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Номер 4, страница 452 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Лабораторные работы. 5. Проверка закона сохранения энергии при действии сил тяжести и упругости - номер 4, страница 452.
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" => 1390594 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-4" "field_display_title" => "4" "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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 7000 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1047 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "426" "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 {#1144 #items: array:2 [ 0 => App\Models\Branch {#1071 #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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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 {#1072 #items: array:1 [ 0 => App\Models\Book {#1075 #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" => 7000 "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 {#1076 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1103 …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" => 7000 "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 {#1076 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1078 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1103 …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 {#1105 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1074} "field_page_start" => "426" "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 {#1072} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1105} ] #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 {#1106 #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" => 1389659 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "5. Проверка закона сохранения энергии при действии сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "450" "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 {#1108 #items: array:1 [ 0 => App\Models\Book {#1109 #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" => 7000 "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 {#1110 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1137 …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" => 7000 "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 {#1110 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1112 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1137 …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 {#1139 #items: array:1 [ 0 => App\Models\Branch {#1140 #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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "426" "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 {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …2} ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_page_start" => "426" "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 {#1142 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 …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" => 1389659 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "5. Проверка закона сохранения энергии при действии сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1107} "field_page_start" => "450" "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 {#1108} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} ] #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 {#1155 #items: array:2 [ 0 => App\Models\Element {#1163 #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" => 1640986 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Edition {#1164 #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" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1166 …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 {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1166 …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 {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1169 …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" => "1390594" "type" => "task" ] "text" => "<p><strong>4.</strong> Оттяните груз вниз на расстояние $\text{A}$ (5–7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний $\text{A}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1688" "height" => 194 "path" => "/media/fizika_10/kasyanov-u/0-lab05/4-1.webp?ts=1757958239" ] ] ] #original: array:7 [ "id" => 1640986 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172} "task" => array:2 [ "refs" => "1390594" "type" => "task" ] "text" => "<p><strong>4.</strong> Оттяните груз вниз на расстояние $\text{A}$ (5–7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний $\text{A}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1688" "height" => 194 "path" => "/media/fizika_10/kasyanov-u/0-lab05/4-1.webp?ts=1757958239" ] ] ] #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 {#1170 #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" => 1693606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\Edition {#1171 #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" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …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" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …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" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 …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" => "1390594" "type" => "task" ] "text" => "<p><strong>4.</strong> Оттяните груз вниз на расстояние A (5—7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний A.</p><p>Амплитуда колебаний — это максимальное смещение колеблющегося тела от его положения равновесия. В данном эксперименте, если пренебречь силами сопротивления (например, сопротивлением воздуха), амплитуда колебаний груза на пружине будет равна расстоянию, на которое груз был первоначально смещен от положения равновесия.</p><p>Порядок выполнения действий:</p><p><strong>1.</strong> Подвесить груз на пружине и дождаться, пока он придет в состояние покоя. Это положение является положением равновесия. Его следует отметить, например, как нулевую отметку на измерительной линейке, расположенной вертикально рядом с грузом.</p><p><strong>2.</strong> Аккуратно оттянуть груз вертикально вниз на расстояние $A$, которое должно находиться в диапазоне от 5 до 7 см (например, можно выбрать $A = 6$ см).</p><p><strong>3.</strong> Отпустить груз без толчка (с нулевой начальной скоростью). Груз начнет совершать вертикальные колебания.</p><p><strong>4.</strong> Измерить с помощью линейки максимальное расстояние, на которое груз отклоняется от положения равновесия во время колебаний. В идеальных условиях (без потерь энергии) это расстояние будет равно начальному смещению.</p><p>Таким образом, если груз был оттянут на 6 см от положения равновесия, то измеренная амплитуда колебаний также составит 6 см.</p><p><strong>Ответ:</strong> Измеренная амплитуда колебаний $A$ будет равна начальному смещению груза от положения равновесия. Согласно условию, это значение должно быть выбрано в диапазоне от 5 до 7 см, например, $A = 6$ см.</p><p><strong>5.</strong> Абсолютную погрешность измерения A, амплитуды колебаний A</p><p>Абсолютная погрешность измерения амплитуды определяется точностью измерительного прибора и методикой измерения.</p><p><strong>Дано:</strong></p><p>Измерение длины проводится с помощью стандартной лабораторной линейки.<br>Цена деления линейки: $c = 1$ мм.</p><p>В системе СИ:<br>$c = 0.001$ м.</p><p><strong>Найти:</strong></p><p>$\Delta A$ — абсолютную погрешность измерения амплитуды.</p><p><strong>Решение:</strong></p><p>Амплитуда $A$ находится как расстояние между положением равновесия $y_0$ и положением максимального отклонения $y_{max}$. Для этого необходимо зафиксировать на шкале линейки два этих положения.</p><p>При однократном прямом измерении абсолютная погрешность отсчета по шкале прибора ($\Delta y_{отсч}$) принимается равной половине цены деления этого прибора.</p><p>$\Delta y_{отсч} = \frac{c}{2} = \frac{1 \text{ мм}}{2} = 0.5 \text{ мм}$</p><p>Полная абсолютная погрешность измерения амплитуды $\Delta A$ складывается из погрешностей определения положения равновесия ($\Delta y_0$) и положения максимального отклонения ($\Delta y_{max}$):</p><p>$\Delta A = \Delta y_0 + \Delta y_{max}$</p><p>Так как обе координаты определяются по одной и той же линейке, погрешность для каждого измерения можно принять равной погрешности отсчета:</p><p>$\Delta A = 0.5 \text{ мм} + 0.5 \text{ мм} = 1 \text{ мм}$</p><p>Переведем полученное значение в сантиметры: $1 \text{ мм} = 0.1 \text{ см}$.</p><p><strong>Ответ:</strong> Абсолютная погрешность измерения амплитуды $A$ составляет $\Delta A = 1 \text{ мм}$ или $0.1 \text{ см}$.</p>" ] #original: array:6 [ "id" => 1693606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1180} "task" => array:2 [ "refs" => "1390594" "type" => "task" ] "text" => "<p><strong>4.</strong> Оттяните груз вниз на расстояние A (5—7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний A.</p><p>Амплитуда колебаний — это максимальное смещение колеблющегося тела от его положения равновесия. В данном эксперименте, если пренебречь силами сопротивления (например, сопротивлением воздуха), амплитуда колебаний груза на пружине будет равна расстоянию, на которое груз был первоначально смещен от положения равновесия.</p><p>Порядок выполнения действий:</p><p><strong>1.</strong> Подвесить груз на пружине и дождаться, пока он придет в состояние покоя. Это положение является положением равновесия. Его следует отметить, например, как нулевую отметку на измерительной линейке, расположенной вертикально рядом с грузом.</p><p><strong>2.</strong> Аккуратно оттянуть груз вертикально вниз на расстояние $A$, которое должно находиться в диапазоне от 5 до 7 см (например, можно выбрать $A = 6$ см).</p><p><strong>3.</strong> Отпустить груз без толчка (с нулевой начальной скоростью). Груз начнет совершать вертикальные колебания.</p><p><strong>4.</strong> Измерить с помощью линейки максимальное расстояние, на которое груз отклоняется от положения равновесия во время колебаний. В идеальных условиях (без потерь энергии) это расстояние будет равно начальному смещению.</p><p>Таким образом, если груз был оттянут на 6 см от положения равновесия, то измеренная амплитуда колебаний также составит 6 см.</p><p><strong>Ответ:</strong> Измеренная амплитуда колебаний $A$ будет равна начальному смещению груза от положения равновесия. Согласно условию, это значение должно быть выбрано в диапазоне от 5 до 7 см, например, $A = 6$ см.</p><p><strong>5.</strong> Абсолютную погрешность измерения A, амплитуды колебаний A</p><p>Абсолютная погрешность измерения амплитуды определяется точностью измерительного прибора и методикой измерения.</p><p><strong>Дано:</strong></p><p>Измерение длины проводится с помощью стандартной лабораторной линейки.<br>Цена деления линейки: $c = 1$ мм.</p><p>В системе СИ:<br>$c = 0.001$ м.</p><p><strong>Найти:</strong></p><p>$\Delta A$ — абсолютную погрешность измерения амплитуды.</p><p><strong>Решение:</strong></p><p>Амплитуда $A$ находится как расстояние между положением равновесия $y_0$ и положением максимального отклонения $y_{max}$. Для этого необходимо зафиксировать на шкале линейки два этих положения.</p><p>При однократном прямом измерении абсолютная погрешность отсчета по шкале прибора ($\Delta y_{отсч}$) принимается равной половине цены деления этого прибора.</p><p>$\Delta y_{отсч} = \frac{c}{2} = \frac{1 \text{ мм}}{2} = 0.5 \text{ мм}$</p><p>Полная абсолютная погрешность измерения амплитуды $\Delta A$ складывается из погрешностей определения положения равновесия ($\Delta y_0$) и положения максимального отклонения ($\Delta y_{max}$):</p><p>$\Delta A = \Delta y_0 + \Delta y_{max}$</p><p>Так как обе координаты определяются по одной и той же линейке, погрешность для каждого измерения можно принять равной погрешности отсчета:</p><p>$\Delta A = 0.5 \text{ мм} + 0.5 \text{ мм} = 1 \text{ мм}$</p><p>Переведем полученное значение в сантиметры: $1 \text{ мм} = 0.1 \text{ см}$.</p><p><strong>Ответ:</strong> Абсолютная погрешность измерения амплитуды $A$ составляет $\Delta A = 1 \text{ мм}$ или $0.1 \text{ см}$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390595" "type" => "task" ] "previous" => array:2 [ "refs" => "1390593" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1160 #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" => 7000 "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 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[ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "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 {#1154 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Term {#1162 #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 {#1158 #items: array:1 [ 0 => App\Models\Term {#1156 #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: 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#guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1178 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1179 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Term {#1182 #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" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Term {#1184 #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" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ 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"field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Term {#1192 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ …6] "field_translit" => "belyy" ] #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "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 {#1147} "field_class" => Illuminate\Database\Eloquent\Collection {#1145} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1151} "field_author" => Illuminate\Database\Eloquent\Collection {#1148} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1154} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_country" => Illuminate\Database\Eloquent\Collection {#1158} "field_city" => Illuminate\Database\Eloquent\Collection {#1159} "field_series" => Illuminate\Database\Eloquent\Collection {#1178} "field_umk" => Illuminate\Database\Eloquent\Collection {#1179} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1181} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1183} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1185} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1187} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1188} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1191} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\BookPage {#1199 #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" => 1391100 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-452" "field_display_title" => "452" "field_folder" => "1" "field_image_name" => "452" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Book {#1160} ] #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 {#1203 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Element {#1212 #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" => 1641600 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1641600 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1391101" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391099" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1568 #items: array:10 [ 0 => App\Models\Task {#1584 #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" => 1390591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1585 …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 {#1586 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1587 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1588 …2} "content" => Illuminate\Database\Eloquent\Collection {#1605 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1607 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1585 …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 {#1586 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1587 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1588 …2} "content" => Illuminate\Database\Eloquent\Collection {#1605 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1607 …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 => "*" ] } 1 => App\Models\Task {#1606 #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" => 1390592 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1608 …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 {#1609 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1610 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1611 …2} "content" => Illuminate\Database\Eloquent\Collection {#1628 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1630 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390592 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1608 …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 {#1609 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1610 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1611 …2} "content" => Illuminate\Database\Eloquent\Collection {#1628 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1630 …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 => "*" ] } 2 => App\Models\Task {#1629 #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" => 1390593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1631 …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 {#1632 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1633 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1634 …2} "content" => Illuminate\Database\Eloquent\Collection {#1651 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1653 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1631 …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 {#1632 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1633 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1634 …2} "content" => Illuminate\Database\Eloquent\Collection {#1651 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1653 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1652 #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" => 1390594 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1654 …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 {#1655 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1656 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1657 …2} "content" => Illuminate\Database\Eloquent\Collection {#1658 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1659 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1390594 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1654 …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 {#1655 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1656 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1657 …2} "content" => Illuminate\Database\Eloquent\Collection {#1658 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1659 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1660 #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" => 1390595 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1661 …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 {#1662 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1663 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1664 …2} "content" => Illuminate\Database\Eloquent\Collection {#1675 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1680 …2} "page" => array:2 [ …2] ] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1665 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1670 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1682 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 8 => App\Models\Task {#1679 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 9 => App\Models\Task {#1715 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391100 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-452" "field_display_title" => "452" "field_folder" => "1" "field_image_name" => "452" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202} "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 {#1203} "content" => Illuminate\Database\Eloquent\Collection {#1213} "next" => array:2 [ "refs" => "1391101" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391099" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1568} ] #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" => 1390594 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "452" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab05-4" "field_display_title" => "4" "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 {#1144} "content" => Illuminate\Database\Eloquent\Collection {#1155} "next" => array:2 [ "refs" => "1390595" "type" => "task" ] "previous" => array:2 [ "refs" => "1390593" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195} "page" => array:2 [ "refs" => "1391100" "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 (с. 452)
Условие. №4 (с. 452)
скриншот условия
4. Оттяните груз вниз на расстояние $\text{A}$ (5–7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний $\text{A}$.
Решение. №4 (с. 452)
4. Оттяните груз вниз на расстояние A (5—7 см) от нового положения равновесия и отпустите его. Измерьте амплитуду колебаний A.
Амплитуда колебаний — это максимальное смещение колеблющегося тела от его положения равновесия. В данном эксперименте, если пренебречь силами сопротивления (например, сопротивлением воздуха), амплитуда колебаний груза на пружине будет равна расстоянию, на которое груз был первоначально смещен от положения равновесия.
Порядок выполнения действий:
1. Подвесить груз на пружине и дождаться, пока он придет в состояние покоя. Это положение является положением равновесия. Его следует отметить, например, как нулевую отметку на измерительной линейке, расположенной вертикально рядом с грузом.
2. Аккуратно оттянуть груз вертикально вниз на расстояние $A$, которое должно находиться в диапазоне от 5 до 7 см (например, можно выбрать $A = 6$ см).
3. Отпустить груз без толчка (с нулевой начальной скоростью). Груз начнет совершать вертикальные колебания.
4. Измерить с помощью линейки максимальное расстояние, на которое груз отклоняется от положения равновесия во время колебаний. В идеальных условиях (без потерь энергии) это расстояние будет равно начальному смещению.
Таким образом, если груз был оттянут на 6 см от положения равновесия, то измеренная амплитуда колебаний также составит 6 см.
Ответ: Измеренная амплитуда колебаний $A$ будет равна начальному смещению груза от положения равновесия. Согласно условию, это значение должно быть выбрано в диапазоне от 5 до 7 см, например, $A = 6$ см.
5. Абсолютную погрешность измерения A, амплитуды колебаний A
Абсолютная погрешность измерения амплитуды определяется точностью измерительного прибора и методикой измерения.
Дано:
Измерение длины проводится с помощью стандартной лабораторной линейки.
Цена деления линейки: $c = 1$ мм.
В системе СИ:
$c = 0.001$ м.
Найти:
$\Delta A$ — абсолютную погрешность измерения амплитуды.
Решение:
Амплитуда $A$ находится как расстояние между положением равновесия $y_0$ и положением максимального отклонения $y_{max}$. Для этого необходимо зафиксировать на шкале линейки два этих положения.
При однократном прямом измерении абсолютная погрешность отсчета по шкале прибора ($\Delta y_{отсч}$) принимается равной половине цены деления этого прибора.
$\Delta y_{отсч} = \frac{c}{2} = \frac{1 \text{ мм}}{2} = 0.5 \text{ мм}$
Полная абсолютная погрешность измерения амплитуды $\Delta A$ складывается из погрешностей определения положения равновесия ($\Delta y_0$) и положения максимального отклонения ($\Delta y_{max}$):
$\Delta A = \Delta y_0 + \Delta y_{max}$
Так как обе координаты определяются по одной и той же линейке, погрешность для каждого измерения можно принять равной погрешности отсчета:
$\Delta A = 0.5 \text{ мм} + 0.5 \text{ мм} = 1 \text{ мм}$
Переведем полученное значение в сантиметры: $1 \text{ мм} = 0.1 \text{ см}$.
Ответ: Абсолютная погрешность измерения амплитуды $A$ составляет $\Delta A = 1 \text{ мм}$ или $0.1 \text{ см}$.
Другие задания:
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