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Страница 231 - гдз по физике 9 класс учебник Шахмаев, Бунчук
Авторы: Шахмаев Н. М., Бунчук А. В.
Тип: Учебник
Издательство: Мнемозина
Год издания: 2007 - 2026
Цвет обложки: голубой
ISBN: 978-5-346-01799-8
Популярные ГДЗ в 9 классе
Cтраница 231
App\Models\BookPage {#1003 // resources/views/models/book_page/default.blade.php #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1436790 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "231" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-231" "field_display_title" => "231" "field_folder" => "1" "field_image_name" => "231" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1008 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1006 #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" => 2906 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1009 #items: array:1 [ 0 => App\Models\Term {#1007 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1010 #items: array:1 [ 0 => App\Models\Term {#1011 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1012 #items: array:1 [ 0 => App\Models\Term {#1013 #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" => 5155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #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 {#1014 #items: array:2 [ 0 => App\Models\Term {#1015 #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" => 6294 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шахмаев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Николай" "field_patronymic" => "Михайлович" "field_surname_rp" => null ] #original: array:12 [ "id" => 6294 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шахмаев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Николай" "field_patronymic" => "Михайлович" "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 {#1016 #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" => 3942 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Бунчук" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алексей" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3942 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Бунчук" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алексей" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1017 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1018 #items: array:1 [ 0 => App\Models\Term {#1019 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1020 #items: array:1 [ 0 => App\Models\Term {#1021 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1022 #items: array:1 [ 0 => App\Models\Term {#1023 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1024 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1025 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1027 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1028 #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" => 33 "created_at" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1030 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "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" => "362" "field_priority" => null "field_default_folder" => "/fizika_09/shahmaev-u/" "field_isbn" => "978-5-346-01799-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1031 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1032 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1033 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #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" => 52 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ "field_accusative_case" => "голубой" "field_creative_case" => "голубым" "field_dative_case" => "голубому" "field_genitive_case" => "голубого" "field_nominative_case" => "голубой" "field_prepositional_case" => "голубом" ] "field_translit" => "goluboy" ] #original: array:6 [ "id" => 52 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "голубой" "field_cases" => array:6 [ "field_accusative_case" => "голубой" "field_creative_case" => "голубым" "field_dative_case" => "голубому" "field_genitive_case" => "голубого" "field_nominative_case" => "голубой" "field_prepositional_case" => "голубом" ] "field_translit" => "goluboy" ] #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" => 2906 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1009} "field_class" => Illuminate\Database\Eloquent\Collection {#1010} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1012} "field_author" => Illuminate\Database\Eloquent\Collection {#1014} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1017} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1018} "field_country" => Illuminate\Database\Eloquent\Collection {#1020} "field_city" => Illuminate\Database\Eloquent\Collection {#1022} "field_series" => Illuminate\Database\Eloquent\Collection {#1024} "field_umk" => Illuminate\Database\Eloquent\Collection {#1025} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1026} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1027} "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1028} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1030} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "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" => "362" "field_priority" => null "field_default_folder" => "/fizika_09/shahmaev-u/" "field_isbn" => "978-5-346-01799-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/shahmaev-u/covers/cover1.webp" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1031} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1032} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1033} "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1034} "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 } "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 {#1036 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Element {#1046 #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" => 1702866 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Edition {#1048 #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" => 6109 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1050 #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" => 5155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #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_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 {#1051 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6109 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1050} "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 {#1051} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053} "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 } "book_page" => array:2 [ "refs" => "1436790" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "231-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/231-1.webp" ] ] ] #original: array:6 [ "id" => 1702866 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1056} "book_page" => array:2 [ "refs" => "1436790" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "231-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/231-1.webp" ] ] ] #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" => Illuminate\Database\Eloquent\Collection {#5837 #items: array:1 [ 0 => App\Models\BookPage {#5836 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:20 [ "id" => 1436791 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "232" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-232" "field_display_title" => "232" "field_folder" => "1" "field_image_name" => "232" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#5842 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#5841 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#5840 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#5876 #items: array:1 [ 0 => App\Models\Element {#5875 #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" => 1702867 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5874 #items: array:1 [ 0 => App\Models\Edition {#1048} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1436791" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "232-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/232-1.webp" ] ] ] #original: array:6 [ "id" => 1702867 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5874} "book_page" => array:2 [ "refs" => "1436791" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "232-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/232-1.webp" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "previous" => array:2 [ "refs" => "1436790" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#5891 #items: [] #escapeWhenCastingToString: false } ] #original: array:20 [ "id" => 1436791 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "232" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-232" "field_display_title" => "232" "field_folder" => "1" "field_image_name" => "232" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#5842} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#5841} "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 {#5840} "content" => Illuminate\Database\Eloquent\Collection {#5876} "previous" => array:2 [ "refs" => "1436790" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#5891} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "previous" => Illuminate\Database\Eloquent\Collection {#5832 #items: array:1 [ 0 => App\Models\BookPage {#5831 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1436789 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "230" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-230" "field_display_title" => "230" "field_folder" => "1" "field_image_name" => "230" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#5833 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#5834 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#5835 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#5845 #items: array:1 [ 0 => App\Models\Element {#5844 #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" => 1702865 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5846 #items: array:1 [ 0 => App\Models\Edition {#1048} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1436789" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "230-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/230-1.webp" ] ] ] #original: array:6 [ "id" => 1702865 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5846} "book_page" => array:2 [ "refs" => "1436789" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "230-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/230-1.webp" ] ] ] #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" => "1436790" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436788" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#5849 #items: array:1 [ 0 => App\Models\Task {#5848 #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" => 1437214 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "230" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/labrab-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#5853 #items: array:1 [ 0 => App\Models\Term {#5850 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#5852 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#5862 #items: array:1 [ 0 => App\Models\Branch {#5861 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1436849 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5863 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "211" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5864 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#5865 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1436849 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5863} "field_page_start" => "211" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5864} "branch_parent" => Illuminate\Database\Eloquent\Collection {#5865} ] #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 {#5894 #items: array:2 [ 0 => App\Models\Branch {#5902 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1436849 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5903 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "211" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5904 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#5905 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1436849 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5903} "field_page_start" => "211" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5904} "branch_parent" => Illuminate\Database\Eloquent\Collection {#5905} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#5906 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1436852 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложение 3. Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5907 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "221" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5908 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#5909 #items: array:1 [ 0 => App\Models\Branch {#5861} ] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1436852 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Приложение 3. Лабораторные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#5907} "field_page_start" => "221" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#5908} "branch_parent" => Illuminate\Database\Eloquent\Collection {#5909} ] #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 {#5854 #items: array:2 [ 0 => App\Models\Element {#5885 #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" => 1702608 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5883 #items: array:1 [ 0 => App\Models\Edition {#1048} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1437214" "type" => "task" ] "text" => "<p><strong>9. Определение массы с помощью пружинного маятника</strong></p><p><strong>Цель работы:</strong> вычислить массу тела из формулы для периода колебаний пружинного маятника:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p><strong>Оборудование:</strong> штатив с лапкой; пружина; измерительная линейка; груз; динамометр; секундомер.</p><p><strong><em>Указания к выполнению работы</em></strong></p><p><strong>1.</strong> Убедитесь, что масса пружины намного меньше массы груза.</p><p><strong>2.</strong> Конец пружины закрепите в лапке штатива, подвесьте к другому концу груз и проверьте, зависит ли период колебаний груза от амплитуды его колебаний. Результаты измерений, подтверждающие ваш вывод, оформите в виде таблицы.</p><p>Рис. 194</p><p><strong><em>Порядок выполнения работы</em></strong></p><p><strong>1.</strong> Измерьте длину нерастянутой и растянутой пружины и вычислите ее жесткость, используя динамометр.</p><p><strong>2.</strong> Определите период вертикальных колебаний пружинного маятника, измерив время сорока колебаний груза (рис. 194).</p><p><strong>3.</strong> Вычислите массу груза, используя формулу для периода колебаний пружинного маятника, и сравните ее с массой этого груза, измеренной с помощью динамометра.</p><p><strong><em>Ответьте на вопрос:</em></strong></p><p>При каких условиях справедлива формула для периода колебаний пружинного маятника?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1770" "height" => 1500 "path" => "/media/fizika_09/shahmaev-u/0-labrab/9-1.webp" ] ] ] #original: array:7 [ "id" => 1702608 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5883} "task" => array:2 [ "refs" => "1437214" "type" => "task" ] "text" => "<p><strong>9. Определение массы с помощью пружинного маятника</strong></p><p><strong>Цель работы:</strong> вычислить массу тела из формулы для периода колебаний пружинного маятника:</p><p>$T = 2\pi\sqrt{\frac{m}{k}}$</p><p><strong>Оборудование:</strong> штатив с лапкой; пружина; измерительная линейка; груз; динамометр; секундомер.</p><p><strong><em>Указания к выполнению работы</em></strong></p><p><strong>1.</strong> Убедитесь, что масса пружины намного меньше массы груза.</p><p><strong>2.</strong> Конец пружины закрепите в лапке штатива, подвесьте к другому концу груз и проверьте, зависит ли период колебаний груза от амплитуды его колебаний. Результаты измерений, подтверждающие ваш вывод, оформите в виде таблицы.</p><p>Рис. 194</p><p><strong><em>Порядок выполнения работы</em></strong></p><p><strong>1.</strong> Измерьте длину нерастянутой и растянутой пружины и вычислите ее жесткость, используя динамометр.</p><p><strong>2.</strong> Определите период вертикальных колебаний пружинного маятника, измерив время сорока колебаний груза (рис. 194).</p><p><strong>3.</strong> Вычислите массу груза, используя формулу для периода колебаний пружинного маятника, и сравните ее с массой этого груза, измеренной с помощью динамометра.</p><p><strong><em>Ответьте на вопрос:</em></strong></p><p>При каких условиях справедлива формула для периода колебаний пружинного маятника?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1770" "height" => 1500 "path" => "/media/fizika_09/shahmaev-u/0-labrab/9-1.webp" ] ] ] #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 {#5884 #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" => 1732529 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5873 #items: array:1 [ 0 => App\Models\Edition {#5882 #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" => 6315 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#5880 #items: array:1 [ 0 => App\Models\Term {#5881 …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 {#5879 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#5877 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#5878 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6315 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#5880} "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 {#5879} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#5877} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#5878} "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" => "1437214" "type" => "task" ] "text" => "<strong>Ответьте на вопрос</strong><p>Формула для периода колебаний пружинного маятника $T = 2\pi\sqrt{\frac{m}{k}}$ является выводом из теоретической модели идеального гармонического осциллятора. Она справедлива при выполнении следующих условий:</p><p><strong>1.</strong> <strong>Упругость пружины.</strong> Колебания должны происходить в пределах упругой деформации пружины. Это означает, что возвращающая сила, действующая на груз, должна строго подчиняться закону Гука: $F_{упр} = -kx$, где $\text{k}$ – жёсткость пружины, а $\text{x}$ – смещение от положения равновесия. Только в этом случае колебания являются гармоническими, а их период не зависит от амплитуды.</p><p><strong>2.</strong> <strong>Пренебрежимо малая масса пружины.</strong> В формуле $\text{m}$ обозначает только массу колеблющегося тела (груза). Масса самой пружины не учитывается. Поэтому формула точна, когда масса пружины намного меньше массы груза ($m_{пружины} \ll m_{груза}$). Если это условие не выполняется, необходимо вносить поправку, учитывающую массу пружины. В этом случае в формулу подставляется приведённая масса системы, равная примерно $m_{груза} + \frac{m_{пружины}}{3}$.</p><p><strong>3.</strong> <strong>Отсутствие сил сопротивления.</strong> Формула выведена для случая, когда на систему не действуют диссипативные силы, такие как сила трения или сопротивление воздуха. В реальных условиях эти силы всегда присутствуют, что приводит к затуханию колебаний (уменьшению амплитуды со временем) и некоторому увеличению периода. Формула справедлива, если этими силами можно пренебречь.</p><p><strong>4.</strong> <strong>Малые колебания.</strong> Хотя для идеальной пружины, подчиняющейся закону Гука, период не зависит от амплитуды, на практике при больших смещениях могут проявляться нелинейные свойства пружины (отклонение от закона Гука) и значительно возрастать влияние сопротивления воздуха. Поэтому для высокой точности измерений амплитуда колебаний должна быть небольшой.</p><p><strong>Ответ:</strong> Формула для периода колебаний пружинного маятника $T = 2\pi\sqrt{\frac{m}{k}}$ справедлива для идеализированной физической модели, в которой: 1) колебания являются гармоническими (сила упругости подчиняется закону Гука); 2) масса пружины пренебрежимо мала по сравнению с массой груза; 3) отсутствуют силы трения и сопротивления среды.</p>" ] #original: array:6 [ "id" => 1732529 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#5873} "task" => array:2 [ "refs" => "1437214" "type" => "task" ] "text" => "<strong>Ответьте на вопрос</strong><p>Формула для периода колебаний пружинного маятника $T = 2\pi\sqrt{\frac{m}{k}}$ является выводом из теоретической модели идеального гармонического осциллятора. Она справедлива при выполнении следующих условий:</p><p><strong>1.</strong> <strong>Упругость пружины.</strong> Колебания должны происходить в пределах упругой деформации пружины. Это означает, что возвращающая сила, действующая на груз, должна строго подчиняться закону Гука: $F_{упр} = -kx$, где $\text{k}$ – жёсткость пружины, а $\text{x}$ – смещение от положения равновесия. Только в этом случае колебания являются гармоническими, а их период не зависит от амплитуды.</p><p><strong>2.</strong> <strong>Пренебрежимо малая масса пружины.</strong> В формуле $\text{m}$ обозначает только массу колеблющегося тела (груза). Масса самой пружины не учитывается. Поэтому формула точна, когда масса пружины намного меньше массы груза ($m_{пружины} \ll m_{груза}$). Если это условие не выполняется, необходимо вносить поправку, учитывающую массу пружины. В этом случае в формулу подставляется приведённая масса системы, равная примерно $m_{груза} + \frac{m_{пружины}}{3}$.</p><p><strong>3.</strong> <strong>Отсутствие сил сопротивления.</strong> Формула выведена для случая, когда на систему не действуют диссипативные силы, такие как сила трения или сопротивление воздуха. В реальных условиях эти силы всегда присутствуют, что приводит к затуханию колебаний (уменьшению амплитуды со временем) и некоторому увеличению периода. Формула справедлива, если этими силами можно пренебречь.</p><p><strong>4.</strong> <strong>Малые колебания.</strong> Хотя для идеальной пружины, подчиняющейся закону Гука, период не зависит от амплитуды, на практике при больших смещениях могут проявляться нелинейные свойства пружины (отклонение от закона Гука) и значительно возрастать влияние сопротивления воздуха. Поэтому для высокой точности измерений амплитуда колебаний должна быть небольшой.</p><p><strong>Ответ:</strong> Формула для периода колебаний пружинного маятника $T = 2\pi\sqrt{\frac{m}{k}}$ справедлива для идеализированной физической модели, в которой: 1) колебания являются гармоническими (сила упругости подчиняется закону Гука); 2) масса пружины пренебрежимо мала по сравнению с массой груза; 3) отсутствуют силы трения и сопротивления среды.</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" => null "type" => "task" ] "previous" => array:2 [ "refs" => "1437213" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#5888 #items: array:1 [ 0 => App\Models\Book {#1006} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436789" "type" => "book_page" ] ] #original: array:24 [ "id" => 1437214 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "230" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/labrab-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#5853} "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 {#5852} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#5862} "parent_branches" => Illuminate\Database\Eloquent\Collection {#5894} "content" => Illuminate\Database\Eloquent\Collection {#5854} "next" => array:2 [ "refs" => null "type" => "task" ] "previous" => array:2 [ "refs" => "1437213" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#5888} "page" => array:2 [ "refs" => "1436789" "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" => 1436789 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "230" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-230" "field_display_title" => "230" "field_folder" => "1" "field_image_name" => "230" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#5833} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#5834} "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 {#5835} "content" => Illuminate\Database\Eloquent\Collection {#5845} "next" => array:2 [ "refs" => "1436790" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436788" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#5849} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "tasks" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1436790 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "231" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-231" "field_display_title" => "231" "field_folder" => "1" "field_image_name" => "231" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1008} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1038} "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 {#1036} "content" => Illuminate\Database\Eloquent\Collection {#1047} "next" => array:2 [ "refs" => "1436791" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436789" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1039} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
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