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Номер 4.42, страница 25 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Механика. 4. Импульс, работа, энергия. Законы сохранения - номер 4.42, страница 25.
App\Models\Task {#1024 // 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" => 1288057 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-42" "field_display_title" => "4.42" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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" => 5401 "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 [ 0 => App\Models\Term {#1034 #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 [ …6] "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 [ …6] "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 {#1035 #items: array:4 [ 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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "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 [ …6] "field_translit" => "vosmoj" ] #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 {#1037 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "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 [ …6] "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 => "*" ] } 2 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #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 {#1039 #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" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #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 {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 #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" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #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 {#1042 #items: array:3 [ 0 => App\Models\Term {#1043 #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" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "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 {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1045 #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" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "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 {#1046 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047 #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" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, zadachnik" ] #original: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, 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 {#1049 #items: array:1 [ 0 => App\Models\Term {#1050 #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 [ …6] "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 [ …6] "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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 [ …6] "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 [ …6] "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 {#1053 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => 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:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #original: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #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 {#1059 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 5401 "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 {#1040} "field_author" => Illuminate\Database\Eloquent\Collection {#1042} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1046} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_country" => Illuminate\Database\Eloquent\Collection {#1049} "field_city" => Illuminate\Database\Eloquent\Collection {#1051} "field_series" => Illuminate\Database\Eloquent\Collection {#1053} "field_umk" => Illuminate\Database\Eloquent\Collection {#1054} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063} "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 {#1065 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "5" "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 {#1065} ] #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 {#1066 #items: array:3 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1067 #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" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1069 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Branch {#1071 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_page_start" => "5" "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 {#1073 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1107 …2} ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_page_start" => "5" "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 {#1073 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1107 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068} "field_page_start" => "5" "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 {#1069} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1108 #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" => 1287871 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Импульс, работа, энергия. Законы сохранения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "20" "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 {#1110 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Branch {#1112 #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" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_page_start" => "5" "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 {#1114 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …2} ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_page_start" => "5" "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 {#1114 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287871 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Импульс, работа, энергия. Законы сохранения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109} "field_page_start" => "20" "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 {#1110} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111} ] #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 {#1153 #items: array:3 [ 0 => App\Models\Element {#1154 #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" => 1477832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Edition {#1156 #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" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1157 …2} "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 {#1159 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1160 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1157 …2} "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 {#1159 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1160 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1161 …2} "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" => "1288057" "type" => "task" ] "text" => "<p><strong>4.42*.</strong> Как вы знаете, мне случалось пересаживаться в полете с одного пушечного ядра на другое, встречное. На сколько изменяется суммарная кинетическая энергия моего тела и ядер при такой пересадке? Рассмотрите два случая:</p><p><strong>1)</strong> неизменной остается скорость оставленного мною ядра;</p><p><strong>2)</strong> неизменной остается скорость ядра, на которое я пересел.</p><p>Ядра имеют одинаковую по модулю скорость $v_0 = 1000 \text{ м/с}$ и массу $M = 100 \text{ кг}$; моя масса $m = 80 \text{ кг}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "42-1.jpg" "alt" => null "width" => "1417" "height" => 491 "path" => "/media/fizika_08/gelfgat-u/0-04/42-1.webp?ts=1756049713" ] ] ] #original: array:7 [ "id" => 1477832 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1155} "task" => array:2 [ "refs" => "1288057" "type" => "task" ] "text" => "<p><strong>4.42*.</strong> Как вы знаете, мне случалось пересаживаться в полете с одного пушечного ядра на другое, встречное. На сколько изменяется суммарная кинетическая энергия моего тела и ядер при такой пересадке? Рассмотрите два случая:</p><p><strong>1)</strong> неизменной остается скорость оставленного мною ядра;</p><p><strong>2)</strong> неизменной остается скорость ядра, на которое я пересел.</p><p>Ядра имеют одинаковую по модулю скорость $v_0 = 1000 \text{ м/с}$ и массу $M = 100 \text{ кг}$; моя масса $m = 80 \text{ кг}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "42-1.jpg" "alt" => null "width" => "1417" "height" => 491 "path" => "/media/fizika_08/gelfgat-u/0-04/42-1.webp?ts=1756049713" ] ] ] #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 {#1162 #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" => 1478248 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1163 #items: array:1 [ 0 => App\Models\Edition {#1164 #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" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1169 …2} "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" => "1288057" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "42-1.jpg" "alt" => null "width" => "1438" "height" => 381 "path" => "/media/fizika_08/gelfgat-u/1-04/42-1.webp?ts=1756049773" ] 1 => array:5 [ "name" => "42-2.jpg" "alt" => null "width" => "1413" "height" => 710 "path" => "/media/fizika_08/gelfgat-u/1-04/42-2.webp?ts=1756049773" ] ] ] #original: array:6 [ "id" => 1478248 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1163} "task" => array:2 [ "refs" => "1288057" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "42-1.jpg" "alt" => null "width" => "1438" "height" => 381 "path" => "/media/fizika_08/gelfgat-u/1-04/42-1.webp?ts=1756049773" ] 1 => array:5 [ "name" => "42-2.jpg" "alt" => null "width" => "1413" "height" => 710 "path" => "/media/fizika_08/gelfgat-u/1-04/42-2.webp?ts=1756049773" ] ] ] #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\Element {#1170 #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" => 1737750 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ 0 => App\Models\Edition {#1172 #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" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 …2} "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" => "1288057" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$v_0 = 1000$ м/с</p><p>$M = 100$ кг</p><p>$m = 80$ кг</p><p><strong>Найти:</strong></p><p>$\Delta E_k$ - изменение суммарной кинетической энергии системы для двух случаев.</p><p><strong>Решение:</strong></p><p>Рассмотрим систему, состоящую из человека и двух ядер. Так как по условию пересадка происходит в полете, можно пренебречь внешними силами (сопротивлением воздуха), а сила тяжести скомпенсирована в вертикальном направлении. Таким образом, систему можно считать замкнутой, и для нее будет выполняться закон сохранения импульса в проекции на горизонтальную ось.</p><p>Направим ось OX в сторону начального движения человека на первом ядре. Обозначим массу человека как $\text{m}$, массу каждого ядра как $\text{M}$, а модуль их начальной скорости как $v_0$.</p><p>До пересадки человек (массой $\text{m}$) и первое ядро (массой $\text{M}$) движутся вместе как единое целое со скоростью $v_0$. Второе ядро движется им навстречу со скоростью $-v_0$.</p><p>Начальный импульс системы:</p><p>$P_{нач} = (m+M)v_0 + M(-v_0) = mv_0 + Mv_0 - Mv_0 = mv_0$</p><p>Начальная суммарная кинетическая энергия системы:</p><p>$E_{k, нач} = \frac{(m+M)v_0^2}{2} + \frac{M(-v_0)^2}{2} = \frac{(m+M)v_0^2}{2} + \frac{Mv_0^2}{2} = \frac{(m+2M)v_0^2}{2}$</p><p><strong>1)</strong> неизменной остается скорость оставленного мною ядра</p><p>После того как человек пересел, скорость первого (оставленного) ядра осталась равной $v_0$. Человек и второе ядро стали двигаться вместе с некоторой конечной скоростью $v_{кон2}$.</p><p>Конечный импульс системы в этом случае:</p><p>$P_{кон1} = Mv_0 + (m+M)v_{кон2}$</p><p>Согласно закону сохранения импульса $P_{нач} = P_{кон1}$:</p><p>$mv_0 = Mv_0 + (m+M)v_{кон2}$</p><p>Из этого уравнения найдем скорость $v_{кон2}$:</p><p>$(m-M)v_0 = (m+M)v_{кон2} \implies v_{кон2} = \frac{m-M}{m+M}v_0$</p><p>Конечная суммарная кинетическая энергия системы:</p><p>$E_{k, кон1} = \frac{Mv_0^2}{2} + \frac{(m+M)v_{кон2}^2}{2} = \frac{Mv_0^2}{2} + \frac{(m+M)}{2} \left( \frac{m-M}{m+M}v_0 \right)^2 = \frac{Mv_0^2}{2} + \frac{(m-M)^2}{2(m+M)}v_0^2$</p><p>Изменение кинетической энергии $\Delta E_{k1}$ равно разности конечной и начальной энергий:</p><p>$\Delta E_{k1} = E_{k, кон1} - E_{k, нач} = \left( \frac{Mv_0^2}{2} + \frac{(m-M)^2 v_0^2}{2(m+M)} \right) - \frac{(m+2M)v_0^2}{2}$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2} \left( M + \frac{(m-M)^2}{m+M} - (m+2M) \right) = \frac{v_0^2}{2(m+M)} \left( M(m+M) + (m-M)^2 - (m+2M)(m+M) \right)$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} \left( Mm+M^2 + m^2-2Mm+M^2 - (m^2+3Mm+2M^2) \right)$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} ( -4Mm ) = -\frac{2mM}{m+M}v_0^2$</p><p>Подставим числовые значения:</p><p>$\Delta E_{k1} = -\frac{2 \cdot 80 \cdot 100}{80+100} \cdot (1000)^2 = -\frac{16000}{180} \cdot 10^6 = -\frac{800}{9} \cdot 10^6 \approx -88.9 \cdot 10^6$ Дж.</p><p>Знак "минус" означает, что энергия системы уменьшилась.</p><p><strong>Ответ:</strong> Суммарная кинетическая энергия уменьшится на $\frac{2mM}{m+M}v_0^2 \approx 88.9$ МДж.</p><p><strong>2)</strong> неизменной остается скорость ядра, на которое я пересел</p><p>В этом случае после пересадки человек и второе ядро движутся вместе со скоростью, равной начальной скорости второго ядра, то есть $-v_0$. Первое ядро при этом приобретает некоторую конечную скорость $v_{кон1}$.</p><p>Конечный импульс системы:</p><p>$P_{кон2} = Mv_{кон1} + (m+M)(-v_0)$</p><p>Согласно закону сохранения импульса $P_{нач} = P_{кон2}$:</p><p>$mv_0 = Mv_{кон1} - (m+M)v_0$</p><p>Из этого уравнения найдем скорость $v_{кон1}$:</p><p>$mv_0 + (m+M)v_0 = Mv_{кон1} \implies (2m+M)v_0 = Mv_{кон1} \implies v_{кон1} = \frac{2m+M}{M}v_0$</p><p>Конечная суммарная кинетическая энергия системы:</p><p>$E_{k, кон2} = \frac{Mv_{кон1}^2}{2} + \frac{(m+M)(-v_0)^2}{2} = \frac{M}{2} \left( \frac{2m+M}{M}v_0 \right)^2 + \frac{(m+M)v_0^2}{2} = \frac{(2m+M)^2}{2M}v_0^2 + \frac{(m+M)v_0^2}{2}$</p><p>Изменение кинетической энергии $\Delta E_{k2}$ равно разности конечной и начальной энергий:</p><p>$\Delta E_{k2} = E_{k, кон2} - E_{k, нач} = \left( \frac{(2m+M)^2 v_0^2}{2M} + \frac{(m+M)v_0^2}{2} \right) - \frac{(m+2M)v_0^2}{2}$</p><p>$\Delta E_{k2} = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} + m+M - (m+2M) \right) = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} - M \right)$</p><p>$\Delta E_{k2} = \frac{v_0^2}{2M} \left( (2m+M)^2 - M^2 \right) = \frac{v_0^2}{2M} (4m^2 + 4mM + M^2 - M^2) = \frac{v_0^2}{2M} (4m^2 + 4mM)$</p><p>$\Delta E_{k2} = \frac{4m(m+M)}{2M}v_0^2 = \frac{2m(m+M)}{M}v_0^2$</p><p>Подставим числовые значения:</p><p>$\Delta E_{k2} = \frac{2 \cdot 80 \cdot (80+100)}{100} \cdot (1000)^2 = \frac{160 \cdot 180}{100} \cdot 10^6 = 288 \cdot 10^6$ Дж.</p><p>Положительный знак означает, что энергия системы увеличилась за счет работы, совершенной человеком при отталкивании от первого ядра.</p><p><strong>Ответ:</strong> Суммарная кинетическая энергия увеличится на $\frac{2m(m+M)}{M}v_0^2 = 288$ МДж.</p>" ] #original: array:6 [ "id" => 1737750 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1171} "task" => array:2 [ "refs" => "1288057" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$v_0 = 1000$ м/с</p><p>$M = 100$ кг</p><p>$m = 80$ кг</p><p><strong>Найти:</strong></p><p>$\Delta E_k$ - изменение суммарной кинетической энергии системы для двух случаев.</p><p><strong>Решение:</strong></p><p>Рассмотрим систему, состоящую из человека и двух ядер. Так как по условию пересадка происходит в полете, можно пренебречь внешними силами (сопротивлением воздуха), а сила тяжести скомпенсирована в вертикальном направлении. Таким образом, систему можно считать замкнутой, и для нее будет выполняться закон сохранения импульса в проекции на горизонтальную ось.</p><p>Направим ось OX в сторону начального движения человека на первом ядре. Обозначим массу человека как $\text{m}$, массу каждого ядра как $\text{M}$, а модуль их начальной скорости как $v_0$.</p><p>До пересадки человек (массой $\text{m}$) и первое ядро (массой $\text{M}$) движутся вместе как единое целое со скоростью $v_0$. Второе ядро движется им навстречу со скоростью $-v_0$.</p><p>Начальный импульс системы:</p><p>$P_{нач} = (m+M)v_0 + M(-v_0) = mv_0 + Mv_0 - Mv_0 = mv_0$</p><p>Начальная суммарная кинетическая энергия системы:</p><p>$E_{k, нач} = \frac{(m+M)v_0^2}{2} + \frac{M(-v_0)^2}{2} = \frac{(m+M)v_0^2}{2} + \frac{Mv_0^2}{2} = \frac{(m+2M)v_0^2}{2}$</p><p><strong>1)</strong> неизменной остается скорость оставленного мною ядра</p><p>После того как человек пересел, скорость первого (оставленного) ядра осталась равной $v_0$. Человек и второе ядро стали двигаться вместе с некоторой конечной скоростью $v_{кон2}$.</p><p>Конечный импульс системы в этом случае:</p><p>$P_{кон1} = Mv_0 + (m+M)v_{кон2}$</p><p>Согласно закону сохранения импульса $P_{нач} = P_{кон1}$:</p><p>$mv_0 = Mv_0 + (m+M)v_{кон2}$</p><p>Из этого уравнения найдем скорость $v_{кон2}$:</p><p>$(m-M)v_0 = (m+M)v_{кон2} \implies v_{кон2} = \frac{m-M}{m+M}v_0$</p><p>Конечная суммарная кинетическая энергия системы:</p><p>$E_{k, кон1} = \frac{Mv_0^2}{2} + \frac{(m+M)v_{кон2}^2}{2} = \frac{Mv_0^2}{2} + \frac{(m+M)}{2} \left( \frac{m-M}{m+M}v_0 \right)^2 = \frac{Mv_0^2}{2} + \frac{(m-M)^2}{2(m+M)}v_0^2$</p><p>Изменение кинетической энергии $\Delta E_{k1}$ равно разности конечной и начальной энергий:</p><p>$\Delta E_{k1} = E_{k, кон1} - E_{k, нач} = \left( \frac{Mv_0^2}{2} + \frac{(m-M)^2 v_0^2}{2(m+M)} \right) - \frac{(m+2M)v_0^2}{2}$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2} \left( M + \frac{(m-M)^2}{m+M} - (m+2M) \right) = \frac{v_0^2}{2(m+M)} \left( M(m+M) + (m-M)^2 - (m+2M)(m+M) \right)$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} \left( Mm+M^2 + m^2-2Mm+M^2 - (m^2+3Mm+2M^2) \right)$</p><p>$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} ( -4Mm ) = -\frac{2mM}{m+M}v_0^2$</p><p>Подставим числовые значения:</p><p>$\Delta E_{k1} = -\frac{2 \cdot 80 \cdot 100}{80+100} \cdot (1000)^2 = -\frac{16000}{180} \cdot 10^6 = -\frac{800}{9} \cdot 10^6 \approx -88.9 \cdot 10^6$ Дж.</p><p>Знак "минус" означает, что энергия системы уменьшилась.</p><p><strong>Ответ:</strong> Суммарная кинетическая энергия уменьшится на $\frac{2mM}{m+M}v_0^2 \approx 88.9$ МДж.</p><p><strong>2)</strong> неизменной остается скорость ядра, на которое я пересел</p><p>В этом случае после пересадки человек и второе ядро движутся вместе со скоростью, равной начальной скорости второго ядра, то есть $-v_0$. Первое ядро при этом приобретает некоторую конечную скорость $v_{кон1}$.</p><p>Конечный импульс системы:</p><p>$P_{кон2} = Mv_{кон1} + (m+M)(-v_0)$</p><p>Согласно закону сохранения импульса $P_{нач} = P_{кон2}$:</p><p>$mv_0 = Mv_{кон1} - (m+M)v_0$</p><p>Из этого уравнения найдем скорость $v_{кон1}$:</p><p>$mv_0 + (m+M)v_0 = Mv_{кон1} \implies (2m+M)v_0 = Mv_{кон1} \implies v_{кон1} = \frac{2m+M}{M}v_0$</p><p>Конечная суммарная кинетическая энергия системы:</p><p>$E_{k, кон2} = \frac{Mv_{кон1}^2}{2} + \frac{(m+M)(-v_0)^2}{2} = \frac{M}{2} \left( \frac{2m+M}{M}v_0 \right)^2 + \frac{(m+M)v_0^2}{2} = \frac{(2m+M)^2}{2M}v_0^2 + \frac{(m+M)v_0^2}{2}$</p><p>Изменение кинетической энергии $\Delta E_{k2}$ равно разности конечной и начальной энергий:</p><p>$\Delta E_{k2} = E_{k, кон2} - E_{k, нач} = \left( \frac{(2m+M)^2 v_0^2}{2M} + \frac{(m+M)v_0^2}{2} \right) - \frac{(m+2M)v_0^2}{2}$</p><p>$\Delta E_{k2} = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} + m+M - (m+2M) \right) = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} - M \right)$</p><p>$\Delta E_{k2} = \frac{v_0^2}{2M} \left( (2m+M)^2 - M^2 \right) = \frac{v_0^2}{2M} (4m^2 + 4mM + M^2 - M^2) = \frac{v_0^2}{2M} (4m^2 + 4mM)$</p><p>$\Delta E_{k2} = \frac{4m(m+M)}{2M}v_0^2 = \frac{2m(m+M)}{M}v_0^2$</p><p>Подставим числовые значения:</p><p>$\Delta E_{k2} = \frac{2 \cdot 80 \cdot (80+100)}{100} \cdot (1000)^2 = \frac{160 \cdot 180}{100} \cdot 10^6 = 288 \cdot 10^6$ Дж.</p><p>Положительный знак означает, что энергия системы увеличилась за счет работы, совершенной человеком при отталкивании от первого ядра.</p><p><strong>Ответ:</strong> Суммарная кинетическая энергия увеличится на $\frac{2m(m+M)}{M}v_0^2 = 288$ МДж.</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" => "1288058" "type" => "task" ] "previous" => array:2 [ "refs" => "1288056" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#2737 #items: array:1 [ 0 => App\Models\BookPage {#1182 #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" => 1340376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-25" "field_display_title" => "25" "field_folder" => "1" "field_image_name" => "25" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1186 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Book {#1187 #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" => 5401 "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 {#1188 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1217 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "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 {#1188 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1217 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "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 {#1220 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Element {#1222 #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" => 1518497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1223 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1518497 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1223 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1340377" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340375" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:8 [ 0 => App\Models\Task {#1231 #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" => 1288051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-36" "field_display_title" => "4.36" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232 …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 {#1234 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1235 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1273 …2} "content" => Illuminate\Database\Eloquent\Collection {#1393 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1418 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-36" "field_display_title" => "4.36" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1232 …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 {#1234 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1235 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1273 …2} "content" => Illuminate\Database\Eloquent\Collection {#1393 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1418 …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 => "*" ] } 1 => App\Models\Task {#1419 #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" => 1288052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-37" "field_display_title" => "4.37" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1420 …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 {#1422 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1423 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1461 …2} "content" => Illuminate\Database\Eloquent\Collection {#1581 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1606 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-37" "field_display_title" => "4.37" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1420 …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 {#1422 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1423 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1461 …2} "content" => Illuminate\Database\Eloquent\Collection {#1581 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1606 …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 => "*" ] } 2 => App\Models\Task {#1607 #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" => 1288053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-38" "field_display_title" => "4.38" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1608 …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 {#1610 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1611 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1649 …2} "content" => Illuminate\Database\Eloquent\Collection {#1769 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1794 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-38" "field_display_title" => "4.38" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1608 …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 {#1610 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1611 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1649 …2} "content" => Illuminate\Database\Eloquent\Collection {#1769 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1794 …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 {#1795 #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" => 1288054 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-39" "field_display_title" => "4.39" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1796 …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 {#1798 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1799 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1837 …2} "content" => Illuminate\Database\Eloquent\Collection {#1957 …2} …4 ] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1983 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#2171 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#2359 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#2547 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1340376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "25" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-25" "field_display_title" => "25" "field_folder" => "1" "field_image_name" => "25" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1186} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1184} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null 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№4.42 (с. 25)
Условие. №4.42 (с. 25)
скриншот условия
4.42*. Как вы знаете, мне случалось пересаживаться в полете с одного пушечного ядра на другое, встречное. На сколько изменяется суммарная кинетическая энергия моего тела и ядер при такой пересадке? Рассмотрите два случая:
1) неизменной остается скорость оставленного мною ядра;
2) неизменной остается скорость ядра, на которое я пересел.
Ядра имеют одинаковую по модулю скорость $v_0 = 1000 \text{ м/с}$ и массу $M = 100 \text{ кг}$; моя масса $m = 80 \text{ кг}$.
Решение. №4.42 (с. 25)
Решение 2. №4.42 (с. 25)
Дано:
$v_0 = 1000$ м/с
$M = 100$ кг
$m = 80$ кг
Найти:
$\Delta E_k$ - изменение суммарной кинетической энергии системы для двух случаев.
Решение:
Рассмотрим систему, состоящую из человека и двух ядер. Так как по условию пересадка происходит в полете, можно пренебречь внешними силами (сопротивлением воздуха), а сила тяжести скомпенсирована в вертикальном направлении. Таким образом, систему можно считать замкнутой, и для нее будет выполняться закон сохранения импульса в проекции на горизонтальную ось.
Направим ось OX в сторону начального движения человека на первом ядре. Обозначим массу человека как $\text{m}$, массу каждого ядра как $\text{M}$, а модуль их начальной скорости как $v_0$.
До пересадки человек (массой $\text{m}$) и первое ядро (массой $\text{M}$) движутся вместе как единое целое со скоростью $v_0$. Второе ядро движется им навстречу со скоростью $-v_0$.
Начальный импульс системы:
$P_{нач} = (m+M)v_0 + M(-v_0) = mv_0 + Mv_0 - Mv_0 = mv_0$
Начальная суммарная кинетическая энергия системы:
$E_{k, нач} = \frac{(m+M)v_0^2}{2} + \frac{M(-v_0)^2}{2} = \frac{(m+M)v_0^2}{2} + \frac{Mv_0^2}{2} = \frac{(m+2M)v_0^2}{2}$
1) неизменной остается скорость оставленного мною ядра
После того как человек пересел, скорость первого (оставленного) ядра осталась равной $v_0$. Человек и второе ядро стали двигаться вместе с некоторой конечной скоростью $v_{кон2}$.
Конечный импульс системы в этом случае:
$P_{кон1} = Mv_0 + (m+M)v_{кон2}$
Согласно закону сохранения импульса $P_{нач} = P_{кон1}$:
$mv_0 = Mv_0 + (m+M)v_{кон2}$
Из этого уравнения найдем скорость $v_{кон2}$:
$(m-M)v_0 = (m+M)v_{кон2} \implies v_{кон2} = \frac{m-M}{m+M}v_0$
Конечная суммарная кинетическая энергия системы:
$E_{k, кон1} = \frac{Mv_0^2}{2} + \frac{(m+M)v_{кон2}^2}{2} = \frac{Mv_0^2}{2} + \frac{(m+M)}{2} \left( \frac{m-M}{m+M}v_0 \right)^2 = \frac{Mv_0^2}{2} + \frac{(m-M)^2}{2(m+M)}v_0^2$
Изменение кинетической энергии $\Delta E_{k1}$ равно разности конечной и начальной энергий:
$\Delta E_{k1} = E_{k, кон1} - E_{k, нач} = \left( \frac{Mv_0^2}{2} + \frac{(m-M)^2 v_0^2}{2(m+M)} \right) - \frac{(m+2M)v_0^2}{2}$
$\Delta E_{k1} = \frac{v_0^2}{2} \left( M + \frac{(m-M)^2}{m+M} - (m+2M) \right) = \frac{v_0^2}{2(m+M)} \left( M(m+M) + (m-M)^2 - (m+2M)(m+M) \right)$
$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} \left( Mm+M^2 + m^2-2Mm+M^2 - (m^2+3Mm+2M^2) \right)$
$\Delta E_{k1} = \frac{v_0^2}{2(m+M)} ( -4Mm ) = -\frac{2mM}{m+M}v_0^2$
Подставим числовые значения:
$\Delta E_{k1} = -\frac{2 \cdot 80 \cdot 100}{80+100} \cdot (1000)^2 = -\frac{16000}{180} \cdot 10^6 = -\frac{800}{9} \cdot 10^6 \approx -88.9 \cdot 10^6$ Дж.
Знак "минус" означает, что энергия системы уменьшилась.
Ответ: Суммарная кинетическая энергия уменьшится на $\frac{2mM}{m+M}v_0^2 \approx 88.9$ МДж.
2) неизменной остается скорость ядра, на которое я пересел
В этом случае после пересадки человек и второе ядро движутся вместе со скоростью, равной начальной скорости второго ядра, то есть $-v_0$. Первое ядро при этом приобретает некоторую конечную скорость $v_{кон1}$.
Конечный импульс системы:
$P_{кон2} = Mv_{кон1} + (m+M)(-v_0)$
Согласно закону сохранения импульса $P_{нач} = P_{кон2}$:
$mv_0 = Mv_{кон1} - (m+M)v_0$
Из этого уравнения найдем скорость $v_{кон1}$:
$mv_0 + (m+M)v_0 = Mv_{кон1} \implies (2m+M)v_0 = Mv_{кон1} \implies v_{кон1} = \frac{2m+M}{M}v_0$
Конечная суммарная кинетическая энергия системы:
$E_{k, кон2} = \frac{Mv_{кон1}^2}{2} + \frac{(m+M)(-v_0)^2}{2} = \frac{M}{2} \left( \frac{2m+M}{M}v_0 \right)^2 + \frac{(m+M)v_0^2}{2} = \frac{(2m+M)^2}{2M}v_0^2 + \frac{(m+M)v_0^2}{2}$
Изменение кинетической энергии $\Delta E_{k2}$ равно разности конечной и начальной энергий:
$\Delta E_{k2} = E_{k, кон2} - E_{k, нач} = \left( \frac{(2m+M)^2 v_0^2}{2M} + \frac{(m+M)v_0^2}{2} \right) - \frac{(m+2M)v_0^2}{2}$
$\Delta E_{k2} = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} + m+M - (m+2M) \right) = \frac{v_0^2}{2} \left( \frac{(2m+M)^2}{M} - M \right)$
$\Delta E_{k2} = \frac{v_0^2}{2M} \left( (2m+M)^2 - M^2 \right) = \frac{v_0^2}{2M} (4m^2 + 4mM + M^2 - M^2) = \frac{v_0^2}{2M} (4m^2 + 4mM)$
$\Delta E_{k2} = \frac{4m(m+M)}{2M}v_0^2 = \frac{2m(m+M)}{M}v_0^2$
Подставим числовые значения:
$\Delta E_{k2} = \frac{2 \cdot 80 \cdot (80+100)}{100} \cdot (1000)^2 = \frac{160 \cdot 180}{100} \cdot 10^6 = 288 \cdot 10^6$ Дж.
Положительный знак означает, что энергия системы увеличилась за счет работы, совершенной человеком при отталкивании от первого ядра.
Ответ: Суммарная кинетическая энергия увеличится на $\frac{2m(m+M)}{M}v_0^2 = 288$ МДж.
Другие задания:
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