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Номер 11, страница 6, часть 2 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 2
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 2. Глава 3. Импульс. Закон сохранения импульса. Параграф 23. Импульс. Изменение импульса материальной точки. Система тел. Закон сохранения импульса - номер 11, страница 6.
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" => 1435038 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => "7" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/23-11" "field_display_title" => "11" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #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" => "3" "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 {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 1203 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #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" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "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 => "*" ] } 1 => App\Models\Term {#1058 #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" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "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" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "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" => "Александрович" "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 {#1059 #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" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 {#1060 #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" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #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:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null …4 ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #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" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #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" => 1203 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "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 {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "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 {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #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 {#1114 #items: array:3 [ 0 => App\Models\Branch {#1124 #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" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1126 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "3" "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 {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #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 {#1128 #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" => 1434830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Закон сохранения импульса" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #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:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => "3" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Закон сохранения импульса" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "3" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1133 #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" => 1434831 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Изменение импульса материальной точки. Система тел. Закон сохранения импульса" "field_branch_order" => "23" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => 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:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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" => "3" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Branch {#1144 #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" => 1434830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Закон сохранения импульса" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1147 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434830 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Закон сохранения импульса" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_page_start" => "3" "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 {#1147} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434831 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Импульс. Изменение импульса материальной точки. Система тел. Закон сохранения импульса" "field_branch_order" => "23" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "3" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1106 #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" => 1698426 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1098 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087} "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" => "1435038" "type" => "task" ] "text" => "<p><strong>11.</strong> Изобразите на рис. 2 векторы скорости точки, рассмотренной в задаче 10, до начала действия силы и через 2 с после начала действия. На рис. 3 изобразите векторы импульса точки в указанные моменты времени, а также импульсы силы, действовавшие на точку за указанное время. Перед изображением векторов импульса силы и векторов импульса точки изобразите вектор импульса силы, модуль которого равен $10 \text{ Н} \cdot \text{ с}$ (красным карандашом), а также вектор импульса точки, модуль которого равен $10 \text{ кг} \cdot \text{ м/с}$ (чёрным карандашом).</p><p><strong>a</strong> Y</p><p>0</p><p>$|\vec{v}| = 6 \text{ м/с}$</p><p>X</p><p><strong>б</strong> Y</p><p>0</p><p>$|\vec{v}| = 6 \text{ м/с}$</p><p>X</p><p>Рис. 2</p><p>Y</p><p>0</p><p>X</p><p>Y</p><p>0</p><p>X</p><p>Рис. 3</p>" "img" => array:2 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1972" "height" => 1388 "path" => "/media/fizika_09/grachev-rt/0-23/11-1.webp?ts=1759402717" ] 1 => array:5 [ "name" => "11-2.jpg" "alt" => null "width" => "1872" "height" => 974 "path" => "/media/fizika_09/grachev-rt/0-23/11-2.webp?ts=1759402717" ] ] ] #original: array:7 [ "id" => 1698426 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1435038" "type" => "task" ] "text" => "<p><strong>11.</strong> Изобразите на рис. 2 векторы скорости точки, рассмотренной в задаче 10, до начала действия силы и через 2 с после начала действия. На рис. 3 изобразите векторы импульса точки в указанные моменты времени, а также импульсы силы, действовавшие на точку за указанное время. Перед изображением векторов импульса силы и векторов импульса точки изобразите вектор импульса силы, модуль которого равен $10 \text{ Н} \cdot \text{ с}$ (красным карандашом), а также вектор импульса точки, модуль которого равен $10 \text{ кг} \cdot \text{ м/с}$ (чёрным карандашом).</p><p><strong>a</strong> Y</p><p>0</p><p>$|\vec{v}| = 6 \text{ м/с}$</p><p>X</p><p><strong>б</strong> Y</p><p>0</p><p>$|\vec{v}| = 6 \text{ м/с}$</p><p>X</p><p>Рис. 2</p><p>Y</p><p>0</p><p>X</p><p>Y</p><p>0</p><p>X</p><p>Рис. 3</p>" "img" => array:2 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1972" "height" => 1388 "path" => "/media/fizika_09/grachev-rt/0-23/11-1.webp?ts=1759402717" ] 1 => array:5 [ "name" => "11-2.jpg" "alt" => null "width" => "1872" "height" => 974 "path" => "/media/fizika_09/grachev-rt/0-23/11-2.webp?ts=1759402717" ] ] ] #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 {#1105 #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" => 1734412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1088 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1041 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1041} "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" => "1435038" "type" => "task" ] "text" => "<p>Поскольку условие задачи 11 ссылается на задачу 10, для решения воспользуемся данными из задачи 10: масса точки $m=2$ кг, на нее начинает действовать сила $F=4$ Н, направленная перпендикулярно начальной скорости (вдоль оси OY).</p><p><strong>Дано:</strong></p><p>$m = 2$ кг</p><p>$|\vec{v_0}| = 6$ м/с (начальная скорость)</p><p>$|\vec{F}| = 4$ Н (действующая сила)</p><p>$\Delta t = 2$ с (время действия силы)</p><p>$|J_{ref}| = 10$ Н·с (эталонный импульс силы для масштаба)</p><p>$|p_{ref}| = 10$ кг·м/с (эталонный импульс точки для масштаба)</p><p>Вектор $\vec{v_0}$ направлен вдоль оси OX. Вектор $\vec{F}$ направлен вдоль оси OY.</p><p>Все данные представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Изобразить векторы: $\vec{v_0}$ (начальная скорость), $\vec{v}$ (конечная скорость), $\vec{p_0}$ (начальный импульс), $\vec{p}$ (конечный импульс), $\vec{J}$ (импульс силы).</p><p><strong>Решение:</strong></p><p>Введем систему координат, как показано на рисунках, с осью X, направленной вправо, и осью Y, направленной вверх. Начало координат поместим в точку, из которой будут начинаться все векторы.</p><p>Тогда начальные условия в векторном виде:</p><p>$\vec{v_0} = (6; 0)$ м/с</p><p>$\vec{F} = (0; 4)$ Н</p><p>Согласно второму закону Ньютона в импульсной форме, изменение импульса точки равно импульсу силы: $\Delta\vec{p} = \vec{J}$, где $\vec{J} = \vec{F}\Delta t$.</p><p>Также $\Delta\vec{p} = \vec{p} - \vec{p_0} = m\vec{v} - m\vec{v_0}$.</p><p>Отсюда $m\vec{v} - m\vec{v_0} = \vec{F}\Delta t$, что позволяет найти конечную скорость $\vec{v} = \vec{v_0} + \frac{\vec{F}\Delta t}{m}$.</p><p><strong>На рис. 2</strong></p><p>На этом рисунке нужно изобразить векторы скорости. Выберем масштаб: пусть одна клетка координатной сетки соответствует 1 м/с.</p><p>1. <i>Вектор начальной скорости $\vec{v_0}$</i>. Он уже дан в условии: его модуль равен 6 м/с, и он направлен вдоль оси OX. В выбранном масштабе это будет вектор, исходящий из начала координат, направленный вправо вдоль оси OX на 6 клеток.</p><p>Координаты вектора: $\vec{v_0} = (6; 0)$ м/с.</p><p>2. <i>Вектор конечной скорости $\vec{v}$</i>. Найдем его компоненты:</p><p>$v_x = v_{0x} + \frac{F_x \Delta t}{m} = 6 + \frac{0 \cdot 2}{2} = 6$ м/с.</p><p>$v_y = v_{0y} + \frac{F_y \Delta t}{m} = 0 + \frac{4 \cdot 2}{2} = 4$ м/с.</p><p>Таким образом, вектор конечной скорости $\vec{v} = (6; 4)$ м/с. В выбранном масштабе это будет вектор, исходящий из начала координат, конец которого находится в точке с координатами (6 клеток; 4 клетки).</p><p><strong>Ответ:</strong> На рис. 2а изображается вектор $\vec{v_0}$, направленный из начала координат в точку (6, 0) по сетке. На рис. 2б изображается вектор $\vec{v}$, направленный из начала координат в точку (6, 4) по сетке (при масштабе 1 клетка = 1 м/с).</p><p><strong>На рис. 3</strong></p><p>На этом рисунке нужно изобразить векторы импульса точки и импульс силы. Согласно условию, сначала нужно задать масштаб, изобразив эталонные векторы. Модули эталонных векторов импульса силы ($10$ Н·с) и импульса точки ($10$ кг·м/с) равны, так как Н·с = кг·м/с. Выберем удобную длину для эталонного вектора, например, 5 клеток. Тогда масштаб: 5 клеток = 10 кг·м/с, или 1 клетка = 2 кг·м/с (и 2 Н·с).</p><p>1. <i>Эталонные векторы (красный и чёрный)</i>. Изображаем любой вектор длиной 5 клеток, например, вдоль оси ОХ. Подписываем его модуль (10 Н·с для красного, 10 кг·м/с для чёрного).</p><p>2. <i>Вектор начального импульса $\vec{p_0}$</i>.</p><p>$\vec{p_0} = m\vec{v_0} = 2 \text{ кг} \cdot (6; 0) \text{ м/с} = (12; 0)$ кг·м/с.</p><p>Длина этого вектора на рисунке: $12 / 2 = 6$ клеток. Он направлен вдоль оси OX. Это вектор из начала координат в точку (6, 0) на сетке.</p><p>3. <i>Вектор импульса силы $\vec{J}$</i>.</p><p>$\vec{J} = \vec{F}\Delta t = (0; 4) \text{ Н} \cdot 2 \text{ с} = (0; 8)$ Н·с.</p><p>Длина этого вектора на рисунке: $8 / 2 = 4$ клетки. Он направлен вдоль оси OY. Это вектор из начала координат в точку (0, 4) на сетке.</p><p>4. <i>Вектор конечного импульса $\vec{p}$</i>.</p><p>$\vec{p} = \vec{p_0} + \vec{J} = (12; 0) + (0; 8) = (12; 8)$ кг·м/с.</p><p>В координатах сетки его конец будет в точке $(12/2; 8/2) = (6; 4)$. Это вектор из начала координат в точку (6, 4) на сетке. Графически этот вектор является диагональю прямоугольника, построенного на векторах $\vec{p_0}$ и $\vec{J}$.</p><p><strong>Ответ:</strong> При масштабе 1 клетка = 2 кг·м/с (или 2 Н·с) на рис. 3 изображаются:</p><ul><li>Эталонный вектор (чёрный) для импульса точки $10$ кг·м/с длиной 5 клеток.</li><li>Эталонный вектор (красный) для импульса силы $10$ Н·с длиной 5 клеток.</li><li>Вектор начального импульса $\vec{p_0}$ из начала координат в точку (6, 0).</li><li>Вектор конечного импульса $\vec{p}$ из начала координат в точку (6, 4).</li><li>Вектор импульса силы $\vec{J}$ из начала координат в точку (0, 4).</li></ul><p></p>" ] #original: array:6 [ "id" => 1734412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1435038" "type" => "task" ] "text" => "<p>Поскольку условие задачи 11 ссылается на задачу 10, для решения воспользуемся данными из задачи 10: масса точки $m=2$ кг, на нее начинает действовать сила $F=4$ Н, направленная перпендикулярно начальной скорости (вдоль оси OY).</p><p><strong>Дано:</strong></p><p>$m = 2$ кг</p><p>$|\vec{v_0}| = 6$ м/с (начальная скорость)</p><p>$|\vec{F}| = 4$ Н (действующая сила)</p><p>$\Delta t = 2$ с (время действия силы)</p><p>$|J_{ref}| = 10$ Н·с (эталонный импульс силы для масштаба)</p><p>$|p_{ref}| = 10$ кг·м/с (эталонный импульс точки для масштаба)</p><p>Вектор $\vec{v_0}$ направлен вдоль оси OX. Вектор $\vec{F}$ направлен вдоль оси OY.</p><p>Все данные представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Изобразить векторы: $\vec{v_0}$ (начальная скорость), $\vec{v}$ (конечная скорость), $\vec{p_0}$ (начальный импульс), $\vec{p}$ (конечный импульс), $\vec{J}$ (импульс силы).</p><p><strong>Решение:</strong></p><p>Введем систему координат, как показано на рисунках, с осью X, направленной вправо, и осью Y, направленной вверх. Начало координат поместим в точку, из которой будут начинаться все векторы.</p><p>Тогда начальные условия в векторном виде:</p><p>$\vec{v_0} = (6; 0)$ м/с</p><p>$\vec{F} = (0; 4)$ Н</p><p>Согласно второму закону Ньютона в импульсной форме, изменение импульса точки равно импульсу силы: $\Delta\vec{p} = \vec{J}$, где $\vec{J} = \vec{F}\Delta t$.</p><p>Также $\Delta\vec{p} = \vec{p} - \vec{p_0} = m\vec{v} - m\vec{v_0}$.</p><p>Отсюда $m\vec{v} - m\vec{v_0} = \vec{F}\Delta t$, что позволяет найти конечную скорость $\vec{v} = \vec{v_0} + \frac{\vec{F}\Delta t}{m}$.</p><p><strong>На рис. 2</strong></p><p>На этом рисунке нужно изобразить векторы скорости. Выберем масштаб: пусть одна клетка координатной сетки соответствует 1 м/с.</p><p>1. <i>Вектор начальной скорости $\vec{v_0}$</i>. Он уже дан в условии: его модуль равен 6 м/с, и он направлен вдоль оси OX. В выбранном масштабе это будет вектор, исходящий из начала координат, направленный вправо вдоль оси OX на 6 клеток.</p><p>Координаты вектора: $\vec{v_0} = (6; 0)$ м/с.</p><p>2. <i>Вектор конечной скорости $\vec{v}$</i>. Найдем его компоненты:</p><p>$v_x = v_{0x} + \frac{F_x \Delta t}{m} = 6 + \frac{0 \cdot 2}{2} = 6$ м/с.</p><p>$v_y = v_{0y} + \frac{F_y \Delta t}{m} = 0 + \frac{4 \cdot 2}{2} = 4$ м/с.</p><p>Таким образом, вектор конечной скорости $\vec{v} = (6; 4)$ м/с. В выбранном масштабе это будет вектор, исходящий из начала координат, конец которого находится в точке с координатами (6 клеток; 4 клетки).</p><p><strong>Ответ:</strong> На рис. 2а изображается вектор $\vec{v_0}$, направленный из начала координат в точку (6, 0) по сетке. На рис. 2б изображается вектор $\vec{v}$, направленный из начала координат в точку (6, 4) по сетке (при масштабе 1 клетка = 1 м/с).</p><p><strong>На рис. 3</strong></p><p>На этом рисунке нужно изобразить векторы импульса точки и импульс силы. Согласно условию, сначала нужно задать масштаб, изобразив эталонные векторы. Модули эталонных векторов импульса силы ($10$ Н·с) и импульса точки ($10$ кг·м/с) равны, так как Н·с = кг·м/с. Выберем удобную длину для эталонного вектора, например, 5 клеток. Тогда масштаб: 5 клеток = 10 кг·м/с, или 1 клетка = 2 кг·м/с (и 2 Н·с).</p><p>1. <i>Эталонные векторы (красный и чёрный)</i>. Изображаем любой вектор длиной 5 клеток, например, вдоль оси ОХ. Подписываем его модуль (10 Н·с для красного, 10 кг·м/с для чёрного).</p><p>2. <i>Вектор начального импульса $\vec{p_0}$</i>.</p><p>$\vec{p_0} = m\vec{v_0} = 2 \text{ кг} \cdot (6; 0) \text{ м/с} = (12; 0)$ кг·м/с.</p><p>Длина этого вектора на рисунке: $12 / 2 = 6$ клеток. Он направлен вдоль оси OX. Это вектор из начала координат в точку (6, 0) на сетке.</p><p>3. <i>Вектор импульса силы $\vec{J}$</i>.</p><p>$\vec{J} = \vec{F}\Delta t = (0; 4) \text{ Н} \cdot 2 \text{ с} = (0; 8)$ Н·с.</p><p>Длина этого вектора на рисунке: $8 / 2 = 4$ клетки. Он направлен вдоль оси OY. Это вектор из начала координат в точку (0, 4) на сетке.</p><p>4. <i>Вектор конечного импульса $\vec{p}$</i>.</p><p>$\vec{p} = \vec{p_0} + \vec{J} = (12; 0) + (0; 8) = (12; 8)$ кг·м/с.</p><p>В координатах сетки его конец будет в точке $(12/2; 8/2) = (6; 4)$. Это вектор из начала координат в точку (6, 4) на сетке. Графически этот вектор является диагональю прямоугольника, построенного на векторах $\vec{p_0}$ и $\vec{J}$.</p><p><strong>Ответ:</strong> При масштабе 1 клетка = 2 кг·м/с (или 2 Н·с) на рис. 3 изображаются:</p><ul><li>Эталонный вектор (чёрный) для импульса точки $10$ кг·м/с длиной 5 клеток.</li><li>Эталонный вектор (красный) для импульса силы $10$ Н·с длиной 5 клеток.</li><li>Вектор начального импульса $\vec{p_0}$ из начала координат в точку (6, 0).</li><li>Вектор конечного импульса $\vec{p}$ из начала координат в точку (6, 4).</li><li>Вектор импульса силы $\vec{J}$ из начала координат в точку (0, 4).</li></ul><p></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" => "1435039" "type" => 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{#1179 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1165 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1170 #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" => 1435181 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/36-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1163 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1167 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1169 …2} "content" => Illuminate\Database\Eloquent\Collection {#1168 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1195 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435181 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/36-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1163 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1167 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1169 …2} "content" => Illuminate\Database\Eloquent\Collection {#1168 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1195 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1435641 "created_at" => 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#relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1435038 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "6" "field_page_end" => "7" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/23-11" "field_display_title" => "11" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1114} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 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№11 (с. 6)
Условие. №11 (с. 6)
скриншот условия
11. Изобразите на рис. 2 векторы скорости точки, рассмотренной в задаче 10, до начала действия силы и через 2 с после начала действия. На рис. 3 изобразите векторы импульса точки в указанные моменты времени, а также импульсы силы, действовавшие на точку за указанное время. Перед изображением векторов импульса силы и векторов импульса точки изобразите вектор импульса силы, модуль которого равен $10 \text{ Н} \cdot \text{ с}$ (красным карандашом), а также вектор импульса точки, модуль которого равен $10 \text{ кг} \cdot \text{ м/с}$ (чёрным карандашом).
a Y
0
$|\vec{v}| = 6 \text{ м/с}$
X
б Y
0
$|\vec{v}| = 6 \text{ м/с}$
X
Рис. 2
Y
0
X
Y
0
X
Рис. 3
Решение. №11 (с. 6)
Поскольку условие задачи 11 ссылается на задачу 10, для решения воспользуемся данными из задачи 10: масса точки $m=2$ кг, на нее начинает действовать сила $F=4$ Н, направленная перпендикулярно начальной скорости (вдоль оси OY).
Дано:
$m = 2$ кг
$|\vec{v_0}| = 6$ м/с (начальная скорость)
$|\vec{F}| = 4$ Н (действующая сила)
$\Delta t = 2$ с (время действия силы)
$|J_{ref}| = 10$ Н·с (эталонный импульс силы для масштаба)
$|p_{ref}| = 10$ кг·м/с (эталонный импульс точки для масштаба)
Вектор $\vec{v_0}$ направлен вдоль оси OX. Вектор $\vec{F}$ направлен вдоль оси OY.
Все данные представлены в системе СИ, перевод не требуется.
Найти:
Изобразить векторы: $\vec{v_0}$ (начальная скорость), $\vec{v}$ (конечная скорость), $\vec{p_0}$ (начальный импульс), $\vec{p}$ (конечный импульс), $\vec{J}$ (импульс силы).
Решение:
Введем систему координат, как показано на рисунках, с осью X, направленной вправо, и осью Y, направленной вверх. Начало координат поместим в точку, из которой будут начинаться все векторы.
Тогда начальные условия в векторном виде:
$\vec{v_0} = (6; 0)$ м/с
$\vec{F} = (0; 4)$ Н
Согласно второму закону Ньютона в импульсной форме, изменение импульса точки равно импульсу силы: $\Delta\vec{p} = \vec{J}$, где $\vec{J} = \vec{F}\Delta t$.
Также $\Delta\vec{p} = \vec{p} - \vec{p_0} = m\vec{v} - m\vec{v_0}$.
Отсюда $m\vec{v} - m\vec{v_0} = \vec{F}\Delta t$, что позволяет найти конечную скорость $\vec{v} = \vec{v_0} + \frac{\vec{F}\Delta t}{m}$.
На рис. 2
На этом рисунке нужно изобразить векторы скорости. Выберем масштаб: пусть одна клетка координатной сетки соответствует 1 м/с.
1. Вектор начальной скорости $\vec{v_0}$. Он уже дан в условии: его модуль равен 6 м/с, и он направлен вдоль оси OX. В выбранном масштабе это будет вектор, исходящий из начала координат, направленный вправо вдоль оси OX на 6 клеток.
Координаты вектора: $\vec{v_0} = (6; 0)$ м/с.
2. Вектор конечной скорости $\vec{v}$. Найдем его компоненты:
$v_x = v_{0x} + \frac{F_x \Delta t}{m} = 6 + \frac{0 \cdot 2}{2} = 6$ м/с.
$v_y = v_{0y} + \frac{F_y \Delta t}{m} = 0 + \frac{4 \cdot 2}{2} = 4$ м/с.
Таким образом, вектор конечной скорости $\vec{v} = (6; 4)$ м/с. В выбранном масштабе это будет вектор, исходящий из начала координат, конец которого находится в точке с координатами (6 клеток; 4 клетки).
Ответ: На рис. 2а изображается вектор $\vec{v_0}$, направленный из начала координат в точку (6, 0) по сетке. На рис. 2б изображается вектор $\vec{v}$, направленный из начала координат в точку (6, 4) по сетке (при масштабе 1 клетка = 1 м/с).
На рис. 3
На этом рисунке нужно изобразить векторы импульса точки и импульс силы. Согласно условию, сначала нужно задать масштаб, изобразив эталонные векторы. Модули эталонных векторов импульса силы ($10$ Н·с) и импульса точки ($10$ кг·м/с) равны, так как Н·с = кг·м/с. Выберем удобную длину для эталонного вектора, например, 5 клеток. Тогда масштаб: 5 клеток = 10 кг·м/с, или 1 клетка = 2 кг·м/с (и 2 Н·с).
1. Эталонные векторы (красный и чёрный). Изображаем любой вектор длиной 5 клеток, например, вдоль оси ОХ. Подписываем его модуль (10 Н·с для красного, 10 кг·м/с для чёрного).
2. Вектор начального импульса $\vec{p_0}$.
$\vec{p_0} = m\vec{v_0} = 2 \text{ кг} \cdot (6; 0) \text{ м/с} = (12; 0)$ кг·м/с.
Длина этого вектора на рисунке: $12 / 2 = 6$ клеток. Он направлен вдоль оси OX. Это вектор из начала координат в точку (6, 0) на сетке.
3. Вектор импульса силы $\vec{J}$.
$\vec{J} = \vec{F}\Delta t = (0; 4) \text{ Н} \cdot 2 \text{ с} = (0; 8)$ Н·с.
Длина этого вектора на рисунке: $8 / 2 = 4$ клетки. Он направлен вдоль оси OY. Это вектор из начала координат в точку (0, 4) на сетке.
4. Вектор конечного импульса $\vec{p}$.
$\vec{p} = \vec{p_0} + \vec{J} = (12; 0) + (0; 8) = (12; 8)$ кг·м/с.
В координатах сетки его конец будет в точке $(12/2; 8/2) = (6; 4)$. Это вектор из начала координат в точку (6, 4) на сетке. Графически этот вектор является диагональю прямоугольника, построенного на векторах $\vec{p_0}$ и $\vec{J}$.
Ответ: При масштабе 1 клетка = 2 кг·м/с (или 2 Н·с) на рис. 3 изображаются:
- Эталонный вектор (чёрный) для импульса точки $10$ кг·м/с длиной 5 клеток.
- Эталонный вектор (красный) для импульса силы $10$ Н·с длиной 5 клеток.
- Вектор начального импульса $\vec{p_0}$ из начала координат в точку (6, 0).
- Вектор конечного импульса $\vec{p}$ из начала координат в точку (6, 4).
- Вектор импульса силы $\vec{J}$ из начала координат в точку (0, 4).
Другие задания:
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