и плотность алюминия из таблицы 5:
$m_{ал} = \rho_{ал} \cdot V_{ал} = 2700 \text{ кг/м³} \cdot 0.0005 \text{ м³} = 1.35 \text{ кг}$.
3. Сравним массы шаров:
$m_{ст} / m_{ал} = 3.9 \text{ кг} / 1.35 \text{ кг} \approx 2.89$.
Масса стального шара почти в 2.9 раза больше массы алюминиевого шара того же объема.
Ответ: объем стального шара равен $0.0005 \text{ м³}$; масса алюминиевого шара такого же объема составляет $1.35 \text{ кг}$; масса стального шара больше массы алюминиевого шара примерно в 2.89 раза.
Задача 2.
Определите сопротивление медного провода длиной 100 м и площадью поперечного сечения 0.5 мм². Какой длины должен быть алюминиевый провод с такой же площадью поперечного сечения, чтобы иметь такое же сопротивление?
Дано:
$l_м = 100 \text{ м}$
$S = 0.5 \text{ мм²}$
$\rho_{э, м} = 1.7 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)
$\rho_{э, ал} = 2.8 \cdot 10^{-8} \text{ Ом·м}$ (из таблицы 6)
$R_{ал} = R_м$
Переведем площадь сечения в систему СИ (м²):
$S = 0.5 \text{ мм²} = 0.5 \cdot (10^{-3} \text{ м})^2 = 0.5 \cdot 10^{-6} \text{ м²}$.
Найти:
$R_м$ - ?
$l_{ал}$ - ?
Решение:
1. Сопротивление проводника вычисляется по формуле $ R = \rho_э \cdot (l/S) $, где $ \rho_э $ – удельное электрическое сопротивление, $ l $ – длина, $ S $ – площадь поперечного сечения.
Найдем сопротивление медного провода, используя данные из условия и таблицы 6:
$ R_м = \rho_{э, м} \cdot (l_м / S) = (1.7 \cdot 10^{-8} \text{ Ом·м} \cdot 100 \text{ м}) / (0.5 \cdot 10^{-6} \text{ м²}) = 3.4 \text{ Ом}$.
2. По условию, сопротивление алюминиевого провода должно быть таким же: $ R_{ал} = R_м = 3.4 \text{ Ом} $.
Из формулы сопротивления $ R_{ал} = \rho_{э, ал} \cdot (l_{ал} / S) $ выразим длину алюминиевого провода $ l_{ал} $:
$ l_{ал} = (R_{ал} \cdot S) / \rho_{э, ал} $.
Подставим числовые значения:
$ l_{ал} = (3.4 \text{ Ом} \cdot 0.5 \cdot 10^{-6} \text{ м²}) / (2.8 \cdot 10^{-8} \text{ Ом·м}) \approx 60.7 \text{ м}$.
Ответ: сопротивление медного провода равно $3.4 \text{ Ом}$; чтобы иметь такое же сопротивление, алюминиевый провод с такой же площадью поперечного сечения должен иметь длину примерно $60.7 \text{ м}$.
Другие задания:
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