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Номер 5, страница 113, часть 1 - гдз по физике 9 класс учебник Генденштейн, Булатова
Авторы: Генденштейн Л. Э., Булатова А. А., Корнильев И. Н., Кошкина А. В.
Тип: Учебник
Издательство: Бином
Год издания: 2016 - 2026
Часть: 1
Цвет обложки: бирюзовый
ISBN: 978-5-9963-3062-1
Популярные ГДЗ в 9 классе
Часть 1. Механические явления. Глава II. Динамика. Параграф 13. Движение системы тел - номер 5, страница 113.
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" => 1433666 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/13-5" "field_display_title" => "5" "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 {#1075 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 2980 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …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" => 2980 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …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 {#1072 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "6" "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 {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1072} ] #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 {#1245 #items: array:4 [ 0 => App\Models\Branch {#1073 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1077 #items: array:1 [ 0 => App\Models\Book {#1078 #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" => 2980 "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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1107 …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" => 2980 "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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1107 …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 {#1109 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1076} "field_page_start" => "6" "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 {#1077} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1109} ] #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 {#1110 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1111 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1112 #items: array:1 [ 0 => App\Models\Book {#1113 #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" => 2980 "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 {#1114 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …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" => 2980 "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 {#1114 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1144 #items: array:1 [ 0 => App\Models\Branch {#1145 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "6" "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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 …2} ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "6" "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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 …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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1111} "field_page_start" => "6" "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 {#1112} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1150 #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" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: array:1 [ 0 => App\Models\Term {#1152 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "59" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Book {#1154 #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" => 2980 "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 {#1155 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1183 …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" => 2980 "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 {#1155 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1183 …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 {#1185 #items: array:1 [ 0 => App\Models\Branch {#1186 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_page_start" => "6" "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 {#1188 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1189 …2} ] #original: array:24 [ "id" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_page_start" => "6" "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 …6 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_page_start" => "59" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1153} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1185} ] #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\Branch {#1195 #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" => 1433222 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Движение системы тел" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:1 [ 0 => App\Models\Term {#1197 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "111" "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 {#1198 #items: array:1 [ 0 => App\Models\Book {#1199 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Branch {#1231 #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 [ …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:24 [ "id" => 1433222 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Движение системы тел" "field_branch_order" => "13" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1196} "field_page_start" => "111" "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 {#1198} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1230} ] #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 {#1246 #items: array:2 [ 0 => App\Models\Element {#1256 #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" => 1696407 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Edition {#1257 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433666" "type" => "task" ] "text" => "<p><strong>5.</strong> Два груза массами $\text{m}$ и $\text{M}$ подвешены на концах лёгкой нерастяжимой нити, переброшенной через блок (рис. 13.3). $M > m$. Трением в блоке и его массой можно пренебречь.</p><p>Рис. 13.3</p><p><strong>а)</strong> Перенесите рисунок в тетрадь и изобразите на нём силы, действующие на каждый груз. Назовите эти силы.</p><p><strong>б)</strong> Как направлены ускорения грузов? Изобразите их на чертеже.</p><p><strong>в)</strong> Равны ли по модулю ускорения грузов? Равны ли по модулю силы натяжения нити, действующие на грузы? Обоснуйте свои ответы.</p><p><strong>г)</strong> Запишите второй закон Ньютона для грузов в проекциях на ось $\text{x}$, направленную вертикально вниз (обозначьте $\text{a}$ модуль ускорения грузов, $\text{T}$ — модуль силы натяжения нити).</p><p><strong>д)</strong> Используя полученные уравнения, выразите модуль ускорения грузов и силу натяжения нити через $\text{M}$ и $\text{m}$.</p><p><strong>е)</strong> Одинаков ли вес грузов? Обоснуйте свой ответ.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1507" "height" => 1060 "path" => "/media/fizika_09/gendenshtejn-u/0-13/5-1.webp?ts=1759348246" ] ] ] #original: array:7 [ "id" => 1696407 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1265} "task" => array:2 [ "refs" => "1433666" "type" => "task" ] "text" => "<p><strong>5.</strong> Два груза массами $\text{m}$ и $\text{M}$ подвешены на концах лёгкой нерастяжимой нити, переброшенной через блок (рис. 13.3). $M > m$. Трением в блоке и его массой можно пренебречь.</p><p>Рис. 13.3</p><p><strong>а)</strong> Перенесите рисунок в тетрадь и изобразите на нём силы, действующие на каждый груз. Назовите эти силы.</p><p><strong>б)</strong> Как направлены ускорения грузов? Изобразите их на чертеже.</p><p><strong>в)</strong> Равны ли по модулю ускорения грузов? Равны ли по модулю силы натяжения нити, действующие на грузы? Обоснуйте свои ответы.</p><p><strong>г)</strong> Запишите второй закон Ньютона для грузов в проекциях на ось $\text{x}$, направленную вертикально вниз (обозначьте $\text{a}$ модуль ускорения грузов, $\text{T}$ — модуль силы натяжения нити).</p><p><strong>д)</strong> Используя полученные уравнения, выразите модуль ускорения грузов и силу натяжения нити через $\text{M}$ и $\text{m}$.</p><p><strong>е)</strong> Одинаков ли вес грузов? Обоснуйте свой ответ.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1507" "height" => 1060 "path" => "/media/fizika_09/gendenshtejn-u/0-13/5-1.webp?ts=1759348246" ] ] ] #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 {#1263 #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" => 1780477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:1 [ 0 => App\Models\Edition {#1264 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433666" "type" => "task" ] "text" => "<p><strong>а)</strong> На каждый груз действуют две силы. Первая — это сила тяжести, направленная вертикально вниз. Для груза массой $\text{m}$ её модуль равен $mg$, а для груза массой $\text{M}$ — $Mg$. Вторая — это сила натяжения нити $\text{T}$, направленная вертикально вверх вдоль нити.</p><p><strong>Ответ:</strong> На каждый груз действуют сила тяжести (направлена вниз) и сила натяжения нити (направлена вверх).</p><p><strong>б)</strong> Поскольку по условию масса $\text{M}$ больше массы $\text{m}$ ($M > m$), то система тел будет двигаться так, что груз большей массы $\text{M}$ будет опускаться, а груз меньшей массы $\text{m}$ — подниматься. Следовательно, вектор ускорения груза $\text{M}$ направлен вертикально вниз, а вектор ускорения груза $\text{m}$ — вертикально вверх.</p><p><strong>Ответ:</strong> Ускорение груза $\text{M}$ направлено вниз, ускорение груза $\text{m}$ направлено вверх.</p><p><strong>в)</strong> Модули ускорения грузов равны. Так как нить нерастяжима, то за одно и то же время грузы проходят одинаковые по модулю расстояния. Это означает, что модули их скоростей и ускорений в любой момент времени равны.</p><p>Модули сил натяжения нити, действующие на грузы, также равны. Это следует из условий, что нить и блок невесомы, а трение в блоке отсутствует. В такой идеальной системе сила натяжения передается по всей длине нити без изменений.</p><p><strong>Ответ:</strong> Да, модули ускорений равны, так как нить нерастяжима. Да, модули сил натяжения равны, так как нить и блок идеальны (невесомы и без трения).</p><p><strong>г)</strong> Запишем второй закон Ньютона ($\vec{F} = m\vec{a}$) для каждого груза в проекции на вертикальную ось $\text{x}$, направленную вниз.</p><p>Для груза массой $\text{M}$: его ускорение $\vec{a}$ направлено вниз, поэтому его проекция на ось $\text{x}$ положительна ($a_x = a$). На груз действуют сила тяжести $Mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).</p><p>$Mg - T = Ma$</p><p>Для груза массой $\text{m}$: его ускорение $\vec{a}$ направлено вверх, поэтому его проекция на ось $\text{x}$ отрицательна ($a_x = -a$). Силы, действующие на него, — это сила тяжести $mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).</p><p>$mg - T = m(-a)$</p><p><strong>Ответ:</strong> Уравнение для груза $\text{M}$: $Mg - T = Ma$. Уравнение для груза $\text{m}$: $mg - T = -ma$.</p><p><strong>д)</strong></p><p><strong>Дано</strong></p><p>Масса первого груза: $\text{m}$</p><p>Масса второго груза: $\text{M}$</p><p>Условие: $M > m$</p><p>Нить и блок идеальные</p><p>Ускорение свободного падения: $\text{g}$</p><p><strong>Найти:</strong></p><p>Модуль ускорения грузов $\text{a}$</p><p>Модуль силы натяжения нити $\text{T}$</p><p><strong>Решение</strong></p><p>Имеем систему из двух уравнений, полученных в пункте (г). Удобнее второе уравнение записать в виде $T - mg = ma$.</p><p>$\begin{cases} Mg - T = Ma \\ T - mg = ma \end{cases}$</p><p>Сложим левые и правые части этих двух уравнений, чтобы исключить силу натяжения $\text{T}$ и найти ускорение $\text{a}$:</p><p>$(Mg - T) + (T - mg) = Ma + ma$</p><p>$Mg - mg = (M + m)a$</p><p>Отсюда выражаем модуль ускорения $\text{a}$:</p><p>$a = \frac{M - m}{M + m}g$</p><p>Теперь подставим полученное выражение для $\text{a}$ во второе уравнение системы ($T - mg = ma$), чтобы найти силу натяжения $\text{T}$:</p><p>$T = ma + mg = m(a + g)$</p><p>$T = m \left( \frac{M - m}{M + m}g + g \right)$</p><p>Вынесем $\text{g}$ за скобки и приведем к общему знаменателю:</p><p>$T = mg \left( \frac{M - m}{M + m} + 1 \right) = mg \left( \frac{M - m + M + m}{M + m} \right)$</p><p>$T = mg \left( \frac{2M}{M + m} \right) = \frac{2Mmg}{M + m}$</p><p><strong>Ответ:</strong> Модуль ускорения грузов $a = \frac{M - m}{M + m}g$, сила натяжения нити $T = \frac{2Mmg}{M + m}$.</p><p><strong>е)</strong> Вес тела — это сила, с которой тело вследствие притяжения к Земле действует на опору или подвес. В данном случае подвесом для обоих грузов является нить. По третьему закону Ньютона, сила, с которой каждый груз действует на нить (то есть его вес $\text{P}$), по модулю равна силе натяжения нити $\text{T}$, с которой нить действует на груз.</p><p>Так как сила натяжения нити $\text{T}$ одинакова по всей длине, то веса обоих грузов во время движения равны: $P_M = P_m = T$.</p><p>Стоит отметить, что вес грузов в данном случае не равен их силе тяжести. Для груза $\text{m}$, движущегося вверх с ускорением, вес $P_m = T$ больше силы тяжести $mg$. Для груза $\text{M}$, движущегося вниз с ускорением, вес $P_M = T$ меньше силы тяжести $Mg$.</p><p><strong>Ответ:</strong> Да, вес грузов во время движения одинаков, так как вес каждого из них по модулю равен силе натяжения нити $\text{T}$, которая одинакова для обоих грузов.</p>" ] #original: array:6 [ "id" => 1780477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1273} "task" => array:2 [ "refs" => "1433666" "type" => "task" ] "text" => "<p><strong>а)</strong> На каждый груз действуют две силы. Первая — это сила тяжести, направленная вертикально вниз. Для груза массой $\text{m}$ её модуль равен $mg$, а для груза массой $\text{M}$ — $Mg$. Вторая — это сила натяжения нити $\text{T}$, направленная вертикально вверх вдоль нити.</p><p><strong>Ответ:</strong> На каждый груз действуют сила тяжести (направлена вниз) и сила натяжения нити (направлена вверх).</p><p><strong>б)</strong> Поскольку по условию масса $\text{M}$ больше массы $\text{m}$ ($M > m$), то система тел будет двигаться так, что груз большей массы $\text{M}$ будет опускаться, а груз меньшей массы $\text{m}$ — подниматься. Следовательно, вектор ускорения груза $\text{M}$ направлен вертикально вниз, а вектор ускорения груза $\text{m}$ — вертикально вверх.</p><p><strong>Ответ:</strong> Ускорение груза $\text{M}$ направлено вниз, ускорение груза $\text{m}$ направлено вверх.</p><p><strong>в)</strong> Модули ускорения грузов равны. Так как нить нерастяжима, то за одно и то же время грузы проходят одинаковые по модулю расстояния. Это означает, что модули их скоростей и ускорений в любой момент времени равны.</p><p>Модули сил натяжения нити, действующие на грузы, также равны. Это следует из условий, что нить и блок невесомы, а трение в блоке отсутствует. В такой идеальной системе сила натяжения передается по всей длине нити без изменений.</p><p><strong>Ответ:</strong> Да, модули ускорений равны, так как нить нерастяжима. Да, модули сил натяжения равны, так как нить и блок идеальны (невесомы и без трения).</p><p><strong>г)</strong> Запишем второй закон Ньютона ($\vec{F} = m\vec{a}$) для каждого груза в проекции на вертикальную ось $\text{x}$, направленную вниз.</p><p>Для груза массой $\text{M}$: его ускорение $\vec{a}$ направлено вниз, поэтому его проекция на ось $\text{x}$ положительна ($a_x = a$). На груз действуют сила тяжести $Mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).</p><p>$Mg - T = Ma$</p><p>Для груза массой $\text{m}$: его ускорение $\vec{a}$ направлено вверх, поэтому его проекция на ось $\text{x}$ отрицательна ($a_x = -a$). Силы, действующие на него, — это сила тяжести $mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).</p><p>$mg - T = m(-a)$</p><p><strong>Ответ:</strong> Уравнение для груза $\text{M}$: $Mg - T = Ma$. Уравнение для груза $\text{m}$: $mg - T = -ma$.</p><p><strong>д)</strong></p><p><strong>Дано</strong></p><p>Масса первого груза: $\text{m}$</p><p>Масса второго груза: $\text{M}$</p><p>Условие: $M > m$</p><p>Нить и блок идеальные</p><p>Ускорение свободного падения: $\text{g}$</p><p><strong>Найти:</strong></p><p>Модуль ускорения грузов $\text{a}$</p><p>Модуль силы натяжения нити $\text{T}$</p><p><strong>Решение</strong></p><p>Имеем систему из двух уравнений, полученных в пункте (г). Удобнее второе уравнение записать в виде $T - mg = ma$.</p><p>$\begin{cases} Mg - T = Ma \\ T - mg = ma \end{cases}$</p><p>Сложим левые и правые части этих двух уравнений, чтобы исключить силу натяжения $\text{T}$ и найти ускорение $\text{a}$:</p><p>$(Mg - T) + (T - mg) = Ma + ma$</p><p>$Mg - mg = (M + m)a$</p><p>Отсюда выражаем модуль ускорения $\text{a}$:</p><p>$a = \frac{M - m}{M + m}g$</p><p>Теперь подставим полученное выражение для $\text{a}$ во второе уравнение системы ($T - mg = ma$), чтобы найти силу натяжения $\text{T}$:</p><p>$T = ma + mg = m(a + g)$</p><p>$T = m \left( \frac{M - m}{M + m}g + g \right)$</p><p>Вынесем $\text{g}$ за скобки и приведем к общему знаменателю:</p><p>$T = mg \left( \frac{M - m}{M + m} + 1 \right) = mg \left( \frac{M - m + M + m}{M + m} \right)$</p><p>$T = mg \left( \frac{2M}{M + m} \right) = \frac{2Mmg}{M + m}$</p><p><strong>Ответ:</strong> Модуль ускорения грузов $a = \frac{M - m}{M + m}g$, сила натяжения нити $T = \frac{2Mmg}{M + m}$.</p><p><strong>е)</strong> Вес тела — это сила, с которой тело вследствие притяжения к Земле действует на опору или подвес. В данном случае подвесом для обоих грузов является нить. По третьему закону Ньютона, сила, с которой каждый груз действует на нить (то есть его вес $\text{P}$), по модулю равна силе натяжения нити $\text{T}$, с которой нить действует на груз.</p><p>Так как сила натяжения нити $\text{T}$ одинакова по всей длине, то веса обоих грузов во время движения равны: $P_M = P_m = T$.</p><p>Стоит отметить, что вес грузов в данном случае не равен их силе тяжести. Для груза $\text{m}$, движущегося вверх с ускорением, вес $P_m = T$ больше силы тяжести $mg$. Для груза $\text{M}$, движущегося вниз с ускорением, вес $P_M = T$ меньше силы тяжести $Mg$.</p><p><strong>Ответ:</strong> Да, вес грузов во время движения одинаков, так как вес каждого из них по модулю равен силе натяжения нити $\text{T}$, которая одинакова для обоих грузов.</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" => "1433667" "type" => "task" ] "previous" => array:2 [ "refs" => "1433665" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ 0 => App\Models\Book {#1253 #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" => 2980 "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 {#1247 #items: array:1 [ 0 => App\Models\Term {#1248 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ 0 => App\Models\Term {#1251 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ 0 => App\Models\Term {#1252 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:4 [ 0 => App\Models\Term {#1271 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1272 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1274 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Term {#1275 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1276 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ 0 => App\Models\Term {#1278 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ 0 => App\Models\Term {#1280 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:1 [ 0 => App\Models\Term {#1282 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1283 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1284 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1285 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1286 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1287 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:1 [ 0 => App\Models\Term {#1289 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1290 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1291 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1292 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1293 #items: array:1 [ 0 => App\Models\Term {#1294 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 2980 "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 {#1247} "field_class" => Illuminate\Database\Eloquent\Collection {#1255} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1249} "field_author" => Illuminate\Database\Eloquent\Collection {#1250} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1276} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1277} "field_country" => Illuminate\Database\Eloquent\Collection {#1279} "field_city" => Illuminate\Database\Eloquent\Collection {#1281} "field_series" => Illuminate\Database\Eloquent\Collection {#1283} "field_umk" => Illuminate\Database\Eloquent\Collection {#1284} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1285} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1286} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1287} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1288} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1290} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1291} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1292} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1293} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #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 {#1302 #items: array:1 [ 0 => App\Models\BookPage {#1301 #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" => 1434754 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-113" "field_display_title" => "113" "field_folder" => "2" "field_image_name" => "113" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1341 #items: array:1 [ 0 => App\Models\Branch {#1303 #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 [ …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 } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1339 #items: array:1 [ 0 => App\Models\Book {#1253} ] #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 {#1340 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1351 #items: array:1 [ 0 => App\Models\Element {#1350 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1434755" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434753" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1344 #items: array:4 [ 0 => App\Models\Task {#1358 #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] } 1 => App\Models\Task {#1397 #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] } 2 => App\Models\Task {#1387 #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] } 3 => App\Models\Task {#1376 #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" => 1434754 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "113" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-113" "field_display_title" => "113" "field_folder" => "2" "field_image_name" => "113" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1341} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1339} "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 {#1340} "content" => Illuminate\Database\Eloquent\Collection {#1351} "next" => array:2 [ "refs" => "1434755" "type" => "book_page" ] "previous" => array:2 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№5 (с. 113)
Условие. №5 (с. 113)
скриншот условия
5. Два груза массами $\text{m}$ и $\text{M}$ подвешены на концах лёгкой нерастяжимой нити, переброшенной через блок (рис. 13.3). $M > m$. Трением в блоке и его массой можно пренебречь.
Рис. 13.3
а) Перенесите рисунок в тетрадь и изобразите на нём силы, действующие на каждый груз. Назовите эти силы.
б) Как направлены ускорения грузов? Изобразите их на чертеже.
в) Равны ли по модулю ускорения грузов? Равны ли по модулю силы натяжения нити, действующие на грузы? Обоснуйте свои ответы.
г) Запишите второй закон Ньютона для грузов в проекциях на ось $\text{x}$, направленную вертикально вниз (обозначьте $\text{a}$ модуль ускорения грузов, $\text{T}$ — модуль силы натяжения нити).
д) Используя полученные уравнения, выразите модуль ускорения грузов и силу натяжения нити через $\text{M}$ и $\text{m}$.
е) Одинаков ли вес грузов? Обоснуйте свой ответ.
Решение. №5 (с. 113)
а) На каждый груз действуют две силы. Первая — это сила тяжести, направленная вертикально вниз. Для груза массой $\text{m}$ её модуль равен $mg$, а для груза массой $\text{M}$ — $Mg$. Вторая — это сила натяжения нити $\text{T}$, направленная вертикально вверх вдоль нити.
Ответ: На каждый груз действуют сила тяжести (направлена вниз) и сила натяжения нити (направлена вверх).
б) Поскольку по условию масса $\text{M}$ больше массы $\text{m}$ ($M > m$), то система тел будет двигаться так, что груз большей массы $\text{M}$ будет опускаться, а груз меньшей массы $\text{m}$ — подниматься. Следовательно, вектор ускорения груза $\text{M}$ направлен вертикально вниз, а вектор ускорения груза $\text{m}$ — вертикально вверх.
Ответ: Ускорение груза $\text{M}$ направлено вниз, ускорение груза $\text{m}$ направлено вверх.
в) Модули ускорения грузов равны. Так как нить нерастяжима, то за одно и то же время грузы проходят одинаковые по модулю расстояния. Это означает, что модули их скоростей и ускорений в любой момент времени равны.
Модули сил натяжения нити, действующие на грузы, также равны. Это следует из условий, что нить и блок невесомы, а трение в блоке отсутствует. В такой идеальной системе сила натяжения передается по всей длине нити без изменений.
Ответ: Да, модули ускорений равны, так как нить нерастяжима. Да, модули сил натяжения равны, так как нить и блок идеальны (невесомы и без трения).
г) Запишем второй закон Ньютона ($\vec{F} = m\vec{a}$) для каждого груза в проекции на вертикальную ось $\text{x}$, направленную вниз.
Для груза массой $\text{M}$: его ускорение $\vec{a}$ направлено вниз, поэтому его проекция на ось $\text{x}$ положительна ($a_x = a$). На груз действуют сила тяжести $Mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).
$Mg - T = Ma$
Для груза массой $\text{m}$: его ускорение $\vec{a}$ направлено вверх, поэтому его проекция на ось $\text{x}$ отрицательна ($a_x = -a$). Силы, действующие на него, — это сила тяжести $mg$ (проекция положительна) и сила натяжения $\text{T}$ (проекция отрицательна).
$mg - T = m(-a)$
Ответ: Уравнение для груза $\text{M}$: $Mg - T = Ma$. Уравнение для груза $\text{m}$: $mg - T = -ma$.
д)
Дано
Масса первого груза: $\text{m}$
Масса второго груза: $\text{M}$
Условие: $M > m$
Нить и блок идеальные
Ускорение свободного падения: $\text{g}$
Найти:
Модуль ускорения грузов $\text{a}$
Модуль силы натяжения нити $\text{T}$
Решение
Имеем систему из двух уравнений, полученных в пункте (г). Удобнее второе уравнение записать в виде $T - mg = ma$.
$\begin{cases} Mg - T = Ma \\ T - mg = ma \end{cases}$
Сложим левые и правые части этих двух уравнений, чтобы исключить силу натяжения $\text{T}$ и найти ускорение $\text{a}$:
$(Mg - T) + (T - mg) = Ma + ma$
$Mg - mg = (M + m)a$
Отсюда выражаем модуль ускорения $\text{a}$:
$a = \frac{M - m}{M + m}g$
Теперь подставим полученное выражение для $\text{a}$ во второе уравнение системы ($T - mg = ma$), чтобы найти силу натяжения $\text{T}$:
$T = ma + mg = m(a + g)$
$T = m \left( \frac{M - m}{M + m}g + g \right)$
Вынесем $\text{g}$ за скобки и приведем к общему знаменателю:
$T = mg \left( \frac{M - m}{M + m} + 1 \right) = mg \left( \frac{M - m + M + m}{M + m} \right)$
$T = mg \left( \frac{2M}{M + m} \right) = \frac{2Mmg}{M + m}$
Ответ: Модуль ускорения грузов $a = \frac{M - m}{M + m}g$, сила натяжения нити $T = \frac{2Mmg}{M + m}$.
е) Вес тела — это сила, с которой тело вследствие притяжения к Земле действует на опору или подвес. В данном случае подвесом для обоих грузов является нить. По третьему закону Ньютона, сила, с которой каждый груз действует на нить (то есть его вес $\text{P}$), по модулю равна силе натяжения нити $\text{T}$, с которой нить действует на груз.
Так как сила натяжения нити $\text{T}$ одинакова по всей длине, то веса обоих грузов во время движения равны: $P_M = P_m = T$.
Стоит отметить, что вес грузов в данном случае не равен их силе тяжести. Для груза $\text{m}$, движущегося вверх с ускорением, вес $P_m = T$ больше силы тяжести $mg$. Для груза $\text{M}$, движущегося вниз с ускорением, вес $P_M = T$ меньше силы тяжести $Mg$.
Ответ: Да, вес грузов во время движения одинаков, так как вес каждого из них по модулю равен силе натяжения нити $\text{T}$, которая одинакова для обоих грузов.
Другие задания:
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