gdz.top
Номер 7, страница 85, часть 1 - гдз по физике 9 класс учебник Генденштейн, Булатова
Авторы: Генденштейн Л. Э., Булатова А. А., Корнильев И. Н., Кошкина А. В.
Тип: Учебник
Издательство: Бином
Год издания: 2016 - 2026
Часть: 1
Цвет обложки: бирюзовый
ISBN: 978-5-9963-3062-1
Популярные ГДЗ в 9 классе
Часть 1. Механические явления. Глава II. Динамика. Параграф 9. Силы упругости - номер 7, страница 85.
App\Models\Task {#1030 // 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" => 1433555 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/09-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #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" => 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 {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #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:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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_page_start" => "6" "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 {#1082 #items: array:1 [ 0 => App\Models\Book {#1049 #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" => 2980 "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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #original: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #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 {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #original: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "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 {#1059 #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" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "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 => "*" ] } 3 => App\Models\Term {#1060 #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" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "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 {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #original: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #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_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Term {#1079 #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" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ …6] "field_translit" => "biruzovyy" ] #original: array:6 [ "id" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ …6] "field_translit" => "biruzovyy" ] #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" => 2980 "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 {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "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" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078} "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 {#1080 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "6" "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 {#1082} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1080} ] #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 {#1113 #items: array:4 [ 0 => App\Models\Branch {#1123 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1125 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124} "field_page_start" => "6" "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 {#1125} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1126} ] #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 {#1127 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1129 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1128} "field_page_start" => "6" "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 {#1129} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1131 #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" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ 0 => App\Models\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "59" "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 {#1134 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Branch {#1142 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_page_start" => "6" "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 {#1145 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 …2} ] #original: array:24 [ "id" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_page_start" => "6" "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 {#1145 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "59" "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 {#1134} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143} ] #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\Branch {#1136 #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" => 1433218 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы упругости" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "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_page_start" => "83" "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 {#1137 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1152 #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" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_page_start" => "59" "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 {#1155 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156 …2} ] #original: array:24 [ "id" => 1433214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Динамика" "field_branch_order" => "II" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_page_start" => "59" "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 {#1155 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433218 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы упругости" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_page_start" => "83" "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 {#1137} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1103 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1696296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Edition {#1104 #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" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433555" "type" => "task" ] "text" => "<p><strong>7.</strong> Когда к пружине подвешен покоящийся груз массой 100 г, её длина равна 10 см, а когда подвешен груз массой 200 г, её длина равна 12 см.</p><p><strong>а)</strong> Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.</p><p><strong>б)</strong> Выразите длину недеформированной пружины через величины, данные в описании ситуации.</p><p><strong>в)</strong> Выразите жёсткость пружины через величины, данные в описании ситуации.</p><p><strong>г)</strong> Чему равны длина недеформированной пружины и её жёсткость?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1502" "height" => 806 "path" => "/media/fizika_09/gendenshtejn-u/0-09/7-1.webp?ts=1759348213" ] ] ] #original: array:7 [ "id" => 1696296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094} "task" => array:2 [ "refs" => "1433555" "type" => "task" ] "text" => "<p><strong>7.</strong> Когда к пружине подвешен покоящийся груз массой 100 г, её длина равна 10 см, а когда подвешен груз массой 200 г, её длина равна 12 см.</p><p><strong>а)</strong> Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.</p><p><strong>б)</strong> Выразите длину недеформированной пружины через величины, данные в описании ситуации.</p><p><strong>в)</strong> Выразите жёсткость пружины через величины, данные в описании ситуации.</p><p><strong>г)</strong> Чему равны длина недеформированной пружины и её жёсткость?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "1502" "height" => 806 "path" => "/media/fizika_09/gendenshtejn-u/0-09/7-1.webp?ts=1759348213" ] ] ] #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 {#1096 #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" => 1780366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Edition {#1097 #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" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433555" "type" => "task" ] "text" => "<p><strong>а) Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.</strong></p><p>Когда груз подвешен к пружине и находится в состоянии покоя, сила упругости пружины $F_{упр}$ уравновешивает силу тяжести, действующую на груз, то есть его вес $\text{P}$. Согласно закону Гука, сила упругости определяется как $F_{упр} = k \cdot \Delta l$, где $\text{k}$ – жёсткость пружины, а $\Delta l$ – её удлинение.</p><p>Рассмотрим первую ситуацию с грузом массой $m_1$:<br>Вес первого груза: $P_1 = m_1 g$.<br>Длина пружины с первым грузом: $l_1$.<br>Удлинение пружины: $\Delta l_1 = l_1 - l_0$.<br>Из условия равновесия ($F_{упр1} = P_1$) получаем первое уравнение: $k(l_1 - l_0) = P_1$.</p><p>Рассмотрим вторую ситуацию с грузом массой $m_2$:<br>Вес второго груза: $P_2 = m_2 g$.<br>Длина пружины со вторым грузом: $l_2$.<br>Удлинение пружины: $\Delta l_2 = l_2 - l_0$.<br>Из условия равновесия ($F_{упр2} = P_2$) получаем второе уравнение: $k(l_2 - l_0) = P_2$.</p><p><strong>Ответ:</strong> Система уравнений, связывающая данные величины: $ \begin{cases} k(l_1 - l_0) = P_1 \\ k(l_2 - l_0) = P_2 \end{cases} $</p><p><strong>б) Выразите длину недеформированной пружины через величины, данные в описании ситуации.</strong></p><p>Для решения используем систему уравнений, подставив в неё выражения для весов $P_1 = m_1 g$ и $P_2 = m_2 g$:<br>$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $<br>Выразим коэффициент жёсткости $\text{k}$ из обоих уравнений:<br>$k = \frac{m_1 g}{l_1 - l_0}$<br>$k = \frac{m_2 g}{l_2 - l_0}$<br>Приравняем правые части этих выражений:<br>$\frac{m_1 g}{l_1 - l_0} = \frac{m_2 g}{l_2 - l_0}$<br>Разделим обе части на $\text{g}$ (так как $g \neq 0$):<br>$\frac{m_1}{l_1 - l_0} = \frac{m_2}{l_2 - l_0}$<br>Преобразуем уравнение, используя основное свойство пропорции:<br>$m_1(l_2 - l_0) = m_2(l_1 - l_0)$<br>Раскроем скобки:<br>$m_1 l_2 - m_1 l_0 = m_2 l_1 - m_2 l_0$<br>Перенесём члены с $l_0$ в одну сторону, а остальные — в другую:<br>$m_2 l_0 - m_1 l_0 = m_2 l_1 - m_1 l_2$<br>Вынесем $l_0$ за скобку:<br>$l_0(m_2 - m_1) = m_2 l_1 - m_1 l_2$<br>Наконец, выразим $l_0$:<br>$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$</p><p><strong>Ответ:</strong> $l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$</p><p><strong>в) Выразите жёсткость пружины через величины, данные в описании ситуации.</strong></p><p>Снова обратимся к системе уравнений:<br>$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $<br>Раскроем скобки в обоих уравнениях:<br>$ \begin{cases} k l_1 - k l_0 = m_1 g \\ k l_2 - k l_0 = m_2 g \end{cases} $<br>Вычтем первое уравнение из второго, чтобы избавиться от неизвестной величины $l_0$:<br>$(k l_2 - k l_0) - (k l_1 - k l_0) = m_2 g - m_1 g$<br>$k l_2 - k l_0 - k l_1 + k l_0 = (m_2 - m_1) g$<br>$k l_2 - k l_1 = (m_2 - m_1) g$<br>Вынесем $\text{k}$ за скобку:<br>$k(l_2 - l_1) = (m_2 - m_1) g$<br>Выразим жёсткость пружины $\text{k}$:<br>$k = \frac{(m_2 - m_1) g}{l_2 - l_1}$</p><p><strong>Ответ:</strong> $k = \frac{(m_2 - m_1) g}{l_2 - l_1}$</p><p><strong>г) Чему равны длина недеформированной пружины и её жёсткость?</strong></p><p><strong>Дано:</strong></p><p>$m_1 = 100 \text{ г}$<br>$l_1 = 10 \text{ см}$<br>$m_2 = 200 \text{ г}$<br>$l_2 = 12 \text{ см}$<br>Ускорение свободного падения $g \approx 9.8 \text{ Н/кг}$.</p><p>Переведём единицы измерения в систему СИ:<br>$m_1 = 0.1 \text{ кг}$<br>$l_1 = 0.1 \text{ м}$<br>$m_2 = 0.2 \text{ кг}$<br>$l_2 = 0.12 \text{ м}$</p><p><strong>Найти:</strong></p><p>$l_0 - ?$<br>$k - ?$</p><p><strong>Решение:</strong></p><p>1. Вычислим длину недеформированной пружины $l_0$, используя формулу из пункта б):<br>$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1} = \frac{0.2 \text{ кг} \cdot 0.1 \text{ м} - 0.1 \text{ кг} \cdot 0.12 \text{ м}}{0.2 \text{ кг} - 0.1 \text{ кг}} = \frac{0.02 - 0.012}{0.1} \text{ м} = \frac{0.008}{0.1} \text{ м} = 0.08 \text{ м}$.<br><br>2. Вычислим жёсткость пружины $\text{k}$, используя формулу из пункта в):<br>$k = \frac{(m_2 - m_1) g}{l_2 - l_1} = \frac{(0.2 \text{ кг} - 0.1 \text{ кг}) \cdot 9.8 \text{ Н/кг}}{0.12 \text{ м} - 0.1 \text{ м}} = \frac{0.1 \text{ кг} \cdot 9.8 \text{ Н/кг}}{0.02 \text{ м}} = \frac{0.98 \text{ Н}}{0.02 \text{ м}} = 49 \text{ Н/м}$.</p><p><strong>Ответ:</strong> Длина недеформированной пружины равна $0.08 \text{ м}$ (или $8 \text{ см}$), а её жёсткость равна $49 \text{ Н/м}$.</p>" ] #original: array:6 [ "id" => 1780366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088} "task" => array:2 [ "refs" => "1433555" "type" => "task" ] "text" => "<p><strong>а) Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.</strong></p><p>Когда груз подвешен к пружине и находится в состоянии покоя, сила упругости пружины $F_{упр}$ уравновешивает силу тяжести, действующую на груз, то есть его вес $\text{P}$. Согласно закону Гука, сила упругости определяется как $F_{упр} = k \cdot \Delta l$, где $\text{k}$ – жёсткость пружины, а $\Delta l$ – её удлинение.</p><p>Рассмотрим первую ситуацию с грузом массой $m_1$:<br>Вес первого груза: $P_1 = m_1 g$.<br>Длина пружины с первым грузом: $l_1$.<br>Удлинение пружины: $\Delta l_1 = l_1 - l_0$.<br>Из условия равновесия ($F_{упр1} = P_1$) получаем первое уравнение: $k(l_1 - l_0) = P_1$.</p><p>Рассмотрим вторую ситуацию с грузом массой $m_2$:<br>Вес второго груза: $P_2 = m_2 g$.<br>Длина пружины со вторым грузом: $l_2$.<br>Удлинение пружины: $\Delta l_2 = l_2 - l_0$.<br>Из условия равновесия ($F_{упр2} = P_2$) получаем второе уравнение: $k(l_2 - l_0) = P_2$.</p><p><strong>Ответ:</strong> Система уравнений, связывающая данные величины: $ \begin{cases} k(l_1 - l_0) = P_1 \\ k(l_2 - l_0) = P_2 \end{cases} $</p><p><strong>б) Выразите длину недеформированной пружины через величины, данные в описании ситуации.</strong></p><p>Для решения используем систему уравнений, подставив в неё выражения для весов $P_1 = m_1 g$ и $P_2 = m_2 g$:<br>$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $<br>Выразим коэффициент жёсткости $\text{k}$ из обоих уравнений:<br>$k = \frac{m_1 g}{l_1 - l_0}$<br>$k = \frac{m_2 g}{l_2 - l_0}$<br>Приравняем правые части этих выражений:<br>$\frac{m_1 g}{l_1 - l_0} = \frac{m_2 g}{l_2 - l_0}$<br>Разделим обе части на $\text{g}$ (так как $g \neq 0$):<br>$\frac{m_1}{l_1 - l_0} = \frac{m_2}{l_2 - l_0}$<br>Преобразуем уравнение, используя основное свойство пропорции:<br>$m_1(l_2 - l_0) = m_2(l_1 - l_0)$<br>Раскроем скобки:<br>$m_1 l_2 - m_1 l_0 = m_2 l_1 - m_2 l_0$<br>Перенесём члены с $l_0$ в одну сторону, а остальные — в другую:<br>$m_2 l_0 - m_1 l_0 = m_2 l_1 - m_1 l_2$<br>Вынесем $l_0$ за скобку:<br>$l_0(m_2 - m_1) = m_2 l_1 - m_1 l_2$<br>Наконец, выразим $l_0$:<br>$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$</p><p><strong>Ответ:</strong> $l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$</p><p><strong>в) Выразите жёсткость пружины через величины, данные в описании ситуации.</strong></p><p>Снова обратимся к системе уравнений:<br>$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $<br>Раскроем скобки в обоих уравнениях:<br>$ \begin{cases} k l_1 - k l_0 = m_1 g \\ k l_2 - k l_0 = m_2 g \end{cases} $<br>Вычтем первое уравнение из второго, чтобы избавиться от неизвестной величины $l_0$:<br>$(k l_2 - k l_0) - (k l_1 - k l_0) = m_2 g - m_1 g$<br>$k l_2 - k l_0 - k l_1 + k l_0 = (m_2 - m_1) g$<br>$k l_2 - k l_1 = (m_2 - m_1) g$<br>Вынесем $\text{k}$ за скобку:<br>$k(l_2 - l_1) = (m_2 - m_1) g$<br>Выразим жёсткость пружины $\text{k}$:<br>$k = \frac{(m_2 - m_1) g}{l_2 - l_1}$</p><p><strong>Ответ:</strong> $k = \frac{(m_2 - m_1) g}{l_2 - l_1}$</p><p><strong>г) Чему равны длина недеформированной пружины и её жёсткость?</strong></p><p><strong>Дано:</strong></p><p>$m_1 = 100 \text{ г}$<br>$l_1 = 10 \text{ см}$<br>$m_2 = 200 \text{ г}$<br>$l_2 = 12 \text{ см}$<br>Ускорение свободного падения $g \approx 9.8 \text{ Н/кг}$.</p><p>Переведём единицы измерения в систему СИ:<br>$m_1 = 0.1 \text{ кг}$<br>$l_1 = 0.1 \text{ м}$<br>$m_2 = 0.2 \text{ кг}$<br>$l_2 = 0.12 \text{ м}$</p><p><strong>Найти:</strong></p><p>$l_0 - ?$<br>$k - ?$</p><p><strong>Решение:</strong></p><p>1. Вычислим длину недеформированной пружины $l_0$, используя формулу из пункта б):<br>$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1} = \frac{0.2 \text{ кг} \cdot 0.1 \text{ м} - 0.1 \text{ кг} \cdot 0.12 \text{ м}}{0.2 \text{ кг} - 0.1 \text{ кг}} = \frac{0.02 - 0.012}{0.1} \text{ м} = \frac{0.008}{0.1} \text{ м} = 0.08 \text{ м}$.<br><br>2. Вычислим жёсткость пружины $\text{k}$, используя формулу из пункта в):<br>$k = \frac{(m_2 - m_1) g}{l_2 - l_1} = \frac{(0.2 \text{ кг} - 0.1 \text{ кг}) \cdot 9.8 \text{ Н/кг}}{0.12 \text{ м} - 0.1 \text{ м}} = \frac{0.1 \text{ кг} \cdot 9.8 \text{ Н/кг}}{0.02 \text{ м}} = \frac{0.98 \text{ Н}}{0.02 \text{ м}} = 49 \text{ Н/м}$.</p><p><strong>Ответ:</strong> Длина недеформированной пружины равна $0.08 \text{ м}$ (или $8 \text{ см}$), а её жёсткость равна $49 \text{ Н/м}$.</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" => "1433556" "type" => "task" ] "previous" => array:2 [ "refs" => "1433554" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1109 #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" => 1434726 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-85" "field_display_title" => "85" "field_folder" => "2" "field_image_name" => "85" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Branch {#1041 #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" => 1433262 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_page_start" => "4" "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 {#1112 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111 …2} ] #original: array:24 [ "id" => 1433262 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_page_start" => "4" "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 {#1112 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1087 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Element {#1116 #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" => 1697450 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1117 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1697450 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1117 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1434727" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434725" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:5 [ 0 => App\Models\Task {#1148 #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" => 1434220 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-138" "field_display_title" => "138" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1159 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1197 …2} "content" => Illuminate\Database\Eloquent\Collection {#1160 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1192 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1434220 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-138" "field_display_title" => "138" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1158 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1159 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1197 …2} "content" => Illuminate\Database\Eloquent\Collection {#1160 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1192 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1195 #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" => 1434221 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-139" "field_display_title" => "139" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1190 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1193 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1163 …2} "content" => Illuminate\Database\Eloquent\Collection {#1164 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1434221 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-139" "field_display_title" => "139" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1190 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1193 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1163 …2} "content" => Illuminate\Database\Eloquent\Collection {#1164 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1179 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1185 #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" => 1434222 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-140" "field_display_title" => "140" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1177 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1181 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1184 …2} "content" => Illuminate\Database\Eloquent\Collection {#1183 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1167 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1434222 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-140" "field_display_title" => "140" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1177 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1181 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1184 …2} "content" => Illuminate\Database\Eloquent\Collection {#1183 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1167 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1174 #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" => 1434223 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1165 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1169 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1173 …2} "content" => Illuminate\Database\Eloquent\Collection {#1172 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1202 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1434223 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/ekzam-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1165 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1169 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1173 …2} "content" => Illuminate\Database\Eloquent\Collection {#1172 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1202 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1196 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1434726 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-85" "field_display_title" => "85" "field_folder" => "2" "field_image_name" => "85" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1034} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1089} "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 {#1087} "content" => Illuminate\Database\Eloquent\Collection {#1114} "next" => array:2 [ "refs" => "1434727" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434725" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1090} ] #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" => 1433555 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/09-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "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 {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1113} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1433556" "type" => "task" ] "previous" => array:2 [ "refs" => "1433554" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1107} "page" => array:2 [ "refs" => "1434726" "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 => "*" ] }
№7 (с. 85)
Условие. №7 (с. 85)
скриншот условия
7. Когда к пружине подвешен покоящийся груз массой 100 г, её длина равна 10 см, а когда подвешен груз массой 200 г, её длина равна 12 см.
а) Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.
б) Выразите длину недеформированной пружины через величины, данные в описании ситуации.
в) Выразите жёсткость пружины через величины, данные в описании ситуации.
г) Чему равны длина недеформированной пружины и её жёсткость?
Решение. №7 (с. 85)
а) Обозначьте длину недеформированной пружины $l_0$, жёсткость пружины $\text{k}$, модули веса первого и второго грузов $P_1$ и $P_2$. Запишите систему уравнений, связывающих эти величины с величинами, данными в описании ситуации.
Когда груз подвешен к пружине и находится в состоянии покоя, сила упругости пружины $F_{упр}$ уравновешивает силу тяжести, действующую на груз, то есть его вес $\text{P}$. Согласно закону Гука, сила упругости определяется как $F_{упр} = k \cdot \Delta l$, где $\text{k}$ – жёсткость пружины, а $\Delta l$ – её удлинение.
Рассмотрим первую ситуацию с грузом массой $m_1$:
Вес первого груза: $P_1 = m_1 g$.
Длина пружины с первым грузом: $l_1$.
Удлинение пружины: $\Delta l_1 = l_1 - l_0$.
Из условия равновесия ($F_{упр1} = P_1$) получаем первое уравнение: $k(l_1 - l_0) = P_1$.
Рассмотрим вторую ситуацию с грузом массой $m_2$:
Вес второго груза: $P_2 = m_2 g$.
Длина пружины со вторым грузом: $l_2$.
Удлинение пружины: $\Delta l_2 = l_2 - l_0$.
Из условия равновесия ($F_{упр2} = P_2$) получаем второе уравнение: $k(l_2 - l_0) = P_2$.
Ответ: Система уравнений, связывающая данные величины: $ \begin{cases} k(l_1 - l_0) = P_1 \\ k(l_2 - l_0) = P_2 \end{cases} $
б) Выразите длину недеформированной пружины через величины, данные в описании ситуации.
Для решения используем систему уравнений, подставив в неё выражения для весов $P_1 = m_1 g$ и $P_2 = m_2 g$:
$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $
Выразим коэффициент жёсткости $\text{k}$ из обоих уравнений:
$k = \frac{m_1 g}{l_1 - l_0}$
$k = \frac{m_2 g}{l_2 - l_0}$
Приравняем правые части этих выражений:
$\frac{m_1 g}{l_1 - l_0} = \frac{m_2 g}{l_2 - l_0}$
Разделим обе части на $\text{g}$ (так как $g \neq 0$):
$\frac{m_1}{l_1 - l_0} = \frac{m_2}{l_2 - l_0}$
Преобразуем уравнение, используя основное свойство пропорции:
$m_1(l_2 - l_0) = m_2(l_1 - l_0)$
Раскроем скобки:
$m_1 l_2 - m_1 l_0 = m_2 l_1 - m_2 l_0$
Перенесём члены с $l_0$ в одну сторону, а остальные — в другую:
$m_2 l_0 - m_1 l_0 = m_2 l_1 - m_1 l_2$
Вынесем $l_0$ за скобку:
$l_0(m_2 - m_1) = m_2 l_1 - m_1 l_2$
Наконец, выразим $l_0$:
$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$
Ответ: $l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1}$
в) Выразите жёсткость пружины через величины, данные в описании ситуации.
Снова обратимся к системе уравнений:
$ \begin{cases} k(l_1 - l_0) = m_1 g \\ k(l_2 - l_0) = m_2 g \end{cases} $
Раскроем скобки в обоих уравнениях:
$ \begin{cases} k l_1 - k l_0 = m_1 g \\ k l_2 - k l_0 = m_2 g \end{cases} $
Вычтем первое уравнение из второго, чтобы избавиться от неизвестной величины $l_0$:
$(k l_2 - k l_0) - (k l_1 - k l_0) = m_2 g - m_1 g$
$k l_2 - k l_0 - k l_1 + k l_0 = (m_2 - m_1) g$
$k l_2 - k l_1 = (m_2 - m_1) g$
Вынесем $\text{k}$ за скобку:
$k(l_2 - l_1) = (m_2 - m_1) g$
Выразим жёсткость пружины $\text{k}$:
$k = \frac{(m_2 - m_1) g}{l_2 - l_1}$
Ответ: $k = \frac{(m_2 - m_1) g}{l_2 - l_1}$
г) Чему равны длина недеформированной пружины и её жёсткость?
Дано:
$m_1 = 100 \text{ г}$
$l_1 = 10 \text{ см}$
$m_2 = 200 \text{ г}$
$l_2 = 12 \text{ см}$
Ускорение свободного падения $g \approx 9.8 \text{ Н/кг}$.
Переведём единицы измерения в систему СИ:
$m_1 = 0.1 \text{ кг}$
$l_1 = 0.1 \text{ м}$
$m_2 = 0.2 \text{ кг}$
$l_2 = 0.12 \text{ м}$
Найти:
$l_0 - ?$
$k - ?$
Решение:
1. Вычислим длину недеформированной пружины $l_0$, используя формулу из пункта б):
$l_0 = \frac{m_2 l_1 - m_1 l_2}{m_2 - m_1} = \frac{0.2 \text{ кг} \cdot 0.1 \text{ м} - 0.1 \text{ кг} \cdot 0.12 \text{ м}}{0.2 \text{ кг} - 0.1 \text{ кг}} = \frac{0.02 - 0.012}{0.1} \text{ м} = \frac{0.008}{0.1} \text{ м} = 0.08 \text{ м}$.
2. Вычислим жёсткость пружины $\text{k}$, используя формулу из пункта в):
$k = \frac{(m_2 - m_1) g}{l_2 - l_1} = \frac{(0.2 \text{ кг} - 0.1 \text{ кг}) \cdot 9.8 \text{ Н/кг}}{0.12 \text{ м} - 0.1 \text{ м}} = \frac{0.1 \text{ кг} \cdot 9.8 \text{ Н/кг}}{0.02 \text{ м}} = \frac{0.98 \text{ Н}}{0.02 \text{ м}} = 49 \text{ Н/м}$.
Ответ: Длина недеформированной пружины равна $0.08 \text{ м}$ (или $8 \text{ см}$), а её жёсткость равна $49 \text{ Н/м}$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 9 класс, для упражнения номер 7 расположенного на странице 85 для 1-й части к учебнику 2016 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №7 (с. 85), авторов: Генденштейн (Лев Элевич), Булатова (Альбина Александрова), Корнильев (Игорь Николаевич), Кошкина (Анжелика Васильевна), 1-й части учебного пособия издательства Бином.