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Номер 24, страница 157, 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 III. Законы сохранения в механике. Параграф 18. Закон сохранения энергии в механике - номер 24, страница 157.
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" => 1433809 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "157" "field_page_end" => "158" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/18-24" "field_display_title" => "24" "field_outside_task" => "0" "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 {#1369 #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 {#1180 …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 {#1180 …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 {#1181 #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" => 1433223 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Законы сохранения в механике" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1182 #items: array:1 [ 0 => App\Models\Term {#1183 #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" => "118" "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 {#1184 #items: array:1 [ 0 => App\Models\Book {#1185 #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 {#1186 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1211 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1186 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1211 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1216 #items: array:1 [ 0 => App\Models\Branch {#1217 #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 {#1218 …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 {#1219 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1220 …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 {#1218 …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 {#1219 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1220 …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" => 1433223 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Законы сохранения в механике" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1182} "field_page_start" => "118" "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 {#1184} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1216} ] #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 {#1257 #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" => 1433228 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Закон сохранения энергии в механике" "field_branch_order" => "18" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Term {#1259 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "149" "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 {#1260 #items: array:1 [ 0 => App\Models\Book {#1261 #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 {#1262 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1264 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1268 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1273 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1274 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1276 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1278 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1280 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1281 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1282 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1283 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1284 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1285 …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 {#1287 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1288 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1289 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1290 …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 {#1262 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1264 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1268 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1273 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1274 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1276 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1278 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1280 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1281 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1282 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1283 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1284 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1285 …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 {#1287 …2} …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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ 0 => App\Models\Branch {#1293 #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" => 1433228 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Закон сохранения энергии в механике" "field_branch_order" => "18" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1258} "field_page_start" => "149" "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 {#1260} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1292} ] #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 {#1370 #items: array:2 [ 0 => App\Models\Element {#1380 #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" => 1696550 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1389 #items: array:1 [ 0 => App\Models\Edition {#1381 #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" => "1433809" "type" => "task" ] "text" => "<p><strong>24.</strong> На рисунке 18.7 изображён график зависимости потенциальной энергии свободно падающего без начальной скорости тела массой 200 г.</p><p>Рис. 18.7</p><p><strong>а)</strong> С какой высоты падало тело?</p><p><strong>б)</strong> Чему равна полная механическая энергия тела через 1,5 с после начала падения?</p><p><strong>в)</strong> Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?</p><p><strong>г)</strong> На какой высоте находилось тело через 1,5 с после начала падения?</p><p><strong>д)</strong> Чему равна скорость тела через 1,5 с после начала падения?</p>" "img" => array:2 [ 0 => array:5 [ "name" => "24-1.jpg" "alt" => null "width" => "1592" "height" => 575 "path" => "/media/fizika_09/gendenshtejn-u/0-18/24-1.webp?ts=1759348300" ] 1 => array:5 [ "name" => "24-2.jpg" "alt" => null "width" => "1572" "height" => 426 "path" => "/media/fizika_09/gendenshtejn-u/0-18/24-2.webp?ts=1759348300" ] ] ] #original: array:7 [ "id" => 1696550 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1389} "task" => array:2 [ "refs" => "1433809" "type" => "task" ] "text" => "<p><strong>24.</strong> На рисунке 18.7 изображён график зависимости потенциальной энергии свободно падающего без начальной скорости тела массой 200 г.</p><p>Рис. 18.7</p><p><strong>а)</strong> С какой высоты падало тело?</p><p><strong>б)</strong> Чему равна полная механическая энергия тела через 1,5 с после начала падения?</p><p><strong>в)</strong> Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?</p><p><strong>г)</strong> На какой высоте находилось тело через 1,5 с после начала падения?</p><p><strong>д)</strong> Чему равна скорость тела через 1,5 с после начала падения?</p>" "img" => array:2 [ 0 => array:5 [ "name" => "24-1.jpg" "alt" => null "width" => "1592" "height" => 575 "path" => "/media/fizika_09/gendenshtejn-u/0-18/24-1.webp?ts=1759348300" ] 1 => array:5 [ "name" => "24-2.jpg" "alt" => null "width" => "1572" "height" => 426 "path" => "/media/fizika_09/gendenshtejn-u/0-18/24-2.webp?ts=1759348300" ] ] ] #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 {#1387 #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" => 1780620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1397 #items: array:1 [ 0 => App\Models\Edition {#1388 #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" => "1433809" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m = 200 \text{ г} = 0.2 \text{ кг}$</p><p>$v_0 = 0 \text{ м/с}$ (свободное падение без начальной скорости)</p><p>Из графика: начальная потенциальная энергия $E_{p0} = 90 \text{ Дж}$ при $t_0 = 0 \text{ с}$</p><p>Ускорение свободного падения $g \approx 10 \text{ м/с}^2$</p><p><strong>Найти:</strong></p><p>а) $\text{H}$ - ?</p><p>б) $\text{E}$ через 1,5 с - ?</p><p>в) $E_k$ и $E_p$ через 1,5 с - ?</p><p>г) $\text{h}$ через 1,5 с - ?</p><p>д) $\text{v}$ через 1,5 с - ?</p><p><strong>Решение:</strong></p><p><strong>а) С какой высоты падало тело?</strong><br>В начальный момент времени ($t=0$) тело покоилось на максимальной высоте $\text{H}$. Вся его механическая энергия была представлена потенциальной энергией. Формула потенциальной энергии: $E_p = mgh$. В начальный момент времени: $E_{p0} = mgH$. Отсюда можем выразить начальную высоту $\text{H}$:<br>$H = \frac{E_{p0}}{mg} = \frac{90 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{90}{2} = 45 \text{ м}$.</p><p><strong>Ответ:</strong> тело падало с высоты 45 м.</p><p><strong>б) Чему равна полная механическая энергия тела через 1,5 с после начала падения?</strong><br>Так как тело падает свободно и сопротивление воздуха не учитывается, действует закон сохранения полной механической энергии. Это означает, что полная механическая энергия тела в любой момент времени остается постоянной и равной ее значению в начальный момент. В начальный момент времени кинетическая энергия $E_{k0} = 0$ (тело покоилось), а потенциальная энергия $E_{p0} = 90 \text{ Дж}$. Полная механическая энергия $E = E_{k0} + E_{p0} = 0 + 90 \text{ Дж} = 90 \text{ Дж}$. Эта величина не изменяется со временем.</p><p><strong>Ответ:</strong> полная механическая энергия через 1,5 с равна 90 Дж.</p><p><strong>в) Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?</strong><br>Найдем высоту тела $\text{h}$ через 1,5 с после начала падения. При свободном падении без начальной скорости высота изменяется по закону: $h(t) = H - \frac{gt^2}{2}$.<br>$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 45 - \frac{10 \cdot 2.25}{2} = 45 - 11.25 = 33.75 \text{ м}$.<br>Теперь можем найти потенциальную энергию в этот момент времени:<br>$E_p(1.5) = mgh(1.5) = 0.2 \text{ кг} \cdot 10 \text{ м/с}^2 \cdot 33.75 \text{ м} = 2 \cdot 33.75 = 67.5 \text{ Дж}$.<br>Кинетическую энергию найдем из закона сохранения энергии: $E = E_k + E_p$.<br>$E_k(1.5) = E - E_p(1.5) = 90 \text{ Дж} - 67.5 \text{ Дж} = 22.5 \text{ Дж}$.</p><p><strong>Ответ:</strong> потенциальная энергия равна 67,5 Дж, кинетическая энергия равна 22,5 Дж.</p><p><strong>г) На какой высоте находилось тело через 1,5 с после начала падения?</strong><br>Высоту тела в этот момент времени мы уже рассчитали в предыдущем пункте. $h(t) = H - \frac{gt^2}{2}$<br>$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 33.75 \text{ м}$.<br>Также можно найти высоту, зная потенциальную энергию $E_p(1.5) = 67.5 \text{ Дж}$:<br>$h(1.5) = \frac{E_p(1.5)}{mg} = \frac{67.5 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{67.5}{2} = 33.75 \text{ м}$.</p><p><strong>Ответ:</strong> тело находилось на высоте 33,75 м.</p><p><strong>д) Чему равна скорость тела через 1,5 с после начала падения?</strong><br>Скорость тела можно найти, зная его кинетическую энергию $E_k(1.5) = 22.5 \text{ Дж}$.<br>Формула кинетической энергии: $E_k = \frac{mv^2}{2}$.<br>Выразим скорость $\text{v}$: $v = \sqrt{\frac{2E_k}{m}}$.<br>$v(1.5) = \sqrt{\frac{2 \cdot 22.5 \text{ Дж}}{0.2 \text{ кг}}} = \sqrt{\frac{45}{0.2}} = \sqrt{225} = 15 \text{ м/с}$.<br>Проверим результат по формуле скорости для свободного падения: $v(t) = gt$.<br>$v(1.5) = 10 \text{ м/с}^2 \cdot 1.5 \text{ с} = 15 \text{ м/с}$. Результаты совпадают.</p><p><strong>Ответ:</strong> скорость тела равна 15 м/с.</p>" ] #original: array:6 [ "id" => 1780620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1397} "task" => array:2 [ "refs" => "1433809" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m = 200 \text{ г} = 0.2 \text{ кг}$</p><p>$v_0 = 0 \text{ м/с}$ (свободное падение без начальной скорости)</p><p>Из графика: начальная потенциальная энергия $E_{p0} = 90 \text{ Дж}$ при $t_0 = 0 \text{ с}$</p><p>Ускорение свободного падения $g \approx 10 \text{ м/с}^2$</p><p><strong>Найти:</strong></p><p>а) $\text{H}$ - ?</p><p>б) $\text{E}$ через 1,5 с - ?</p><p>в) $E_k$ и $E_p$ через 1,5 с - ?</p><p>г) $\text{h}$ через 1,5 с - ?</p><p>д) $\text{v}$ через 1,5 с - ?</p><p><strong>Решение:</strong></p><p><strong>а) С какой высоты падало тело?</strong><br>В начальный момент времени ($t=0$) тело покоилось на максимальной высоте $\text{H}$. Вся его механическая энергия была представлена потенциальной энергией. Формула потенциальной энергии: $E_p = mgh$. В начальный момент времени: $E_{p0} = mgH$. Отсюда можем выразить начальную высоту $\text{H}$:<br>$H = \frac{E_{p0}}{mg} = \frac{90 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{90}{2} = 45 \text{ м}$.</p><p><strong>Ответ:</strong> тело падало с высоты 45 м.</p><p><strong>б) Чему равна полная механическая энергия тела через 1,5 с после начала падения?</strong><br>Так как тело падает свободно и сопротивление воздуха не учитывается, действует закон сохранения полной механической энергии. Это означает, что полная механическая энергия тела в любой момент времени остается постоянной и равной ее значению в начальный момент. В начальный момент времени кинетическая энергия $E_{k0} = 0$ (тело покоилось), а потенциальная энергия $E_{p0} = 90 \text{ Дж}$. Полная механическая энергия $E = E_{k0} + E_{p0} = 0 + 90 \text{ Дж} = 90 \text{ Дж}$. Эта величина не изменяется со временем.</p><p><strong>Ответ:</strong> полная механическая энергия через 1,5 с равна 90 Дж.</p><p><strong>в) Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?</strong><br>Найдем высоту тела $\text{h}$ через 1,5 с после начала падения. При свободном падении без начальной скорости высота изменяется по закону: $h(t) = H - \frac{gt^2}{2}$.<br>$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 45 - \frac{10 \cdot 2.25}{2} = 45 - 11.25 = 33.75 \text{ м}$.<br>Теперь можем найти потенциальную энергию в этот момент времени:<br>$E_p(1.5) = mgh(1.5) = 0.2 \text{ кг} \cdot 10 \text{ м/с}^2 \cdot 33.75 \text{ м} = 2 \cdot 33.75 = 67.5 \text{ Дж}$.<br>Кинетическую энергию найдем из закона сохранения энергии: $E = E_k + E_p$.<br>$E_k(1.5) = E - E_p(1.5) = 90 \text{ Дж} - 67.5 \text{ Дж} = 22.5 \text{ Дж}$.</p><p><strong>Ответ:</strong> потенциальная энергия равна 67,5 Дж, кинетическая энергия равна 22,5 Дж.</p><p><strong>г) На какой высоте находилось тело через 1,5 с после начала падения?</strong><br>Высоту тела в этот момент времени мы уже рассчитали в предыдущем пункте. $h(t) = H - \frac{gt^2}{2}$<br>$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 33.75 \text{ м}$.<br>Также можно найти высоту, зная потенциальную энергию $E_p(1.5) = 67.5 \text{ Дж}$:<br>$h(1.5) = \frac{E_p(1.5)}{mg} = \frac{67.5 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{67.5}{2} = 33.75 \text{ м}$.</p><p><strong>Ответ:</strong> тело находилось на высоте 33,75 м.</p><p><strong>д) Чему равна скорость тела через 1,5 с после начала падения?</strong><br>Скорость тела можно найти, зная его кинетическую энергию $E_k(1.5) = 22.5 \text{ Дж}$.<br>Формула кинетической энергии: $E_k = \frac{mv^2}{2}$.<br>Выразим скорость $\text{v}$: $v = \sqrt{\frac{2E_k}{m}}$.<br>$v(1.5) = \sqrt{\frac{2 \cdot 22.5 \text{ Дж}}{0.2 \text{ кг}}} = \sqrt{\frac{45}{0.2}} = \sqrt{225} = 15 \text{ м/с}$.<br>Проверим результат по формуле скорости для свободного падения: $v(t) = gt$.<br>$v(1.5) = 10 \text{ м/с}^2 \cdot 1.5 \text{ с} = 15 \text{ м/с}$. Результаты совпадают.</p><p><strong>Ответ:</strong> скорость тела равна 15 м/с.</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" => "1433810" "type" => "task" ] "previous" => array:2 [ "refs" => "1433808" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1421 #items: array:1 [ 0 => App\Models\Book {#1377 #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 {#1371 #items: array:1 [ 0 => App\Models\Term {#1372 #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 {#1379 #items: array:1 [ 0 => App\Models\Term {#1375 #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 {#1373 #items: array:1 [ 0 => App\Models\Term {#1376 #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 {#1374 #items: array:4 [ 0 => App\Models\Term {#1395 #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 {#1396 #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 {#1398 #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] 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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 {#1403 #items: array:1 [ 0 => App\Models\Term {#1404 #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 {#1405 #items: array:1 [ 0 => App\Models\Term {#1406 #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 {#1407 #items: [] #escapeWhenCastingToString: false } "field_umk" => 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#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" => 1434798 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "157" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-157" "field_display_title" => "157" "field_folder" => "2" "field_image_name" => "157" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1465 #items: array:1 [ 0 => App\Models\Branch {#1427 #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: [] 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№24 (с. 157)
Условие. №24 (с. 157)
скриншот условия
24. На рисунке 18.7 изображён график зависимости потенциальной энергии свободно падающего без начальной скорости тела массой 200 г.
Рис. 18.7
а) С какой высоты падало тело?
б) Чему равна полная механическая энергия тела через 1,5 с после начала падения?
в) Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?
г) На какой высоте находилось тело через 1,5 с после начала падения?
д) Чему равна скорость тела через 1,5 с после начала падения?
Решение. №24 (с. 157)
Дано:
$m = 200 \text{ г} = 0.2 \text{ кг}$
$v_0 = 0 \text{ м/с}$ (свободное падение без начальной скорости)
Из графика: начальная потенциальная энергия $E_{p0} = 90 \text{ Дж}$ при $t_0 = 0 \text{ с}$
Ускорение свободного падения $g \approx 10 \text{ м/с}^2$
Найти:
а) $\text{H}$ - ?
б) $\text{E}$ через 1,5 с - ?
в) $E_k$ и $E_p$ через 1,5 с - ?
г) $\text{h}$ через 1,5 с - ?
д) $\text{v}$ через 1,5 с - ?
Решение:
а) С какой высоты падало тело?
В начальный момент времени ($t=0$) тело покоилось на максимальной высоте $\text{H}$. Вся его механическая энергия была представлена потенциальной энергией. Формула потенциальной энергии: $E_p = mgh$. В начальный момент времени: $E_{p0} = mgH$. Отсюда можем выразить начальную высоту $\text{H}$:
$H = \frac{E_{p0}}{mg} = \frac{90 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{90}{2} = 45 \text{ м}$.
Ответ: тело падало с высоты 45 м.
б) Чему равна полная механическая энергия тела через 1,5 с после начала падения?
Так как тело падает свободно и сопротивление воздуха не учитывается, действует закон сохранения полной механической энергии. Это означает, что полная механическая энергия тела в любой момент времени остается постоянной и равной ее значению в начальный момент. В начальный момент времени кинетическая энергия $E_{k0} = 0$ (тело покоилось), а потенциальная энергия $E_{p0} = 90 \text{ Дж}$. Полная механическая энергия $E = E_{k0} + E_{p0} = 0 + 90 \text{ Дж} = 90 \text{ Дж}$. Эта величина не изменяется со временем.
Ответ: полная механическая энергия через 1,5 с равна 90 Дж.
в) Чему равны кинетическая и потенциальная энергия тела через 1,5 с после начала падения?
Найдем высоту тела $\text{h}$ через 1,5 с после начала падения. При свободном падении без начальной скорости высота изменяется по закону: $h(t) = H - \frac{gt^2}{2}$.
$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 45 - \frac{10 \cdot 2.25}{2} = 45 - 11.25 = 33.75 \text{ м}$.
Теперь можем найти потенциальную энергию в этот момент времени:
$E_p(1.5) = mgh(1.5) = 0.2 \text{ кг} \cdot 10 \text{ м/с}^2 \cdot 33.75 \text{ м} = 2 \cdot 33.75 = 67.5 \text{ Дж}$.
Кинетическую энергию найдем из закона сохранения энергии: $E = E_k + E_p$.
$E_k(1.5) = E - E_p(1.5) = 90 \text{ Дж} - 67.5 \text{ Дж} = 22.5 \text{ Дж}$.
Ответ: потенциальная энергия равна 67,5 Дж, кинетическая энергия равна 22,5 Дж.
г) На какой высоте находилось тело через 1,5 с после начала падения?
Высоту тела в этот момент времени мы уже рассчитали в предыдущем пункте. $h(t) = H - \frac{gt^2}{2}$
$h(1.5) = 45 \text{ м} - \frac{10 \text{ м/с}^2 \cdot (1.5 \text{ с})^2}{2} = 33.75 \text{ м}$.
Также можно найти высоту, зная потенциальную энергию $E_p(1.5) = 67.5 \text{ Дж}$:
$h(1.5) = \frac{E_p(1.5)}{mg} = \frac{67.5 \text{ Дж}}{0.2 \text{ кг} \cdot 10 \text{ м/с}^2} = \frac{67.5}{2} = 33.75 \text{ м}$.
Ответ: тело находилось на высоте 33,75 м.
д) Чему равна скорость тела через 1,5 с после начала падения?
Скорость тела можно найти, зная его кинетическую энергию $E_k(1.5) = 22.5 \text{ Дж}$.
Формула кинетической энергии: $E_k = \frac{mv^2}{2}$.
Выразим скорость $\text{v}$: $v = \sqrt{\frac{2E_k}{m}}$.
$v(1.5) = \sqrt{\frac{2 \cdot 22.5 \text{ Дж}}{0.2 \text{ кг}}} = \sqrt{\frac{45}{0.2}} = \sqrt{225} = 15 \text{ м/с}$.
Проверим результат по формуле скорости для свободного падения: $v(t) = gt$.
$v(1.5) = 10 \text{ м/с}^2 \cdot 1.5 \text{ с} = 15 \text{ м/с}$. Результаты совпадают.
Ответ: скорость тела равна 15 м/с.
Другие задания:
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