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Номер 2.16, страница 11 - гдз по физике 9 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-09-038216-8
Популярные ГДЗ в 9 классе
II. Механические колебания и волны - номер 2.16, страница 11.
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" => 1424130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-16" "field_display_title" => "2.16" "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" => 1424065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Механические колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "10" "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" => 2549 "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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#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:3 [ 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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#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:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#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" => 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 {#1048 #items: array:1 [ 0 => App\Models\Term {#1049 #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 {#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:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "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" => "pererabotannoe i dopolnennoe" ] #original: array:6 [ "id" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "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" => "pererabotannoe i dopolnennoe" ] #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 {#1057 #items: array:1 [ 0 => App\Models\Term {#1042} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 #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 [ "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" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "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" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 2549 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1032} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1039} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1052} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1058} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1060} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1061} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "II. Механические колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "10" "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 {#1063} ] #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 {#1064 #items: array:1 [ 0 => App\Models\Branch {#1023} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:2 [ 0 => App\Models\Element {#1066 #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" => 1673748 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Edition {#1068 #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" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] …10 } ] #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 {#1071 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1069} "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 {#1071} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1073} "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" => "1424130" "type" => "task" ] "text" => "<p><strong>2.16</strong> Как, находясь в космическом корабле на орбите, определить массу груза, если в вашем распоряжении имеется пружина, набор грузов известной массы и секундомер?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1741" "height" => 254 "path" => "/media/fizika_09/artemenkov-z/0-2/16-1.webp?ts=1758726373" ] ] ] #original: array:7 [ "id" => 1673748 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1067} "task" => array:2 [ "refs" => "1424130" "type" => "task" ] "text" => "<p><strong>2.16</strong> Как, находясь в космическом корабле на орбите, определить массу груза, если в вашем распоряжении имеется пружина, набор грузов известной массы и секундомер?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1741" "height" => 254 "path" => "/media/fizika_09/artemenkov-z/0-2/16-1.webp?ts=1758726373" ] ] ] #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 {#1074 #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" => 1695290 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Edition {#1076 #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" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 …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 {#1079 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1079} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1080} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081} "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" => "1424130" "type" => "task" ] "text" => "<p>В условиях невесомости, характерной для космического корабля на орбите, традиционные способы взвешивания, основанные на силе тяжести, не работают. Массу тела можно определить, используя ее инертные свойства. Для этого можно создать колебательную систему — пружинный маятник, период колебаний которого зависит от массы тела и жесткости пружины.</p><p><strong>Дано:</strong></p><p>Пружина с неизвестной жесткостью $k$.</p><p>Набор грузов известной массы (эталонные грузы), например, груз с массой $m_1$.</p><p>Секундомер.</p><p>Груз с неизвестной массой $m_x$.</p><p><strong>Найти:</strong></p><p>Массу груза $m_x$.</p><p><strong>Решение:</strong></p><p>Метод основан на измерении периода колебаний пружинного маятника. Период $T$ гармонических колебаний груза массой $m$ на пружине жесткостью $k$ определяется формулой:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p>Поскольку жесткость пружины $k$ нам неизвестна, необходимо провести два эксперимента: один с эталонным грузом для калибровки системы, а второй — с исследуемым грузом.</p><p><strong>1.</strong> <strong>Калибровка системы.</strong><br>Закрепим один конец пружины на неподвижной части корабля, а к другому концу прикрепим эталонный груз известной массы $m_1$. Приведем систему в колебательное движение, сместив груз из положения равновесия. С помощью секундомера измерим время $t_1$, за которое система совершит $N$ полных колебаний (для повышения точности $N$ лучше взять побольше, например, 10 или 20). Период колебаний эталонного груза будет равен:</p><p>$T_1 = \frac{t_1}{N}$</p><p>Согласно формуле периода, можно записать:</p><p>$T_1 = 2\pi\sqrt{\frac{m_1}{k}}$</p><p>Возведем обе части в квадрат: $T_1^2 = 4\pi^2 \frac{m_1}{k}$</p><p><strong>2.</strong> <strong>Измерение массы неизвестного груза.</strong><br>Заменим эталонный груз на исследуемый груз с неизвестной массой $m_x$. Снова приведем систему в колебание и измерим время $t_x$, за которое система совершит то же самое число $N$ полных колебаний. Период колебаний исследуемого груза будет равен:</p><p>$T_x = \frac{t_x}{N}$</p><p>Для этого периода справедливо соотношение:</p><p>$T_x = 2\pi\sqrt{\frac{m_x}{k}}$</p><p>Возведем обе части в квадрат: $T_x^2 = 4\pi^2 \frac{m_x}{k}$</p><p><strong>3.</strong> <strong>Расчет неизвестной массы.</strong><br>Мы получили систему из двух уравнений:</p><p>$\begin{cases} T_1^2 = 4\pi^2 \frac{m_1}{k} \\ T_x^2 = 4\pi^2 \frac{m_x}{k} \end{cases}$</p><p>Разделим второе уравнение на первое. Жесткость пружины $k$ и множитель $4\pi^2$ сократятся:</p><p>$\frac{T_x^2}{T_1^2} = \frac{m_x}{m_1}$</p><p>Отсюда выразим искомую массу $m_x$:</p><p>$m_x = m_1 \frac{T_x^2}{T_1^2}$</p><p>Подставим выражения для периодов через измеренные времена $t_1$ и $t_x$:</p><p>$m_x = m_1 \frac{(t_x/N)^2}{(t_1/N)^2} = m_1 \frac{t_x^2}{t_1^2} = m_1 \left(\frac{t_x}{t_1}\right)^2$</p><p>Таким образом, для определения массы груза необходимо прикрепить к пружине эталонный груз массой $m_1$, измерить время $t_1$ для $N$ колебаний, затем заменить его на исследуемый груз, измерить время $t_x$ для тех же $N$ колебаний и рассчитать массу $m_x$ по полученной формуле.</p><p><strong>Ответ:</strong> Необходимо создать пружинный маятник. Сначала нужно измерить с помощью секундомера время $t_1$ некоторого числа полных колебаний $N$ для груза известной массы $m_1$. Затем, не меняя число колебаний $N$, измерить время $t_x$ для груза с неизвестной массой $m_x$. Искомая масса вычисляется по формуле: $m_x = m_1 \left(\frac{t_x}{t_1}\right)^2$.</p>" ] #original: array:6 [ "id" => 1695290 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1075} "task" => array:2 [ "refs" => "1424130" "type" => "task" ] "text" => "<p>В условиях невесомости, характерной для космического корабля на орбите, традиционные способы взвешивания, основанные на силе тяжести, не работают. Массу тела можно определить, используя ее инертные свойства. Для этого можно создать колебательную систему — пружинный маятник, период колебаний которого зависит от массы тела и жесткости пружины.</p><p><strong>Дано:</strong></p><p>Пружина с неизвестной жесткостью $k$.</p><p>Набор грузов известной массы (эталонные грузы), например, груз с массой $m_1$.</p><p>Секундомер.</p><p>Груз с неизвестной массой $m_x$.</p><p><strong>Найти:</strong></p><p>Массу груза $m_x$.</p><p><strong>Решение:</strong></p><p>Метод основан на измерении периода колебаний пружинного маятника. Период $T$ гармонических колебаний груза массой $m$ на пружине жесткостью $k$ определяется формулой:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p>Поскольку жесткость пружины $k$ нам неизвестна, необходимо провести два эксперимента: один с эталонным грузом для калибровки системы, а второй — с исследуемым грузом.</p><p><strong>1.</strong> <strong>Калибровка системы.</strong><br>Закрепим один конец пружины на неподвижной части корабля, а к другому концу прикрепим эталонный груз известной массы $m_1$. Приведем систему в колебательное движение, сместив груз из положения равновесия. С помощью секундомера измерим время $t_1$, за которое система совершит $N$ полных колебаний (для повышения точности $N$ лучше взять побольше, например, 10 или 20). Период колебаний эталонного груза будет равен:</p><p>$T_1 = \frac{t_1}{N}$</p><p>Согласно формуле периода, можно записать:</p><p>$T_1 = 2\pi\sqrt{\frac{m_1}{k}}$</p><p>Возведем обе части в квадрат: $T_1^2 = 4\pi^2 \frac{m_1}{k}$</p><p><strong>2.</strong> <strong>Измерение массы неизвестного груза.</strong><br>Заменим эталонный груз на исследуемый груз с неизвестной массой $m_x$. Снова приведем систему в колебание и измерим время $t_x$, за которое система совершит то же самое число $N$ полных колебаний. Период колебаний исследуемого груза будет равен:</p><p>$T_x = \frac{t_x}{N}$</p><p>Для этого периода справедливо соотношение:</p><p>$T_x = 2\pi\sqrt{\frac{m_x}{k}}$</p><p>Возведем обе части в квадрат: $T_x^2 = 4\pi^2 \frac{m_x}{k}$</p><p><strong>3.</strong> <strong>Расчет неизвестной массы.</strong><br>Мы получили систему из двух уравнений:</p><p>$\begin{cases} T_1^2 = 4\pi^2 \frac{m_1}{k} \\ T_x^2 = 4\pi^2 \frac{m_x}{k} \end{cases}$</p><p>Разделим второе уравнение на первое. Жесткость пружины $k$ и множитель $4\pi^2$ сократятся:</p><p>$\frac{T_x^2}{T_1^2} = \frac{m_x}{m_1}$</p><p>Отсюда выразим искомую массу $m_x$:</p><p>$m_x = m_1 \frac{T_x^2}{T_1^2}$</p><p>Подставим выражения для периодов через измеренные времена $t_1$ и $t_x$:</p><p>$m_x = m_1 \frac{(t_x/N)^2}{(t_1/N)^2} = m_1 \frac{t_x^2}{t_1^2} = m_1 \left(\frac{t_x}{t_1}\right)^2$</p><p>Таким образом, для определения массы груза необходимо прикрепить к пружине эталонный груз массой $m_1$, измерить время $t_1$ для $N$ колебаний, затем заменить его на исследуемый груз, измерить время $t_x$ для тех же $N$ колебаний и рассчитать массу $m_x$ по полученной формуле.</p><p><strong>Ответ:</strong> Необходимо создать пружинный маятник. Сначала нужно измерить с помощью секундомера время $t_1$ некоторого числа полных колебаний $N$ для груза известной массы $m_1$. Затем, не меняя число колебаний $N$, измерить время $t_x$ для груза с неизвестной массой $m_x$. Искомая масса вычисляется по формуле: $m_x = m_1 \left(\frac{t_x}{t_1}\right)^2$.</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" => "1424131" "type" => "task" ] "previous" => array:2 [ "refs" => "1424129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1030} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\BookPage {#1096 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-12" "field_display_title" => "2.12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256} "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 {#1266} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1262} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260} "content" => Illuminate\Database\Eloquent\Collection {#1291} "next" => array:2 [ "refs" => "1424127" "type" => "task" ] "previous" => array:2 [ "refs" => "1424125" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1293} "page" => array:2 [ "refs" => "1424361" "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 {#1292 #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" => 1424127 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-13" "field_display_title" => "2.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:1 [ 0 => App\Models\Term {#1217 …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 {#1295 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1314 #items: array:2 [ 0 => App\Models\Element {#1298 …30} 1 => App\Models\Element {#1306 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424128" "type" => "task" ] "previous" => array:2 [ "refs" => "1424126" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1316 #items: array:1 [ 0 => App\Models\Book {#1099} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424361" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424127 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-13" "field_display_title" => "2.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294} "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 {#1295} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297} "content" => Illuminate\Database\Eloquent\Collection {#1314} "next" => array:2 [ "refs" => "1424128" "type" => "task" ] "previous" => array:2 [ "refs" => "1424126" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1316} "page" => array:2 [ "refs" => "1424361" "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 {#1315 #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" => 1424128 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-14" "field_display_title" => "2.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 #items: array:1 [ 0 => App\Models\Term {#1217 …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 {#1318 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1319 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1337 #items: array:2 [ 0 => App\Models\Element {#1321 …30} 1 => App\Models\Element {#1329 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424129" "type" => "task" ] "previous" => array:2 [ "refs" => "1424127" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1339 #items: array:1 [ 0 => App\Models\Book {#1099} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424361" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424128 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-14" "field_display_title" => "2.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317} "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 {#1318} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1319} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320} "content" => Illuminate\Database\Eloquent\Collection {#1337} "next" => array:2 [ "refs" => "1424129" "type" => "task" ] "previous" => array:2 [ "refs" => "1424127" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1339} "page" => array:2 [ "refs" => "1424361" "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 {#1338 #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" => 1424129 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-15" "field_display_title" => "2.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1340 #items: array:1 [ 0 => App\Models\Term {#1217 …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 {#1341 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1342 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1343 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1360 #items: array:2 [ 0 => App\Models\Element {#1344 …30} 1 => App\Models\Element {#1352 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424130" "type" => "task" ] "previous" => array:2 [ "refs" => "1424128" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1362 #items: array:1 [ 0 => App\Models\Book {#1099} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424361" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424129 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-15" "field_display_title" => "2.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1340} "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 {#1341} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1343} "content" => Illuminate\Database\Eloquent\Collection {#1360} "next" => array:2 [ "refs" => "1424130" "type" => "task" ] "previous" => array:2 [ "refs" => "1424128" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1362} "page" => array:2 [ "refs" => "1424361" "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 {#1361 #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" => 1424130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-16" "field_display_title" => "2.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1363 #items: array:1 [ 0 => App\Models\Term {#1217 …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 {#1364 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1365 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1366 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1383 #items: array:2 [ 0 => App\Models\Element {#1367 …30} 1 => App\Models\Element {#1375 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424131" "type" => "task" ] "previous" => array:2 [ "refs" => "1424129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1385 #items: array:1 [ 0 => App\Models\Book {#1099} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424361" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-16" "field_display_title" => "2.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1363} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1364} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1365} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1366} "content" => Illuminate\Database\Eloquent\Collection {#1383} "next" => array:2 [ "refs" => "1424131" "type" => "task" ] "previous" => array:2 [ "refs" => "1424129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1385} "page" => array:2 [ "refs" => "1424361" "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 => "*" ] } 6 => App\Models\Task {#1384 #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" => 1424131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-17" "field_display_title" => "2.17" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1386 #items: array:1 [ 0 => App\Models\Term {#1217 …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 {#1387 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1389 #items: array:1 [ 0 => App\Models\Branch {#1218 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1400 #items: array:2 [ 0 => App\Models\Element {#1408 …30} 1 => App\Models\Element {#1410 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424132" "type" => "task" ] "previous" => array:2 [ "refs" => "1424130" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1405 #items: array:1 [ 0 => App\Models\Book {#1099} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424361" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424131 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-17" "field_display_title" => "2.17" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1386} "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 {#1387} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1389} "content" => Illuminate\Database\Eloquent\Collection {#1400} "next" => array:2 [ "refs" => "1424132" "type" => "task" ] "previous" => array:2 [ "refs" => "1424130" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1405} "page" => array:2 [ "refs" => "1424361" "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" => 1424361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/page-11" "field_display_title" => "11" "field_folder" => "1" "field_image_name" => "11" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1098} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1132} "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 {#1130} "content" => Illuminate\Database\Eloquent\Collection {#1141} "next" => array:2 [ "refs" => "1424362" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424360" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1202} ] #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" => 1424130 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "11" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/2-16" "field_display_title" => "2.16" "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 {#1064} "content" => Illuminate\Database\Eloquent\Collection {#1065} "next" => array:2 [ "refs" => "1424131" "type" => "task" ] "previous" => array:2 [ "refs" => "1424129" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082} "page" => array:2 [ "refs" => "1424361" "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 => "*" ] }
№2.16 (с. 11)
Условие. №2.16 (с. 11)
скриншот условия
2.16 Как, находясь в космическом корабле на орбите, определить массу груза, если в вашем распоряжении имеется пружина, набор грузов известной массы и секундомер?
Решение. №2.16 (с. 11)
В условиях невесомости, характерной для космического корабля на орбите, традиционные способы взвешивания, основанные на силе тяжести, не работают. Массу тела можно определить, используя ее инертные свойства. Для этого можно создать колебательную систему — пружинный маятник, период колебаний которого зависит от массы тела и жесткости пружины.
Дано:
Пружина с неизвестной жесткостью $k$.
Набор грузов известной массы (эталонные грузы), например, груз с массой $m_1$.
Секундомер.
Груз с неизвестной массой $m_x$.
Найти:
Массу груза $m_x$.
Решение:
Метод основан на измерении периода колебаний пружинного маятника. Период $T$ гармонических колебаний груза массой $m$ на пружине жесткостью $k$ определяется формулой:
$T = 2\pi\sqrt{\frac{m}{k}}$
Поскольку жесткость пружины $k$ нам неизвестна, необходимо провести два эксперимента: один с эталонным грузом для калибровки системы, а второй — с исследуемым грузом.
1. Калибровка системы.
Закрепим один конец пружины на неподвижной части корабля, а к другому концу прикрепим эталонный груз известной массы $m_1$. Приведем систему в колебательное движение, сместив груз из положения равновесия. С помощью секундомера измерим время $t_1$, за которое система совершит $N$ полных колебаний (для повышения точности $N$ лучше взять побольше, например, 10 или 20). Период колебаний эталонного груза будет равен:
$T_1 = \frac{t_1}{N}$
Согласно формуле периода, можно записать:
$T_1 = 2\pi\sqrt{\frac{m_1}{k}}$
Возведем обе части в квадрат: $T_1^2 = 4\pi^2 \frac{m_1}{k}$
2. Измерение массы неизвестного груза.
Заменим эталонный груз на исследуемый груз с неизвестной массой $m_x$. Снова приведем систему в колебание и измерим время $t_x$, за которое система совершит то же самое число $N$ полных колебаний. Период колебаний исследуемого груза будет равен:
$T_x = \frac{t_x}{N}$
Для этого периода справедливо соотношение:
$T_x = 2\pi\sqrt{\frac{m_x}{k}}$
Возведем обе части в квадрат: $T_x^2 = 4\pi^2 \frac{m_x}{k}$
3. Расчет неизвестной массы.
Мы получили систему из двух уравнений:
$\begin{cases} T_1^2 = 4\pi^2 \frac{m_1}{k} \\ T_x^2 = 4\pi^2 \frac{m_x}{k} \end{cases}$
Разделим второе уравнение на первое. Жесткость пружины $k$ и множитель $4\pi^2$ сократятся:
$\frac{T_x^2}{T_1^2} = \frac{m_x}{m_1}$
Отсюда выразим искомую массу $m_x$:
$m_x = m_1 \frac{T_x^2}{T_1^2}$
Подставим выражения для периодов через измеренные времена $t_1$ и $t_x$:
$m_x = m_1 \frac{(t_x/N)^2}{(t_1/N)^2} = m_1 \frac{t_x^2}{t_1^2} = m_1 \left(\frac{t_x}{t_1}\right)^2$
Таким образом, для определения массы груза необходимо прикрепить к пружине эталонный груз массой $m_1$, измерить время $t_1$ для $N$ колебаний, затем заменить его на исследуемый груз, измерить время $t_x$ для тех же $N$ колебаний и рассчитать массу $m_x$ по полученной формуле.
Ответ: Необходимо создать пружинный маятник. Сначала нужно измерить с помощью секундомера время $t_1$ некоторого числа полных колебаний $N$ для груза известной массы $m_1$. Затем, не меняя число колебаний $N$, измерить время $t_x$ для груза с неизвестной массой $m_x$. Искомая масса вычисляется по формуле: $m_x = m_1 \left(\frac{t_x}{t_1}\right)^2$.
Другие задания:
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