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Номер 11, страница 449 - 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. 4. Движение тела по окружности под действием сил тяжести и упругости - номер 11, страница 449.
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" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "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 #items: array:1 [ 0 => App\Models\Term {#1042 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "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 {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 } "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 {#1108 #items: array:2 [ 0 => App\Models\Branch {#1116 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 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 {#1117 #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 {#1150 #items: array:1 [ 0 => App\Models\Book {#1118 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 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 {#1120 #items: array:1 [ 0 => App\Models\Term {#1119 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #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 {#1123 #items: array:1 [ 0 => App\Models\Term {#1124 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "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 ] #original: array:12 [ "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 {#1127 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #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 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "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 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "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 {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "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 {#1143 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1147 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "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 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "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 {#1120} "field_class" => Illuminate\Database\Eloquent\Collection {#1121} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123} "field_author" => Illuminate\Database\Eloquent\Collection {#1125} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1127} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_country" => Illuminate\Database\Eloquent\Collection {#1130} "field_city" => Illuminate\Database\Eloquent\Collection {#1132} "field_series" => Illuminate\Database\Eloquent\Collection {#1134} "field_umk" => Illuminate\Database\Eloquent\Collection {#1135} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1136} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142} "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 {#1143} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145} "field_url" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #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 {#1117} "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 {#1150} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1149 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1389658 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Движение тела по окружности под действием сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "446" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389658 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Движение тела по окружности под действием сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "446" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1099 #items: array:2 [ 0 => App\Models\Element {#1091 #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" => 1640965 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Edition {#1089 #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 {#1087 #items: array:1 [ 0 => App\Models\Term {#1090 …30} ] #escapeWhenCastingToString: false } "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 {#1088 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087} "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 {#1088} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1085} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1390586" "type" => "task" ] "text" => "<p><strong>11.</strong> Оттяните маятник от положения равновесия на расстояние, равное радиусу окружности $\text{R}$, и определите показания динамометра. При этом погрешность измерения силы принимается равной цене деления шкалы динамометра.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1691" "height" => 297 "path" => "/media/fizika_10/kasyanov-u/0-lab04/11-1.webp?ts=1757958229" ] ] ] #original: array:7 [ "id" => 1640965 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1083} "task" => array:2 [ "refs" => "1390586" "type" => "task" ] "text" => "<p><strong>11.</strong> Оттяните маятник от положения равновесия на расстояние, равное радиусу окружности $\text{R}$, и определите показания динамометра. При этом погрешность измерения силы принимается равной цене деления шкалы динамометра.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1691" "height" => 297 "path" => "/media/fizika_10/kasyanov-u/0-lab04/11-1.webp?ts=1757958229" ] ] ] #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 {#1084 #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" => 1693598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Edition {#1082 #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 {#1081 #items: array:1 [ 0 => App\Models\Term {#1080 …30} ] #escapeWhenCastingToString: false } "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 {#1078 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "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 {#1081} "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 {#1078} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1076} "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" => "1390586" "type" => "task" ] "text" => "<p><strong>Решение</strong><br>Данное задание является инструкцией к проведению физического эксперимента. Для определения показаний динамометра необходимо рассмотреть силы, действующие на маятник в состоянии равновесия.<br>Будем считать маятник материальной точкой массой $m$, подвешенной на нерастяжимой и невесомой нити длиной $L$. Согласно условию, "радиус окружности $R$" — это радиус дуги, по которой движется маятник, то есть $R=L$. Условие "оттяните маятник от положения равновесия на расстояние, равное радиусу окружности" наиболее корректно интерпретировать как смещение маятника на такое расстояние, что длина хорды, соединяющей положение равновесия и новое положение маятника, равна $L$.<br>Когда маятник оттянут в сторону и удерживается динамометром в состоянии покоя, на него действуют три силы:<br>1. Сила тяжести $\vec{F_g}$, равная $mg$ и направленная вертикально вниз.<br>2. Сила натяжения нити $\vec{T}$, направленная вдоль нити к точке подвеса.<br>3. Горизонтальная сила упругости $\vec{F}$, создаваемая динамометром. Её величину и нужно определить.<br>Так как маятник находится в равновесии, сумма векторов всех действующих на него сил равна нулю:<br>$\vec{F} + \vec{T} + \vec{F_g} = 0$<br>Выберем систему координат с осью $OX$, направленной горизонтально (вдоль силы $\vec{F}$), и осью $OY$, направленной вертикально вверх. Пусть нить маятника отклонена на угол $\theta$ от вертикали. Тогда уравнения равновесия в проекциях на оси будут выглядеть так:<br>на ось $OX$: $F - T \sin(\theta) = 0$<br>на ось $OY$: $T \cos(\theta) - mg = 0$<br>Из второго уравнения выразим силу натяжения нити: $T = \frac{mg}{\cos(\theta)}$.<br>Подставим это выражение в первое уравнение:<br>$F - \left(\frac{mg}{\cos(\theta)}\right) \sin(\theta) = 0$<br>Отсюда находим искомую силу $F$:<br>$F = mg \frac{\sin(\theta)}{\cos(\theta)} = mg \tan(\theta)$<br>Теперь определим угол $\theta$. Рассмотрим треугольник, вершинами которого являются точка подвеса, положение равновесия маятника и его смещенное положение. Две стороны этого треугольника равны длине нити $L$, а третья сторона (хорда) по условию также равна $L$. Следовательно, этот треугольник является равносторонним, и все его углы равны $60^\circ$. Угол отклонения нити от вертикали $\theta$ как раз является углом при вершине этого треугольника, то есть $\theta = 60^\circ$.<br>Подставим значение угла в формулу для силы:<br>$F = mg \tan(60^\circ) = mg\sqrt{3}$<br>Таким образом, показания динамометра будут равны $mg\sqrt{3}$. Чтобы получить численное значение, необходимо знать массу маятника $m$. Например, если $m = 100$ г $(0.1$ кг) и $g \approx 9.8$ м/с², то $F = 0.1 \cdot 9.8 \cdot \sqrt{3} \approx 1.7$ Н.<br>Погрешность измерения силы $\Delta F$ по условию принимается равной цене деления шкалы динамометра. Если, например, цена деления равна $0.1$ Н, то результат измерения следует записать в виде $F = (1.7 \pm 0.1)$ Н.</p><p><strong>Ответ:</strong> Показания динамометра определяются по формуле $F = mg\sqrt{3}$, где $m$ – масса маятника, а $g$ – ускорение свободного падения. Результат измерения должен быть представлен в виде $(F_{изм} \pm \Delta F)$, где $F_{изм}$ – значение силы, измеренное динамометром, а $\Delta F$ – погрешность измерения, равная цене деления шкалы динамометра.</p>" ] #original: array:6 [ "id" => 1693598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107} "task" => array:2 [ "refs" => "1390586" "type" => "task" ] "text" => "<p><strong>Решение</strong><br>Данное задание является инструкцией к проведению физического эксперимента. Для определения показаний динамометра необходимо рассмотреть силы, действующие на маятник в состоянии равновесия.<br>Будем считать маятник материальной точкой массой $m$, подвешенной на нерастяжимой и невесомой нити длиной $L$. Согласно условию, "радиус окружности $R$" — это радиус дуги, по которой движется маятник, то есть $R=L$. Условие "оттяните маятник от положения равновесия на расстояние, равное радиусу окружности" наиболее корректно интерпретировать как смещение маятника на такое расстояние, что длина хорды, соединяющей положение равновесия и новое положение маятника, равна $L$.<br>Когда маятник оттянут в сторону и удерживается динамометром в состоянии покоя, на него действуют три силы:<br>1. Сила тяжести $\vec{F_g}$, равная $mg$ и направленная вертикально вниз.<br>2. Сила натяжения нити $\vec{T}$, направленная вдоль нити к точке подвеса.<br>3. Горизонтальная сила упругости $\vec{F}$, создаваемая динамометром. Её величину и нужно определить.<br>Так как маятник находится в равновесии, сумма векторов всех действующих на него сил равна нулю:<br>$\vec{F} + \vec{T} + \vec{F_g} = 0$<br>Выберем систему координат с осью $OX$, направленной горизонтально (вдоль силы $\vec{F}$), и осью $OY$, направленной вертикально вверх. Пусть нить маятника отклонена на угол $\theta$ от вертикали. Тогда уравнения равновесия в проекциях на оси будут выглядеть так:<br>на ось $OX$: $F - T \sin(\theta) = 0$<br>на ось $OY$: $T \cos(\theta) - mg = 0$<br>Из второго уравнения выразим силу натяжения нити: $T = \frac{mg}{\cos(\theta)}$.<br>Подставим это выражение в первое уравнение:<br>$F - \left(\frac{mg}{\cos(\theta)}\right) \sin(\theta) = 0$<br>Отсюда находим искомую силу $F$:<br>$F = mg \frac{\sin(\theta)}{\cos(\theta)} = mg \tan(\theta)$<br>Теперь определим угол $\theta$. Рассмотрим треугольник, вершинами которого являются точка подвеса, положение равновесия маятника и его смещенное положение. Две стороны этого треугольника равны длине нити $L$, а третья сторона (хорда) по условию также равна $L$. Следовательно, этот треугольник является равносторонним, и все его углы равны $60^\circ$. Угол отклонения нити от вертикали $\theta$ как раз является углом при вершине этого треугольника, то есть $\theta = 60^\circ$.<br>Подставим значение угла в формулу для силы:<br>$F = mg \tan(60^\circ) = mg\sqrt{3}$<br>Таким образом, показания динамометра будут равны $mg\sqrt{3}$. Чтобы получить численное значение, необходимо знать массу маятника $m$. Например, если $m = 100$ г $(0.1$ кг) и $g \approx 9.8$ м/с², то $F = 0.1 \cdot 9.8 \cdot \sqrt{3} \approx 1.7$ Н.<br>Погрешность измерения силы $\Delta F$ по условию принимается равной цене деления шкалы динамометра. Если, например, цена деления равна $0.1$ Н, то результат измерения следует записать в виде $F = (1.7 \pm 0.1)$ Н.</p><p><strong>Ответ:</strong> Показания динамометра определяются по формуле $F = mg\sqrt{3}$, где $m$ – масса маятника, а $g$ – ускорение свободного падения. Результат измерения должен быть представлен в виде $(F_{изм} \pm \Delta F)$, где $F_{изм}$ – значение силы, измеренное динамометром, а $\Delta F$ – погрешность измерения, равная цене деления шкалы динамометра.</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" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1093 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\BookPage {#1103 #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" => 1391097 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-449" "field_display_title" => "449" "field_folder" => "1" "field_image_name" => "449" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Element {#1115 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1641597 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Edition {#1089} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "449-1.jpg" "alt" => null "width" => "1861" "height" => 2528 "path" => "/media/fizika_10/kasyanov-u/0-1/449-1.webp?ts=1757958797" ] ] ] #original: array:6 [ "id" => 1641597 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109} "book_page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "449-1.jpg" "alt" => null "width" => "1861" "height" => 2528 "path" => "/media/fizika_10/kasyanov-u/0-1/449-1.webp?ts=1757958797" ] ] ] #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" => "1391098" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391096" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:6 [ 0 => App\Models\Task {#1255 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:2 [ 0 => App\Models\Element {#1270 …30} 1 => App\Models\Element {#1272 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390586" "type" => "task" ] "previous" => array:2 [ "refs" => "1390584" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259} "content" => Illuminate\Database\Eloquent\Collection {#1261} "next" => array:2 [ "refs" => "1390586" "type" => "task" ] "previous" => array:2 [ "refs" => "1390584" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1267} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1262 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1269 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:2 [ 0 => App\Models\Element {#1091} 1 => App\Models\Element {#1084} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1269} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263} "content" => Illuminate\Database\Eloquent\Collection {#1266} "next" => array:2 [ "refs" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1264} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1274 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1276 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:2 [ 0 => App\Models\Element {#1289 …30} 1 => App\Models\Element {#1291 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275} "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 {#1276} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278} "content" => Illuminate\Database\Eloquent\Collection {#1280} "next" => array:2 [ "refs" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1281 #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" => 1390588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-13" "field_display_title" => "13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1288 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1283 #items: array:2 [ 0 => App\Models\Element {#1301 …30} 1 => App\Models\Element {#1303 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390589" "type" => "task" ] "previous" => array:2 [ "refs" => "1390587" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1298 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-13" "field_display_title" => "13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1279} "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 {#1288} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1284} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1282} "content" => Illuminate\Database\Eloquent\Collection {#1283} "next" => array:2 [ "refs" => "1390589" "type" => "task" ] "previous" => array:2 [ "refs" => "1390587" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1298} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1293 #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" => 1390589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1285 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1300 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ 0 => App\Models\Branch {#1116} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:2 [ 0 => App\Models\Branch {#1116} 1 => App\Models\Branch {#1149} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1295 #items: array:2 [ 0 => App\Models\Element {#1313 …30} 1 => App\Models\Element {#1315 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390590" "type" => "task" ] "previous" => array:2 [ "refs" => "1390588" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1310 #items: array:1 [ 0 => App\Models\Book {#1118} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1285} "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 {#1300} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1294} "content" => Illuminate\Database\Eloquent\Collection {#1295} "next" => array:2 [ "refs" => "1390590" "type" => "task" ] "previous" => array:2 [ "refs" => "1390588" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1310} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1305 #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" => 1390590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1312 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1308 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1307 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390591" "type" => "task" ] "previous" => array:2 [ "refs" => "1390589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1322 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1297} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1312} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1308} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306} "content" => Illuminate\Database\Eloquent\Collection {#1307} "next" => array:2 [ "refs" => "1390591" "type" => "task" ] "previous" => array:2 [ "refs" => "1390589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1322} "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391097 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-449" "field_display_title" => "449" "field_folder" => "1" "field_image_name" => "449" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1075} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1100} "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 {#1101} "content" => Illuminate\Database\Eloquent\Collection {#1111} "next" => array:2 [ "refs" => "1391098" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391096" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1108} "content" => Illuminate\Database\Eloquent\Collection {#1099} "next" => array:2 [ "refs" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1093} "page" => array:2 [ "refs" => "1391097" "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 => "*" ] }
№11 (с. 449)
Условие. №11 (с. 449)
скриншот условия
11. Оттяните маятник от положения равновесия на расстояние, равное радиусу окружности $\text{R}$, и определите показания динамометра. При этом погрешность измерения силы принимается равной цене деления шкалы динамометра.
Решение. №11 (с. 449)
Решение
Данное задание является инструкцией к проведению физического эксперимента. Для определения показаний динамометра необходимо рассмотреть силы, действующие на маятник в состоянии равновесия.
Будем считать маятник материальной точкой массой $m$, подвешенной на нерастяжимой и невесомой нити длиной $L$. Согласно условию, "радиус окружности $R$" — это радиус дуги, по которой движется маятник, то есть $R=L$. Условие "оттяните маятник от положения равновесия на расстояние, равное радиусу окружности" наиболее корректно интерпретировать как смещение маятника на такое расстояние, что длина хорды, соединяющей положение равновесия и новое положение маятника, равна $L$.
Когда маятник оттянут в сторону и удерживается динамометром в состоянии покоя, на него действуют три силы:
1. Сила тяжести $\vec{F_g}$, равная $mg$ и направленная вертикально вниз.
2. Сила натяжения нити $\vec{T}$, направленная вдоль нити к точке подвеса.
3. Горизонтальная сила упругости $\vec{F}$, создаваемая динамометром. Её величину и нужно определить.
Так как маятник находится в равновесии, сумма векторов всех действующих на него сил равна нулю:
$\vec{F} + \vec{T} + \vec{F_g} = 0$
Выберем систему координат с осью $OX$, направленной горизонтально (вдоль силы $\vec{F}$), и осью $OY$, направленной вертикально вверх. Пусть нить маятника отклонена на угол $\theta$ от вертикали. Тогда уравнения равновесия в проекциях на оси будут выглядеть так:
на ось $OX$: $F - T \sin(\theta) = 0$
на ось $OY$: $T \cos(\theta) - mg = 0$
Из второго уравнения выразим силу натяжения нити: $T = \frac{mg}{\cos(\theta)}$.
Подставим это выражение в первое уравнение:
$F - \left(\frac{mg}{\cos(\theta)}\right) \sin(\theta) = 0$
Отсюда находим искомую силу $F$:
$F = mg \frac{\sin(\theta)}{\cos(\theta)} = mg \tan(\theta)$
Теперь определим угол $\theta$. Рассмотрим треугольник, вершинами которого являются точка подвеса, положение равновесия маятника и его смещенное положение. Две стороны этого треугольника равны длине нити $L$, а третья сторона (хорда) по условию также равна $L$. Следовательно, этот треугольник является равносторонним, и все его углы равны $60^\circ$. Угол отклонения нити от вертикали $\theta$ как раз является углом при вершине этого треугольника, то есть $\theta = 60^\circ$.
Подставим значение угла в формулу для силы:
$F = mg \tan(60^\circ) = mg\sqrt{3}$
Таким образом, показания динамометра будут равны $mg\sqrt{3}$. Чтобы получить численное значение, необходимо знать массу маятника $m$. Например, если $m = 100$ г $(0.1$ кг) и $g \approx 9.8$ м/с², то $F = 0.1 \cdot 9.8 \cdot \sqrt{3} \approx 1.7$ Н.
Погрешность измерения силы $\Delta F$ по условию принимается равной цене деления шкалы динамометра. Если, например, цена деления равна $0.1$ Н, то результат измерения следует записать в виде $F = (1.7 \pm 0.1)$ Н.
Ответ: Показания динамометра определяются по формуле $F = mg\sqrt{3}$, где $m$ – масса маятника, а $g$ – ускорение свободного падения. Результат измерения должен быть представлен в виде $(F_{изм} \pm \Delta F)$, где $F_{изм}$ – значение силы, измеренное динамометром, а $\Delta F$ – погрешность измерения, равная цене деления шкалы динамометра.
Другие задания:
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