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Номер 12, страница 449 - гдз по физике 10 класс учебник Касьянов
Авторы: Касьянов В. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2021 - 2026
Уровень обучения: углублённый
Цвет обложки: белый самолет и молнии изображены
ISBN: 978-5-09-103621-3
Популярные ГДЗ в 10 классе
Лабораторные работы. 4. Движение тела по окружности под действием сил тяжести и упругости - номер 12, страница 449.
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" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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" => 7000 "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1040 #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" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4566 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Касьянов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Валерий" "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 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1041 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 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:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => 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: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 {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1048 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #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" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ "field_accusative_case" => "углубленный" "field_creative_case" => "углубленным" "field_dative_case" => "углубленному" "field_genitive_case" => "углубленного" "field_nominative_case" => "углубленный" "field_prepositional_case" => "углубленном" ] "field_translit" => "uglublennyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "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" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "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" => "/10-klass/fizika/kasyanov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 7000 "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 {#1041} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042} "field_country" => Illuminate\Database\Eloquent\Collection {#1044} "field_city" => Illuminate\Database\Eloquent\Collection {#1046} "field_series" => Illuminate\Database\Eloquent\Collection {#1048} "field_umk" => Illuminate\Database\Eloquent\Collection {#1049} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_publication_number" => "11" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => "самолет и молнии изображены" "field_publication_year" => "2021" "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" => "984" "field_priority" => null "field_default_folder" => "/fizika_10/kasyanov-u/" "field_isbn" => "978-5-09-103621-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/kasyanov-u/covers/cover1.webp?ts=1757588862" "alt" => "" "width" => "1604" "height" => "2397" ] ] "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" => "/10-klass/fizika/kasyanov-uchebnik" "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" => 381 "subject" => 556 "class_subject" => 494 ] ] #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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "426" "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:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1064 #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" => 1389658 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Движение тела по окружности под действием сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "446" "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 {#1066 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Branch {#1068 #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" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "426" "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 {#1070 #items: array:1 [ 0 => App\Models\Book {#1071 …30} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1389652 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069} "field_page_start" => "426" "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 {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #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" => 1389658 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Движение тела по окружности под действием сил тяжести и упругости" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "446" "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 {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067} ] #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 {#1102 #items: array:2 [ 0 => App\Models\Element {#1103 #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" => 1640968 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Edition {#1105 #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" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ 0 => App\Models\Term {#1107 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106} "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 {#1108} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110} "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" => "1390587" "type" => "task" ] "text" => "<p><strong>12.</strong> Вычислите правую часть равенства (9) $ \Pi_9 = \frac{F}{m} $. При этом масса груза равна:</p><p>$ m \pm \Delta m = (100 \pm 0,5) $ г.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1708" "height" => 300 "path" => "/media/fizika_10/kasyanov-u/0-lab04/12-1.webp?ts=1757958229" ] ] ] #original: array:7 [ "id" => 1640968 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104} "task" => array:2 [ "refs" => "1390587" "type" => "task" ] "text" => "<p><strong>12.</strong> Вычислите правую часть равенства (9) $ \Pi_9 = \frac{F}{m} $. При этом масса груза равна:</p><p>$ m \pm \Delta m = (100 \pm 0,5) $ г.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1708" "height" => 300 "path" => "/media/fizika_10/kasyanov-u/0-lab04/12-1.webp?ts=1757958229" ] ] ] #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 {#1111 #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" => 1693599 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\Edition {#1113 #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" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Term {#1115 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6145 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118} "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" => "1390587" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m \pm \Delta m = (100 \pm 0,5) \text{ г}$</p><p><em>Для вычисления правой части равенства необходимо значение силы $F$ и ее абсолютной погрешности $\Delta F$, которые в условии задачи отсутствуют. Поэтому решение будет представлено в общем виде и в виде примера с использованием гипотетического значения силы, которое могло быть получено в предыдущих заданиях, например, $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$.</em></p><p>Перевод в систему СИ:<br>$m = 100 \text{ г} = 0,1 \text{ кг}$<br>$\Delta m = 0,5 \text{ г} = 0,0005 \text{ кг}$</p><p><strong>Найти:</strong></p><p>$П_9 = \frac{F}{m}$ и ее погрешность $\Delta П_9$.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сначала вычислим основное значение величины $П_9$, подставив средние значения $F$ и $m$ в формулу:</p><p>$П_9 = \frac{F}{m} = \frac{1,00 \text{ Н}}{0,1 \text{ кг}} = 10,0 \frac{\text{Н}}{\text{кг}} = 10,0 \frac{\text{м}}{\text{с}^2}$</p><p><strong>2.</strong> Для нахождения погрешности косвенного измерения $\Delta П_9$ необходимо сначала найти относительные погрешности измеряемых величин $F$ и $m$.</p><p>Относительная погрешность массы $m$:</p><p>$\varepsilon_m = \frac{\Delta m}{m} = \frac{0,0005 \text{ кг}}{0,1 \text{ кг}} = 0,005$</p><p>Относительная погрешность силы $F$ (для нашего примера):</p><p>$\varepsilon_F = \frac{\Delta F}{F} = \frac{0,02 \text{ Н}}{1,00 \text{ Н}} = 0,02$</p><p><strong>3.</strong> Относительная погрешность величины $П_9$, которая является частным двух величин, находится по формуле:</p><p>$\varepsilon_{П_9} = \sqrt{(\varepsilon_F)^2 + (\varepsilon_m)^2}$</p><p>Подставим вычисленные значения:</p><p>$\varepsilon_{П_9} = \sqrt{(0,02)^2 + (0,005)^2} = \sqrt{0,0004 + 0,000025} = \sqrt{0,000425} \approx 0,0206$</p><p><strong>4.</strong> Теперь можно найти абсолютную погрешность $\Delta П_9$:</p><p>$\Delta П_9 = П_9 \cdot \varepsilon_{П_9} = 10,0 \frac{\text{м}}{\text{с}^2} \cdot 0,0206 \approx 0,206 \frac{\text{м}}{\text{с}^2}$</p><p><strong>5.</strong> Согласно правилам обработки результатов измерений, значение погрешности округляется до одной значащей цифры.</p><p>$\Delta П_9 \approx 0,2 \frac{\text{м}}{\text{с}^2}$</p><p><strong>6.</strong> Основное значение $П_9$ округляется до того же десятичного разряда, что и погрешность (в данном случае — до десятых).</p><p>$П_9 = 10,0 \frac{\text{м}}{\text{с}^2}$</p><p><strong>7.</strong> Окончательный результат записывается в виде $П_9 \pm \Delta П_9$.</p><p><strong>Ответ:</strong> так как в условии задачи не предоставлено значение силы $F$, дать однозначный численный ответ невозможно. В случае, если было измерено значение силы $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$, то правая часть равенства будет равна $П_9 = (10,0 \pm 0,2) \frac{\text{м}}{\text{с}^2}$.</p>" ] #original: array:6 [ "id" => 1693599 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112} "task" => array:2 [ "refs" => "1390587" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m \pm \Delta m = (100 \pm 0,5) \text{ г}$</p><p><em>Для вычисления правой части равенства необходимо значение силы $F$ и ее абсолютной погрешности $\Delta F$, которые в условии задачи отсутствуют. Поэтому решение будет представлено в общем виде и в виде примера с использованием гипотетического значения силы, которое могло быть получено в предыдущих заданиях, например, $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$.</em></p><p>Перевод в систему СИ:<br>$m = 100 \text{ г} = 0,1 \text{ кг}$<br>$\Delta m = 0,5 \text{ г} = 0,0005 \text{ кг}$</p><p><strong>Найти:</strong></p><p>$П_9 = \frac{F}{m}$ и ее погрешность $\Delta П_9$.</p><p><strong>Решение:</strong></p><p><strong>1.</strong> Сначала вычислим основное значение величины $П_9$, подставив средние значения $F$ и $m$ в формулу:</p><p>$П_9 = \frac{F}{m} = \frac{1,00 \text{ Н}}{0,1 \text{ кг}} = 10,0 \frac{\text{Н}}{\text{кг}} = 10,0 \frac{\text{м}}{\text{с}^2}$</p><p><strong>2.</strong> Для нахождения погрешности косвенного измерения $\Delta П_9$ необходимо сначала найти относительные погрешности измеряемых величин $F$ и $m$.</p><p>Относительная погрешность массы $m$:</p><p>$\varepsilon_m = \frac{\Delta m}{m} = \frac{0,0005 \text{ кг}}{0,1 \text{ кг}} = 0,005$</p><p>Относительная погрешность силы $F$ (для нашего примера):</p><p>$\varepsilon_F = \frac{\Delta F}{F} = \frac{0,02 \text{ Н}}{1,00 \text{ Н}} = 0,02$</p><p><strong>3.</strong> Относительная погрешность величины $П_9$, которая является частным двух величин, находится по формуле:</p><p>$\varepsilon_{П_9} = \sqrt{(\varepsilon_F)^2 + (\varepsilon_m)^2}$</p><p>Подставим вычисленные значения:</p><p>$\varepsilon_{П_9} = \sqrt{(0,02)^2 + (0,005)^2} = \sqrt{0,0004 + 0,000025} = \sqrt{0,000425} \approx 0,0206$</p><p><strong>4.</strong> Теперь можно найти абсолютную погрешность $\Delta П_9$:</p><p>$\Delta П_9 = П_9 \cdot \varepsilon_{П_9} = 10,0 \frac{\text{м}}{\text{с}^2} \cdot 0,0206 \approx 0,206 \frac{\text{м}}{\text{с}^2}$</p><p><strong>5.</strong> Согласно правилам обработки результатов измерений, значение погрешности округляется до одной значащей цифры.</p><p>$\Delta П_9 \approx 0,2 \frac{\text{м}}{\text{с}^2}$</p><p><strong>6.</strong> Основное значение $П_9$ округляется до того же десятичного разряда, что и погрешность (в данном случае — до десятых).</p><p>$П_9 = 10,0 \frac{\text{м}}{\text{с}^2}$</p><p><strong>7.</strong> Окончательный результат записывается в виде $П_9 \pm \Delta П_9$.</p><p><strong>Ответ:</strong> так как в условии задачи не предоставлено значение силы $F$, дать однозначный численный ответ невозможно. В случае, если было измерено значение силы $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$, то правая часть равенства будет равна $П_9 = (10,0 \pm 0,2) \frac{\text{м}}{\text{с}^2}$.</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" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ 0 => App\Models\BookPage {#1124 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] 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#fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1229 #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" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #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 {#1231 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ 0 => App\Models\Branch {#1174 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:2 [ 0 => App\Models\Branch {#1174 …30} 1 => App\Models\Branch {#1179 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:2 [ 0 => App\Models\Element {#1235 …30} 1 => App\Models\Element {#1237 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Book {#1128} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1230} "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 {#1231} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1233} "content" => Illuminate\Database\Eloquent\Collection {#1234} "next" => array:2 [ "refs" => "1390587" "type" => "task" ] "previous" => array:2 [ "refs" => "1390585" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239} "page" => array:2 [ "refs" => "1391097" "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 {#1240 #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" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #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 {#1242 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Branch {#1174 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:2 [ 0 => App\Models\Branch {#1174 …30} 1 => App\Models\Branch {#1179 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:2 [ 0 => App\Models\Element {#1246 …30} 1 => App\Models\Element {#1248 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Book {#1128} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241} "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 {#1242} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244} "content" => Illuminate\Database\Eloquent\Collection {#1245} "next" => array:2 [ "refs" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250} "page" => array:2 [ "refs" => "1391097" "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 {#1251 #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" => 1390588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-13" "field_display_title" => "13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #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 {#1253 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:1 [ 0 => App\Models\Branch {#1174 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:2 [ 0 => App\Models\Branch {#1174 …30} 1 => App\Models\Branch {#1179 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:2 [ 0 => App\Models\Element {#1257 …30} 1 => App\Models\Element {#1259 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390589" "type" => "task" ] "previous" => array:2 [ "refs" => "1390587" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ 0 => App\Models\Book {#1128} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-13" "field_display_title" => "13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252} "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 {#1253} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1254} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1255} "content" => Illuminate\Database\Eloquent\Collection {#1256} "next" => array:2 [ "refs" => "1390589" "type" => "task" ] "previous" => array:2 [ "refs" => "1390587" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1261} "page" => array:2 [ "refs" => "1391097" "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 {#1262 #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" => 1390589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #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 {#1264 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Branch {#1174 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1266 #items: array:2 [ 0 => App\Models\Branch {#1174 …30} 1 => App\Models\Branch {#1179 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:2 [ 0 => App\Models\Element {#1268 …30} 1 => App\Models\Element {#1270 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390590" "type" => "task" ] "previous" => array:2 [ "refs" => "1390588" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:1 [ 0 => App\Models\Book {#1128} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-14" "field_display_title" => "14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263} "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 {#1264} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1266} "content" => Illuminate\Database\Eloquent\Collection {#1267} "next" => array:2 [ "refs" => "1390590" "type" => "task" ] "previous" => array:2 [ "refs" => "1390588" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1272} "page" => array:2 [ "refs" => "1391097" "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 {#1273 #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" => 1390590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1274 #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 {#1275 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1390591" "type" => "task" ] "previous" => array:2 [ "refs" => "1390589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1283 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1391097" "type" => "book_page" ] ] #original: array:24 [ "id" => 1390590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-15" "field_display_title" => "15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1274} "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 {#1275} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1276} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1277} "content" => Illuminate\Database\Eloquent\Collection {#1278} "next" => array:2 [ "refs" => "1390591" "type" => "task" ] "previous" => array:2 [ "refs" => "1390589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1283} "page" => array:2 [ "refs" => "1391097" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1391097 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_url" => "/10-klass/fizika/kasyanov-uchebnik/page-449" "field_display_title" => "449" "field_folder" => "1" "field_image_name" => "449" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1126} "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} "content" => Illuminate\Database\Eloquent\Collection {#1159} "next" => array:2 [ "refs" => "1391098" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1391096" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1168} ] #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" => 1390587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "449" "field_page_end" => null "field_url" => "/10-klass/fizika/kasyanov-uchebnik/lab04-12" "field_display_title" => "12" "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 {#1102} "next" => array:2 [ "refs" => "1390588" "type" => "task" ] "previous" => array:2 [ "refs" => "1390586" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1119} "page" => array:2 [ "refs" => "1391097" "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 => "*" ] }
№12 (с. 449)
Условие. №12 (с. 449)
скриншот условия
12. Вычислите правую часть равенства (9) $ \Pi_9 = \frac{F}{m} $. При этом масса груза равна:
$ m \pm \Delta m = (100 \pm 0,5) $ г.
Решение. №12 (с. 449)
Дано:
$m \pm \Delta m = (100 \pm 0,5) \text{ г}$
Для вычисления правой части равенства необходимо значение силы $F$ и ее абсолютной погрешности $\Delta F$, которые в условии задачи отсутствуют. Поэтому решение будет представлено в общем виде и в виде примера с использованием гипотетического значения силы, которое могло быть получено в предыдущих заданиях, например, $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$.
Перевод в систему СИ:
$m = 100 \text{ г} = 0,1 \text{ кг}$
$\Delta m = 0,5 \text{ г} = 0,0005 \text{ кг}$
Найти:
$П_9 = \frac{F}{m}$ и ее погрешность $\Delta П_9$.
Решение:
1. Сначала вычислим основное значение величины $П_9$, подставив средние значения $F$ и $m$ в формулу:
$П_9 = \frac{F}{m} = \frac{1,00 \text{ Н}}{0,1 \text{ кг}} = 10,0 \frac{\text{Н}}{\text{кг}} = 10,0 \frac{\text{м}}{\text{с}^2}$
2. Для нахождения погрешности косвенного измерения $\Delta П_9$ необходимо сначала найти относительные погрешности измеряемых величин $F$ и $m$.
Относительная погрешность массы $m$:
$\varepsilon_m = \frac{\Delta m}{m} = \frac{0,0005 \text{ кг}}{0,1 \text{ кг}} = 0,005$
Относительная погрешность силы $F$ (для нашего примера):
$\varepsilon_F = \frac{\Delta F}{F} = \frac{0,02 \text{ Н}}{1,00 \text{ Н}} = 0,02$
3. Относительная погрешность величины $П_9$, которая является частным двух величин, находится по формуле:
$\varepsilon_{П_9} = \sqrt{(\varepsilon_F)^2 + (\varepsilon_m)^2}$
Подставим вычисленные значения:
$\varepsilon_{П_9} = \sqrt{(0,02)^2 + (0,005)^2} = \sqrt{0,0004 + 0,000025} = \sqrt{0,000425} \approx 0,0206$
4. Теперь можно найти абсолютную погрешность $\Delta П_9$:
$\Delta П_9 = П_9 \cdot \varepsilon_{П_9} = 10,0 \frac{\text{м}}{\text{с}^2} \cdot 0,0206 \approx 0,206 \frac{\text{м}}{\text{с}^2}$
5. Согласно правилам обработки результатов измерений, значение погрешности округляется до одной значащей цифры.
$\Delta П_9 \approx 0,2 \frac{\text{м}}{\text{с}^2}$
6. Основное значение $П_9$ округляется до того же десятичного разряда, что и погрешность (в данном случае — до десятых).
$П_9 = 10,0 \frac{\text{м}}{\text{с}^2}$
7. Окончательный результат записывается в виде $П_9 \pm \Delta П_9$.
Ответ: так как в условии задачи не предоставлено значение силы $F$, дать однозначный численный ответ невозможно. В случае, если было измерено значение силы $F \pm \Delta F = (1,00 \pm 0,02) \text{ Н}$, то правая часть равенства будет равна $П_9 = (10,0 \pm 0,2) \frac{\text{м}}{\text{с}^2}$.
Другие задания:
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