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Номер 9.27, страница 49 - гдз по физике 8 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2010 - 2026
Цвет обложки: фиолетовый
ISBN: 978-5-09-046040-8
Популярные ГДЗ в 8 классе
IX. Основы динамики - номер 9.27, страница 49.
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Основы динамики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "47" "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 {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #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" => 1646 "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 {#1032 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1032} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1039} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1052} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 {#1062 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1460052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IX. Основы динамики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "47" "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 {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #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 {#1063 #items: array:1 [ 0 => App\Models\Branch {#1023} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:2 [ 0 => App\Models\Element {#1065 #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" => 1753852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Edition {#1067 #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" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #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 {#1070 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1068} "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 {#1070} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1071} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1072} "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" => "1460354" "type" => "task" ] "text" => "<p><strong>9.27</strong> Пуля вылетает из винтовки в горизонтальном направлении со скоростью 850 м/с. Какую скорость приобретает винтовка при отдаче, если её масса больше массы пули в 500 раз?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "27-1.jpg" "alt" => null "width" => "1773" "height" => 267 "path" => "/media/fizika_08/artemenkov-zd/0-09/27-1.webp?ts=1760701812" ] ] ] #original: array:7 [ "id" => 1753852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1066} "task" => array:2 [ "refs" => "1460354" "type" => "task" ] "text" => "<p><strong>9.27</strong> Пуля вылетает из винтовки в горизонтальном направлении со скоростью 850 м/с. Какую скорость приобретает винтовка при отдаче, если её масса больше массы пули в 500 раз?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "27-1.jpg" "alt" => null "width" => "1773" "height" => 267 "path" => "/media/fizika_08/artemenkov-zd/0-09/27-1.webp?ts=1760701812" ] ] ] #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 {#1073 #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" => 1821959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Edition {#1075 #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" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ …1] #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 {#1078 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "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 {#1078} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080} "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" => "1460354" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Скорость пули, $v_п = 850$ м/с.</p><p>Соотношение масс, $m_в = 500 \cdot m_п$, где $m_в$ — масса винтовки, $m_п$ — масса пули.</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Скорость винтовки при отдаче, $v_в$ — ?</p><p><strong>Решение:</strong></p><p>Для решения этой задачи воспользуемся законом сохранения импульса. Рассмотрим систему, состоящую из винтовки и пули. До выстрела оба тела покоятся, поэтому суммарный импульс системы равен нулю.<br>$\vec{p}_{до} = 0$</p><p>В момент выстрела внутренние силы (давление пороховых газов) приводят тела в движение. Пуля летит в одном направлении, а винтовка движется в противоположном (отдача). Так как внешними силами в горизонтальном направлении можно пренебречь, импульс системы "пуля-винтовка" сохраняется. Суммарный импульс системы после выстрела также должен быть равен нулю.<br>$\vec{p}_{после} = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$</p><p>Согласно закону сохранения импульса:<br>$\vec{p}_{до} = \vec{p}_{после}$<br>$0 = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$</p><p>Отсюда следует, что импульсы пули и винтовки после выстрела равны по модулю и противоположны по направлению:<br>$m_в \cdot \vec{v_в} = - m_п \cdot \vec{v_п}$</p><p>Перейдем к модулям (скалярным величинам), чтобы найти величину скорости (скорость).<br>$m_в \cdot v_в = m_п \cdot v_п$</p><p>Выразим скорость винтовки $v_в$:<br>$v_в = \frac{m_п \cdot v_п}{m_в}$</p><p>Из условия задачи известно, что масса винтовки в 500 раз больше массы пули, то есть $m_в = 500 \cdot m_п$. Подставим это соотношение в нашу формулу:<br>$v_в = \frac{m_п \cdot v_п}{500 \cdot m_п}$</p><p>Масса пули $m_п$ в числителе и знаменателе сокращается:<br>$v_в = \frac{v_п}{500}$</p><p>Подставим известное значение скорости пули и вычислим скорость винтовки:<br>$v_в = \frac{850 \text{ м/с}}{500} = 1.7 \text{ м/с}$</p><p><strong>Ответ:</strong> скорость, которую приобретает винтовка при отдаче, равна 1,7 м/с.</p>" ] #original: array:6 [ "id" => 1821959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074} "task" => array:2 [ "refs" => "1460354" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Скорость пули, $v_п = 850$ м/с.</p><p>Соотношение масс, $m_в = 500 \cdot m_п$, где $m_в$ — масса винтовки, $m_п$ — масса пули.</p><p>Все данные представлены в системе СИ.</p><p><strong>Найти:</strong></p><p>Скорость винтовки при отдаче, $v_в$ — ?</p><p><strong>Решение:</strong></p><p>Для решения этой задачи воспользуемся законом сохранения импульса. Рассмотрим систему, состоящую из винтовки и пули. До выстрела оба тела покоятся, поэтому суммарный импульс системы равен нулю.<br>$\vec{p}_{до} = 0$</p><p>В момент выстрела внутренние силы (давление пороховых газов) приводят тела в движение. Пуля летит в одном направлении, а винтовка движется в противоположном (отдача). Так как внешними силами в горизонтальном направлении можно пренебречь, импульс системы "пуля-винтовка" сохраняется. Суммарный импульс системы после выстрела также должен быть равен нулю.<br>$\vec{p}_{после} = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$</p><p>Согласно закону сохранения импульса:<br>$\vec{p}_{до} = \vec{p}_{после}$<br>$0 = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$</p><p>Отсюда следует, что импульсы пули и винтовки после выстрела равны по модулю и противоположны по направлению:<br>$m_в \cdot \vec{v_в} = - m_п \cdot \vec{v_п}$</p><p>Перейдем к модулям (скалярным величинам), чтобы найти величину скорости (скорость).<br>$m_в \cdot v_в = m_п \cdot v_п$</p><p>Выразим скорость винтовки $v_в$:<br>$v_в = \frac{m_п \cdot v_п}{m_в}$</p><p>Из условия задачи известно, что масса винтовки в 500 раз больше массы пули, то есть $m_в = 500 \cdot m_п$. Подставим это соотношение в нашу формулу:<br>$v_в = \frac{m_п \cdot v_п}{500 \cdot m_п}$</p><p>Масса пули $m_п$ в числителе и знаменателе сокращается:<br>$v_в = \frac{v_п}{500}$</p><p>Подставим известное значение скорости пули и вычислим скорость винтовки:<br>$v_в = \frac{850 \text{ м/с}}{500} = 1.7 \text{ м/с}$</p><p><strong>Ответ:</strong> скорость, которую приобретает винтовка при отдаче, равна 1,7 м/с.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460355" "type" => "task" ] "previous" => array:2 [ "refs" => "1460353" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Book {#1082 #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" => 1646 "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 {#1083 #items: array:1 [ 0 => App\Models\Term {#1084 #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" 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#fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Term {#1086 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" 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"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 {#1089 #items: array:3 [ 0 => App\Models\Term {#1090 #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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "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 => "*" ] } 1 => App\Models\Term {#1091 #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" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1092 #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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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 {#1093 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1095 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #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 {#1096 #items: array:1 [ 0 => App\Models\Term {#1097 #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 {#1098 #items: array:1 [ 0 => App\Models\Term {#1099 #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 {#1100 #items: array:1 [ 0 => App\Models\Term {#1101 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ 0 => App\Models\Term {#1092} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Term {#1111 #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" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1083} "field_class" => Illuminate\Database\Eloquent\Collection {#1085} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087} "field_author" => Illuminate\Database\Eloquent\Collection {#1089} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1093} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1094} "field_country" => Illuminate\Database\Eloquent\Collection {#1096} "field_city" => Illuminate\Database\Eloquent\Collection {#1098} "field_series" => Illuminate\Database\Eloquent\Collection {#1100} "field_umk" => Illuminate\Database\Eloquent\Collection {#1102} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1103} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1104} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1105} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1106} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1107} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1108} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1109} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1110} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\BookPage {#1125 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1462346 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-49" "field_display_title" => "49" "field_folder" => "1" "field_image_name" => "49" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Book {#1128 #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" => 1646 "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 {#1130 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1151 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1130} "field_class" => Illuminate\Database\Eloquent\Collection {#1131} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133} "field_author" => Illuminate\Database\Eloquent\Collection {#1135} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_country" => Illuminate\Database\Eloquent\Collection {#1142} "field_city" => Illuminate\Database\Eloquent\Collection {#1144} "field_series" => Illuminate\Database\Eloquent\Collection {#1146} "field_umk" => Illuminate\Database\Eloquent\Collection {#1148} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1149} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1150} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1151} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1152} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ 0 => App\Models\Element {#1159 #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" => 1753907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1753907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162} "book_page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1462347" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462345" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1786 #items: array:7 [ 0 => App\Models\Task {#1168 #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" => 1460348 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-21" "field_display_title" => "9.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1209 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460349" "type" => "task" ] "previous" => array:2 [ "refs" => "1460347" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460348 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-21" "field_display_title" => "9.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1171} "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 {#1172} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1173} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1208} "content" => Illuminate\Database\Eloquent\Collection {#1209} "next" => array:2 [ "refs" => "1460349" "type" => "task" ] "previous" => array:2 [ "refs" => "1460347" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1226} "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1257 #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" => 1460349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-22" "field_display_title" => "9.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1260 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460350" "type" => "task" ] "previous" => array:2 [ "refs" => "1460348" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1314 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-22" "field_display_title" => "9.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258} "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 {#1260} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1296} "content" => Illuminate\Database\Eloquent\Collection {#1297} "next" => array:2 [ "refs" => "1460350" "type" => "task" ] "previous" => array:2 [ "refs" => "1460348" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1314} "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1345 #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" => 1460350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-23" "field_display_title" => "9.23" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1346 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1348 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1349 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1384 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1385 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460351" "type" => "task" ] "previous" => array:2 [ "refs" => "1460349" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1402 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-23" "field_display_title" => "9.23" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1346} "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 {#1348} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1349} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1384} "content" => Illuminate\Database\Eloquent\Collection {#1385} "next" => array:2 [ "refs" => "1460351" "type" => "task" ] "previous" => array:2 [ "refs" => "1460349" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1402} "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1433 #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" => 1460351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-24" "field_display_title" => "9.24" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1434 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1436 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1437 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1472 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1473 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460352" "type" => "task" ] "previous" => array:2 [ "refs" => "1460350" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1490 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-24" "field_display_title" => "9.24" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1434} "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 {#1436} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1437} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1472} "content" => Illuminate\Database\Eloquent\Collection {#1473} "next" => array:2 [ "refs" => "1460352" "type" => "task" ] "previous" => array:2 [ "refs" => "1460350" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1490} "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1521 #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" => 1460352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-25" "field_display_title" => "9.25" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1522 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1524 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1525 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1560 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1561 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460353" "type" => "task" ] "previous" => array:2 [ "refs" => "1460351" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1578 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-25" "field_display_title" => "9.25" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1522} "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 {#1524} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1525} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1560} "content" => Illuminate\Database\Eloquent\Collection {#1561} "next" => array:2 [ "refs" => "1460353" "type" => "task" ] "previous" => array:2 [ "refs" => "1460351" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1578} "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1609 #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" => 1460353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-26" "field_display_title" => "9.26" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1610 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1612 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1613 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1648 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1649 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460354" "type" => "task" ] "previous" => array:2 [ "refs" => "1460352" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1666 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462346" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-26" "field_display_title" => "9.26" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1610} "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 {#1612} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1613} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1648} "content" => Illuminate\Database\Eloquent\Collection {#1649} "next" => array:2 [ "refs" => "1460354" "type" => "task" ] "previous" => array:2 [ "refs" => "1460352" …1 ] "book" => Illuminate\Database\Eloquent\Collection {#1666} "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 => "*" ] } 6 => App\Models\Task {#1697 #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" => 1460354 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-27" "field_display_title" => "9.27" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1698 …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 {#1700 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1701 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1736 …2} "content" => Illuminate\Database\Eloquent\Collection {#1737 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1754 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460354 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-27" "field_display_title" => "9.27" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1698 …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 {#1700 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1701 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1736 …2} "content" => 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=> null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158} "content" => Illuminate\Database\Eloquent\Collection {#1170} "next" => array:2 [ "refs" => "1462347" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462345" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1786} ] #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" => 1460354 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-27" "field_display_title" => "9.27" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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 {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1063} "content" => Illuminate\Database\Eloquent\Collection {#1064} "next" => array:2 [ "refs" => "1460355" "type" => "task" ] "previous" => array:2 [ "refs" => "1460353" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1081} "page" => array:2 [ "refs" => "1462346" "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 => "*" ] }
№9.27 (с. 49)
Условие. №9.27 (с. 49)
скриншот условия
9.27 Пуля вылетает из винтовки в горизонтальном направлении со скоростью 850 м/с. Какую скорость приобретает винтовка при отдаче, если её масса больше массы пули в 500 раз?
Решение. №9.27 (с. 49)
Дано:
Скорость пули, $v_п = 850$ м/с.
Соотношение масс, $m_в = 500 \cdot m_п$, где $m_в$ — масса винтовки, $m_п$ — масса пули.
Все данные представлены в системе СИ.
Найти:
Скорость винтовки при отдаче, $v_в$ — ?
Решение:
Для решения этой задачи воспользуемся законом сохранения импульса. Рассмотрим систему, состоящую из винтовки и пули. До выстрела оба тела покоятся, поэтому суммарный импульс системы равен нулю.
$\vec{p}_{до} = 0$
В момент выстрела внутренние силы (давление пороховых газов) приводят тела в движение. Пуля летит в одном направлении, а винтовка движется в противоположном (отдача). Так как внешними силами в горизонтальном направлении можно пренебречь, импульс системы "пуля-винтовка" сохраняется. Суммарный импульс системы после выстрела также должен быть равен нулю.
$\vec{p}_{после} = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$
Согласно закону сохранения импульса:
$\vec{p}_{до} = \vec{p}_{после}$
$0 = m_п \cdot \vec{v_п} + m_в \cdot \vec{v_в}$
Отсюда следует, что импульсы пули и винтовки после выстрела равны по модулю и противоположны по направлению:
$m_в \cdot \vec{v_в} = - m_п \cdot \vec{v_п}$
Перейдем к модулям (скалярным величинам), чтобы найти величину скорости (скорость).
$m_в \cdot v_в = m_п \cdot v_п$
Выразим скорость винтовки $v_в$:
$v_в = \frac{m_п \cdot v_п}{m_в}$
Из условия задачи известно, что масса винтовки в 500 раз больше массы пули, то есть $m_в = 500 \cdot m_п$. Подставим это соотношение в нашу формулу:
$v_в = \frac{m_п \cdot v_п}{500 \cdot m_п}$
Масса пули $m_п$ в числителе и знаменателе сокращается:
$v_в = \frac{v_п}{500}$
Подставим известное значение скорости пули и вычислим скорость винтовки:
$v_в = \frac{850 \text{ м/с}}{500} = 1.7 \text{ м/с}$
Ответ: скорость, которую приобретает винтовка при отдаче, равна 1,7 м/с.
Другие задания:
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