gdz.top
Задание 1, страница 196, 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. Лабораторные работы. 3. Сложение сил - страница 196.
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" => 1433913 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "196" "field_page_end" => "197" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/labrab3-1" "field_display_title" => "Задание 1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Branch {#1035 #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 {#1038 #items: array:1 [ 0 => App\Models\Term {#1037 #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 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "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 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "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 {#1039 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #connection: "mysql" …29 } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:4 [ 0 => App\Models\Term {#1048 …30} 1 => App\Models\Term {#1049 …30} 2 => App\Models\Term {#1050 …30} 3 => App\Models\Term {#1051 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 …30} ] #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 {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "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 {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #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 {#1038} "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 {#1039} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #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 {#1110 #items: array:3 [ 0 => App\Models\Branch {#1120 #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 {#1124 #items: array:1 [ 0 => App\Models\Term {#1121 #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 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "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 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "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 {#1156 #items: array:1 [ 0 => App\Models\Book {#1123 #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 {#1125 #items: array:1 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Term {#1127 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #original: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:4 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #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\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #original: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Term {#1148 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #original: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition_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 {#1149 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Term {#1153 #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" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ "field_accusative_case" => "бирюзовый" "field_creative_case" => "бирюзовым" "field_dative_case" => "бирюзовому" "field_genitive_case" => "бирюзового" "field_nominative_case" => "бирюзовый" "field_prepositional_case" => "бирюзовом" ] "field_translit" => "biruzovyy" ] #original: array:6 [ "id" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ "field_accusative_case" => "бирюзовый" "field_creative_case" => "бирюзовым" "field_dative_case" => "бирюзовому" "field_genitive_case" => "бирюзового" "field_nominative_case" => "бирюзовый" "field_prepositional_case" => "бирюзовом" ] "field_translit" => "biruzovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1125} "field_class" => Illuminate\Database\Eloquent\Collection {#1126} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1128} "field_author" => Illuminate\Database\Eloquent\Collection {#1130} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1135} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_country" => Illuminate\Database\Eloquent\Collection {#1138} "field_city" => Illuminate\Database\Eloquent\Collection {#1140} "field_series" => Illuminate\Database\Eloquent\Collection {#1142} "field_umk" => Illuminate\Database\Eloquent\Collection {#1143} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1144} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1145} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1147} "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 {#1149} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1150} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1151} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1152} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 #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 {#1124} "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 {#1156} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154} ] #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 {#1155 #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" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1157 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "194" "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 {#1158 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1159 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1157} "field_page_start" => "194" "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 {#1158} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1159} ] #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 {#1160 #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" => 1433237 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "3. Сложение сил" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "196" "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 {#1162 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ 0 => App\Models\Branch {#1170 #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" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "194" "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 {#1173 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433234 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1172} "field_page_start" => "194" "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 {#1173} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1174} ] #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" => 1433237 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "3. Сложение сил" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161} "field_page_start" => "196" "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 {#1162} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1171} ] #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 {#1072 #items: array:2 [ 0 => App\Models\Element {#1101 #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" => 1697077 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1102 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099 #items: array:1 [ 0 => App\Models\Term {#1100 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1099} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433913" "type" => "task" ] "text" => "<p><strong>3. Сложение сил</strong></p><p><strong><em>Цель работы:</em></strong> измерить равнодействующую двух сил, направленных одинаково, и равнодействующую двух сил, направленных под прямым углом друг к другу.</p><p><strong><em>Оборудование:</em></strong> металлическое колечко<sup>1)</sup>, два груза неизвестной массы<sup>2)</sup>, три динамометра, угольник, нити.</p><p><strong>Ход работы</strong></p><p><strong>Задание 1. Измерение равнодействующих двух сил, направленных одинаково.</strong></p><p>• Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.</p><p>• Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.</p><p>• Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.</p><p>• Сравните сумму модулей сил $\vec{P_1}$ и $\vec{P_2}$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1626" "height" => 878 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab3/1-1.webp?ts=1759348497" ] 1 => array:5 [ "name" => "1-2.jpg" "alt" => null "width" => "1599" "height" => 536 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab3/1-2.webp?ts=1759348497" ] ] ] #original: array:7 [ "id" => 1697077 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1433913" "type" => "task" ] "text" => "<p><strong>3. Сложение сил</strong></p><p><strong><em>Цель работы:</em></strong> измерить равнодействующую двух сил, направленных одинаково, и равнодействующую двух сил, направленных под прямым углом друг к другу.</p><p><strong><em>Оборудование:</em></strong> металлическое колечко<sup>1)</sup>, два груза неизвестной массы<sup>2)</sup>, три динамометра, угольник, нити.</p><p><strong>Ход работы</strong></p><p><strong>Задание 1. Измерение равнодействующих двух сил, направленных одинаково.</strong></p><p>• Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.</p><p>• Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.</p><p>• Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.</p><p>• Сравните сумму модулей сил $\vec{P_1}$ и $\vec{P_2}$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1626" "height" => 878 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab3/1-1.webp?ts=1759348497" ] 1 => array:5 [ "name" => "1-2.jpg" "alt" => null "width" => "1599" "height" => 536 "path" => "/media/fizika_09/gendenshtejn-u/0-labrab3/1-2.webp?ts=1759348497" ] ] ] #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 {#1094 #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" => 1781147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1095 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Term {#1093 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1091} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433913" "type" => "task" ] "text" => "<p>Поскольку в задании описан ход лабораторной работы, для его выполнения необходимо провести реальные измерения. Ниже представлен пример выполнения этой работы с гипотетическими, но реалистичными данными.</p><p><strong>Дано:</strong></p><p>Результаты гипотетических измерений, полученные с помощью динамометра с ценой деления $C = 0.1 \, \text{Н}$. Абсолютная погрешность прямого измерения принимается равной половине цены деления: $\Delta = C/2 = 0.05 \, \text{Н}$.</p><p>Вес первого тела: $P_1 = (2.00 \pm 0.05) \, \text{Н}$</p><p>Вес второго тела: $P_2 = (3.00 \pm 0.05) \, \text{Н}$</p><p>Сила, измеренная динамометром при совместном подвешивании двух тел: $F = (5.00 \pm 0.05) \, \text{Н}$</p><p><strong>Найти:</strong></p><p>Сравнить сумму модулей сил $P_1$ и $P_2$ с модулем силы $\text{F}$ с учётом погрешностей и сделать вывод.</p><p><strong>Решение:</strong></p><p><strong>Задание 1. Измерение равнодействующей двух сил, направленных одинаково.</strong></p><p><strong>Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.</strong></p><p>Подвешиваем поочередно два груза к динамометру и фиксируем его показания. Погрешность измерения равна половине цены деления шкалы динамометра. Пусть цена деления составляет $0.1 \, \text{Н}$, тогда погрешность равна $0.05 \, \text{Н}$.</p><p>Результаты измерений:</p><p>Вес первого груза: $P_1 = (2.00 \pm 0.05) \, \text{Н}$.</p><p>Вес второго груза: $P_2 = (3.00 \pm 0.05) \, \text{Н}$.</p><p>Ответ: $P_1 = (2.00 \pm 0.05) \, \text{Н}$; $P_2 = (3.00 \pm 0.05) \, \text{Н}$.</p><p><strong>Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.</strong></p><p>К металлическому кольцу привязываем оба груза. Кольцо с грузами подвешиваем на крючок динамометра. На кольцо действуют две силы $P_1$ и $P_2$, направленные вертикально вниз. Динамометр показывает силу $\text{F}$, которая уравновешивает суммарное действие этих двух сил. Записываем показания динамометра:</p><p>$F = (5.00 \pm 0.05) \, \text{Н}$.</p><p>Ответ: $F = (5.00 \pm 0.05) \, \text{Н}$.</p><p><strong>Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.</strong></p><p>На рисунке изображаем точку, символизирующую кольцо. Из этой точки рисуем три вектора сил. Векторы сил $\vec{P}_1$ и $\vec{P}_2$ направлены вертикально вниз. Вектор силы $\vec{F}$, с которой динамометр действует на кольцо, направлен вертикально вверх. Длины векторов выбираем в соответствии с масштабом. Например, в масштабе 1 см : 1 Н, длина вектора $\vec{P}_1$ будет равна 2.0 см, вектора $\vec{P}_2$ — 3.0 см. Длина вектора $\vec{F}$ будет равна 5.0 см, что соответствует сумме длин векторов $\vec{P}_1$ и $\vec{P}_2$.</p><p>Ответ: Схематический рисунок представляет собой точку, из которой направлены два вектора $\vec{P}_1$ и $\vec{P}_2$ вертикально вниз и один уравновешивающий их вектор $\vec{F}$ вертикально вверх. В масштабе 1 см : 1 Н, длины векторов равны $l_1=2.0$ см, $l_2=3.0$ см, $l_F=5.0$ см.</p><p><strong>Сравните сумму модулей сил $\vec{P}_1$ и $\vec{P}_2$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.</strong></p><p>Вычислим сумму модулей сил $P_1$ и $P_2$ и погрешность этой суммы.</p><p>Сумма модулей: $P_{сумм} = P_1 + P_2 = 2.00 \, \text{Н} + 3.00 \, \text{Н} = 5.00 \, \text{Н}$.</p><p>При сложении величин их абсолютные погрешности складываются:</p><p>$\Delta P_{сумм} = \Delta P_1 + \Delta P_2 = 0.05 \, \text{Н} + 0.05 \, \text{Н} = 0.10 \, \text{Н}$.</p><p>Таким образом, расчетное значение суммы сил: $P_{сумм} = (5.00 \pm 0.10) \, \text{Н}$.</p><p>Сравним это значение с экспериментально измеренным значением силы $F = (5.00 \pm 0.05) \, \text{Н}$.</p><p>Интервал для расчетного значения: $[5.00 - 0.10; 5.00 + 0.10]$, то есть $[4.90; 5.10] \, \text{Н}$.</p><p>Интервал для измеренного значения: $[5.00 - 0.05; 5.00 + 0.05]$, то есть $[4.95; 5.05] \, \text{Н}$.</p><p>Интервал измеренных значений $[4.95; 5.05]$ полностью содержится в интервале расчетных значений $[4.90; 5.10]$. Это подтверждает, что в пределах погрешности измерений модуль силы $\text{F}$ равен сумме модулей сил $P_1$ и $P_2$.</p><p>Вывод: Эксперимент подтвердил, что равнодействующая двух сил, направленных по одной прямой в одну сторону, направлена в ту же сторону, а её модуль равен сумме модулей составляющих сил. Математически это выражается формулой: $F = P_1 + P_2$.</p><p>Ответ: Сравнение показало, что измеренное значение $F = (5.00 \pm 0.05) \, \text{Н}$ и расчетное значение суммы $P_1 + P_2 = (5.00 \pm 0.10) \, \text{Н}$ совпадают в пределах погрешности. Вывод: модуль равнодействующей двух сил, направленных в одну сторону, равен сумме модулей этих сил.</p>" ] #original: array:6 [ "id" => 1781147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1433913" "type" => "task" ] "text" => "<p>Поскольку в задании описан ход лабораторной работы, для его выполнения необходимо провести реальные измерения. Ниже представлен пример выполнения этой работы с гипотетическими, но реалистичными данными.</p><p><strong>Дано:</strong></p><p>Результаты гипотетических измерений, полученные с помощью динамометра с ценой деления $C = 0.1 \, \text{Н}$. Абсолютная погрешность прямого измерения принимается равной половине цены деления: $\Delta = C/2 = 0.05 \, \text{Н}$.</p><p>Вес первого тела: $P_1 = (2.00 \pm 0.05) \, \text{Н}$</p><p>Вес второго тела: $P_2 = (3.00 \pm 0.05) \, \text{Н}$</p><p>Сила, измеренная динамометром при совместном подвешивании двух тел: $F = (5.00 \pm 0.05) \, \text{Н}$</p><p><strong>Найти:</strong></p><p>Сравнить сумму модулей сил $P_1$ и $P_2$ с модулем силы $\text{F}$ с учётом погрешностей и сделать вывод.</p><p><strong>Решение:</strong></p><p><strong>Задание 1. Измерение равнодействующей двух сил, направленных одинаково.</strong></p><p><strong>Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.</strong></p><p>Подвешиваем поочередно два груза к динамометру и фиксируем его показания. Погрешность измерения равна половине цены деления шкалы динамометра. Пусть цена деления составляет $0.1 \, \text{Н}$, тогда погрешность равна $0.05 \, \text{Н}$.</p><p>Результаты измерений:</p><p>Вес первого груза: $P_1 = (2.00 \pm 0.05) \, \text{Н}$.</p><p>Вес второго груза: $P_2 = (3.00 \pm 0.05) \, \text{Н}$.</p><p>Ответ: $P_1 = (2.00 \pm 0.05) \, \text{Н}$; $P_2 = (3.00 \pm 0.05) \, \text{Н}$.</p><p><strong>Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.</strong></p><p>К металлическому кольцу привязываем оба груза. Кольцо с грузами подвешиваем на крючок динамометра. На кольцо действуют две силы $P_1$ и $P_2$, направленные вертикально вниз. Динамометр показывает силу $\text{F}$, которая уравновешивает суммарное действие этих двух сил. Записываем показания динамометра:</p><p>$F = (5.00 \pm 0.05) \, \text{Н}$.</p><p>Ответ: $F = (5.00 \pm 0.05) \, \text{Н}$.</p><p><strong>Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.</strong></p><p>На рисунке изображаем точку, символизирующую кольцо. Из этой точки рисуем три вектора сил. Векторы сил $\vec{P}_1$ и $\vec{P}_2$ направлены вертикально вниз. Вектор силы $\vec{F}$, с которой динамометр действует на кольцо, направлен вертикально вверх. Длины векторов выбираем в соответствии с масштабом. Например, в масштабе 1 см : 1 Н, длина вектора $\vec{P}_1$ будет равна 2.0 см, вектора $\vec{P}_2$ — 3.0 см. Длина вектора $\vec{F}$ будет равна 5.0 см, что соответствует сумме длин векторов $\vec{P}_1$ и $\vec{P}_2$.</p><p>Ответ: Схематический рисунок представляет собой точку, из которой направлены два вектора $\vec{P}_1$ и $\vec{P}_2$ вертикально вниз и один уравновешивающий их вектор $\vec{F}$ вертикально вверх. В масштабе 1 см : 1 Н, длины векторов равны $l_1=2.0$ см, $l_2=3.0$ см, $l_F=5.0$ см.</p><p><strong>Сравните сумму модулей сил $\vec{P}_1$ и $\vec{P}_2$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.</strong></p><p>Вычислим сумму модулей сил $P_1$ и $P_2$ и погрешность этой суммы.</p><p>Сумма модулей: $P_{сумм} = P_1 + P_2 = 2.00 \, \text{Н} + 3.00 \, \text{Н} = 5.00 \, \text{Н}$.</p><p>При сложении величин их абсолютные погрешности складываются:</p><p>$\Delta P_{сумм} = \Delta P_1 + \Delta P_2 = 0.05 \, \text{Н} + 0.05 \, \text{Н} = 0.10 \, \text{Н}$.</p><p>Таким образом, расчетное значение суммы сил: $P_{сумм} = (5.00 \pm 0.10) \, \text{Н}$.</p><p>Сравним это значение с экспериментально измеренным значением силы $F = (5.00 \pm 0.05) \, \text{Н}$.</p><p>Интервал для расчетного значения: $[5.00 - 0.10; 5.00 + 0.10]$, то есть $[4.90; 5.10] \, \text{Н}$.</p><p>Интервал для измеренного значения: $[5.00 - 0.05; 5.00 + 0.05]$, то есть $[4.95; 5.05] \, \text{Н}$.</p><p>Интервал измеренных значений $[4.95; 5.05]$ полностью содержится в интервале расчетных значений $[4.90; 5.10]$. Это подтверждает, что в пределах погрешности измерений модуль силы $\text{F}$ равен сумме модулей сил $P_1$ и $P_2$.</p><p>Вывод: Эксперимент подтвердил, что равнодействующая двух сил, направленных по одной прямой в одну сторону, направлена в ту же сторону, а её модуль равен сумме модулей составляющих сил. Математически это выражается формулой: $F = P_1 + P_2$.</p><p>Ответ: Сравнение показало, что измеренное значение $F = (5.00 \pm 0.05) \, \text{Н}$ и расчетное значение суммы $P_1 + P_2 = (5.00 \pm 0.10) \, \text{Н}$ совпадают в пределах погрешности. Вывод: модуль равнодействующей двух сил, направленных в одну сторону, равен сумме модулей этих сил.</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" => "1433914" "type" => "task" ] "previous" => array:2 [ "refs" => "1433912" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1123} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\BookPage {#1078 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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array:2 [ "refs" => "1434595" "type" => "book_page" ] ] #original: array:24 [ "id" => 1433913 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "196" "field_page_end" => "197" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/labrab3-1" "field_display_title" => "Задание 1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1363} "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 {#1378} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1383} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1385} "content" => Illuminate\Database\Eloquent\Collection {#1382} "next" => array:2 [ "refs" => "1433914" "type" => "task" ] "previous" => array:2 [ "refs" => "1433912" "type" => "task" ] "book" 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"field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1111} "content" => Illuminate\Database\Eloquent\Collection {#1167} "next" => array:2 [ "refs" => "1434596" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434594" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1274} ] #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" => 1433913 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "196" "field_page_end" => "197" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/labrab3-1" "field_display_title" => "Задание 1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036} "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 {#1034} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1110} "content" => Illuminate\Database\Eloquent\Collection {#1072} "next" => array:2 [ "refs" => "1433914" "type" => "task" ] "previous" => array:2 [ "refs" => "1433912" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105} "page" => array:2 [ "refs" => "1434595" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
Задание 1 (с. 196)
Условие. Задание 1 (с. 196)
скриншот условия
3. Сложение сил
Цель работы: измерить равнодействующую двух сил, направленных одинаково, и равнодействующую двух сил, направленных под прямым углом друг к другу.
Оборудование: металлическое колечко1), два груза неизвестной массы2), три динамометра, угольник, нити.
Ход работы
Задание 1. Измерение равнодействующих двух сил, направленных одинаково.
• Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.
• Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.
• Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.
• Сравните сумму модулей сил $\vec{P_1}$ и $\vec{P_2}$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.
Решение. Задание 1 (с. 196)
Поскольку в задании описан ход лабораторной работы, для его выполнения необходимо провести реальные измерения. Ниже представлен пример выполнения этой работы с гипотетическими, но реалистичными данными.
Дано:
Результаты гипотетических измерений, полученные с помощью динамометра с ценой деления $C = 0.1 \, \text{Н}$. Абсолютная погрешность прямого измерения принимается равной половине цены деления: $\Delta = C/2 = 0.05 \, \text{Н}$.
Вес первого тела: $P_1 = (2.00 \pm 0.05) \, \text{Н}$
Вес второго тела: $P_2 = (3.00 \pm 0.05) \, \text{Н}$
Сила, измеренная динамометром при совместном подвешивании двух тел: $F = (5.00 \pm 0.05) \, \text{Н}$
Найти:
Сравнить сумму модулей сил $P_1$ и $P_2$ с модулем силы $\text{F}$ с учётом погрешностей и сделать вывод.
Решение:
Задание 1. Измерение равнодействующей двух сил, направленных одинаково.
Измерьте динамометром вес $P_1$ и $P_2$ двух предложенных вам тел. Запишите результаты измерений с указанием погрешностей в тетрадь.
Подвешиваем поочередно два груза к динамометру и фиксируем его показания. Погрешность измерения равна половине цены деления шкалы динамометра. Пусть цена деления составляет $0.1 \, \text{Н}$, тогда погрешность равна $0.05 \, \text{Н}$.
Результаты измерений:
Вес первого груза: $P_1 = (2.00 \pm 0.05) \, \text{Н}$.
Вес второго груза: $P_2 = (3.00 \pm 0.05) \, \text{Н}$.
Ответ: $P_1 = (2.00 \pm 0.05) \, \text{Н}$; $P_2 = (3.00 \pm 0.05) \, \text{Н}$.
Привяжите к металлическому колечку два тела весом $P_1$ и $P_2$. Зацепив колечко крючком динамометра, медленно поднимите его. Запишите показания $\text{F}$ динамометра с указанием погрешности в тетрадь.
К металлическому кольцу привязываем оба груза. Кольцо с грузами подвешиваем на крючок динамометра. На кольцо действуют две силы $P_1$ и $P_2$, направленные вертикально вниз. Динамометр показывает силу $\text{F}$, которая уравновешивает суммарное действие этих двух сил. Записываем показания динамометра:
$F = (5.00 \pm 0.05) \, \text{Н}$.
Ответ: $F = (5.00 \pm 0.05) \, \text{Н}$.
Сделайте в тетради схематический рисунок, указав на нём в выбранном вами масштабе направление и модули действующих на колечко сил.
На рисунке изображаем точку, символизирующую кольцо. Из этой точки рисуем три вектора сил. Векторы сил $\vec{P}_1$ и $\vec{P}_2$ направлены вертикально вниз. Вектор силы $\vec{F}$, с которой динамометр действует на кольцо, направлен вертикально вверх. Длины векторов выбираем в соответствии с масштабом. Например, в масштабе 1 см : 1 Н, длина вектора $\vec{P}_1$ будет равна 2.0 см, вектора $\vec{P}_2$ — 3.0 см. Длина вектора $\vec{F}$ будет равна 5.0 см, что соответствует сумме длин векторов $\vec{P}_1$ и $\vec{P}_2$.
Ответ: Схематический рисунок представляет собой точку, из которой направлены два вектора $\vec{P}_1$ и $\vec{P}_2$ вертикально вниз и один уравновешивающий их вектор $\vec{F}$ вертикально вверх. В масштабе 1 см : 1 Н, длины векторов равны $l_1=2.0$ см, $l_2=3.0$ см, $l_F=5.0$ см.
Сравните сумму модулей сил $\vec{P}_1$ и $\vec{P}_2$ с модулем силы $\vec{F}$ (с учётом погрешностей). Запишите вывод, который вы сделали по результатам сравнения.
Вычислим сумму модулей сил $P_1$ и $P_2$ и погрешность этой суммы.
Сумма модулей: $P_{сумм} = P_1 + P_2 = 2.00 \, \text{Н} + 3.00 \, \text{Н} = 5.00 \, \text{Н}$.
При сложении величин их абсолютные погрешности складываются:
$\Delta P_{сумм} = \Delta P_1 + \Delta P_2 = 0.05 \, \text{Н} + 0.05 \, \text{Н} = 0.10 \, \text{Н}$.
Таким образом, расчетное значение суммы сил: $P_{сумм} = (5.00 \pm 0.10) \, \text{Н}$.
Сравним это значение с экспериментально измеренным значением силы $F = (5.00 \pm 0.05) \, \text{Н}$.
Интервал для расчетного значения: $[5.00 - 0.10; 5.00 + 0.10]$, то есть $[4.90; 5.10] \, \text{Н}$.
Интервал для измеренного значения: $[5.00 - 0.05; 5.00 + 0.05]$, то есть $[4.95; 5.05] \, \text{Н}$.
Интервал измеренных значений $[4.95; 5.05]$ полностью содержится в интервале расчетных значений $[4.90; 5.10]$. Это подтверждает, что в пределах погрешности измерений модуль силы $\text{F}$ равен сумме модулей сил $P_1$ и $P_2$.
Вывод: Эксперимент подтвердил, что равнодействующая двух сил, направленных по одной прямой в одну сторону, направлена в ту же сторону, а её модуль равен сумме модулей составляющих сил. Математически это выражается формулой: $F = P_1 + P_2$.
Ответ: Сравнение показало, что измеренное значение $F = (5.00 \pm 0.05) \, \text{Н}$ и расчетное значение суммы $P_1 + P_2 = (5.00 \pm 0.10) \, \text{Н}$ совпадают в пределах погрешности. Вывод: модуль равнодействующей двух сил, направленных в одну сторону, равен сумме модулей этих сил.
Другие задания:
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