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Номер 2, страница 82 - 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
Глава 6. Силы в механике. Параграф 19. Сила всемирного тяготения - номер 2, страница 82.
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" => 1436962 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-2" "field_display_title" => "2" "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" => 1436815 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы в механике" "field_branch_order" => "6" "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" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => "79" "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 {#1080 #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" => 2906 "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#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" => 5155 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-10 13:58:26" "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 {#1056 #items: array:2 [ 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" => 6294 "created_at" => "2026-04-10 13:58:26" "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" => "2026-04-10 13:58:26" "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 {#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" => 3942 "created_at" => "2026-04-10 13:58:26" "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" => "2026-04-10 13:58:26" "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 {#1059 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#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:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#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" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072 #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?ts=1759080267" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #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" => "2026-04-10 13:58:26" "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" => "2026-04-10 13:58:26" "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" => "2026-04-10 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 {#1059} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060} "field_country" => Illuminate\Database\Eloquent\Collection {#1062} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1066} "field_umk" => Illuminate\Database\Eloquent\Collection {#1067} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_publication_number" => "4" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1070} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1072} "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?ts=1759080267" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/shahmaev-u/covers/cover1.webp?ts=1759080267" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1073} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1074} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_url" => "/9-klass/fizika/shahmaev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1076} "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 {#1078 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436815 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы в механике" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "79" "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} ] #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 {#1109 #items: array:2 [ 0 => App\Models\Branch {#1117 #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" => 1436815 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы в механике" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "79" "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 {#1119 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436815 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Силы в механике" "field_branch_order" => "6" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_page_start" => "79" "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 {#1119} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1120} ] #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 {#1121 #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" => 1436816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сила всемирного тяготения" "field_branch_order" => "19" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1122 #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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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" => "79" "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 {#1124 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1436816 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Сила всемирного тяготения" "field_branch_order" => "19" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "79" "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 {#1124} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1123} ] #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 {#1100 #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" => 1702383 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #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" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Term {#1099 #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" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мнемозина" "field_cases" => null "field_translit" => "mnemozina" ] #original: array:6 [ "id" => 5155 "created_at" => "2026-04-10 13:58:26" "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 {#1096 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6109 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097} "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 {#1096} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1095} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094} "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" => "1436962" "type" => "task" ] "text" => "<p><strong>2.</strong> Как изменится сила притяжения между двумя телами, если одно из них заменить другим, масса которого втрое больше?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1573" "height" => 183 "path" => "/media/fizika_09/shahmaev-u/0-19/2-1.webp?ts=1759448821" ] ] ] #original: array:7 [ "id" => 1702383 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1436962" "type" => "task" ] "text" => "<p><strong>2.</strong> Как изменится сила притяжения между двумя телами, если одно из них заменить другим, масса которого втрое больше?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1573" "height" => 183 "path" => "/media/fizika_09/shahmaev-u/0-19/2-1.webp?ts=1759448821" ] ] ] #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 {#1092 #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" => 1732304 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Edition {#1093 #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" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1091 #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" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null …2 ] "field_translit" => "gemini 2.5 pro" ] #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" "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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6315 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084} "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" => "1436962" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m_{1}, m_{2}$ - начальные массы тел</p><p>$m'_{1} = 3m_{1}$ - новая масса первого тела</p><p>$\text{r}$ - расстояние между телами (постоянное)</p><p><strong>Найти:</strong></p><p>Во сколько раз изменится сила притяжения, т.е. найти отношение $\frac{F_{2}}{F_{1}}$</p><p><strong>Решение:</strong></p><p>Сила гравитационного притяжения между двумя телами описывается законом всемирного тяготения:</p><p>$F = G \frac{m_{1} m_{2}}{r^2}$</p><p>где $\text{G}$ - гравитационная постоянная, $m_{1}$ и $m_{2}$ - массы взаимодействующих тел, а $\text{r}$ - расстояние между их центрами.</p><p>Изначальная сила притяжения ($F_{1}$) между двумя телами с массами $m_{1}$ и $m_{2}$ равна:</p><p>$F_{1} = G \frac{m_{1} m_{2}}{r^2}$</p><p>После замены одного из тел на тело с массой втрое большей (например, $m_{1}$ заменяется на $m'_{1} = 3m_{1}$), новая сила притяжения ($F_{2}$) будет равна:</p><p>$F_{2} = G \frac{m'_{1} m_{2}}{r^2} = G \frac{(3m_{1}) m_{2}}{r^2}$</p><p>Чтобы определить, как изменилась сила, найдем отношение новой силы $F_{2}$ к первоначальной $F_{1}$:</p><p>$\frac{F_{2}}{F_{1}} = \frac{G \frac{3m_{1} m_{2}}{r^2}}{G \frac{m_{1} m_{2}}{r^2}}$</p><p>Сокращая одинаковые множители в числителе и знаменателе ($G, m_{1}, m_{2}, r^2$), получаем:</p><p>$\frac{F_{2}}{F_{1}} = 3$</p><p>Таким образом, сила притяжения прямо пропорциональна произведению масс тел. Если масса одного из тел увеличивается в 3 раза, то и сила их взаимного притяжения увеличивается в 3 раза.</p><p><strong>Ответ:</strong> Сила притяжения увеличится в 3 раза.</p>" ] #original: array:6 [ "id" => 1732304 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082} "task" => array:2 [ "refs" => "1436962" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$m_{1}, m_{2}$ - начальные массы тел</p><p>$m'_{1} = 3m_{1}$ - новая масса первого тела</p><p>$\text{r}$ - расстояние между телами (постоянное)</p><p><strong>Найти:</strong></p><p>Во сколько раз изменится сила притяжения, т.е. найти отношение $\frac{F_{2}}{F_{1}}$</p><p><strong>Решение:</strong></p><p>Сила гравитационного притяжения между двумя телами описывается законом всемирного тяготения:</p><p>$F = G \frac{m_{1} m_{2}}{r^2}$</p><p>где $\text{G}$ - гравитационная постоянная, $m_{1}$ и $m_{2}$ - массы взаимодействующих тел, а $\text{r}$ - расстояние между их центрами.</p><p>Изначальная сила притяжения ($F_{1}$) между двумя телами с массами $m_{1}$ и $m_{2}$ равна:</p><p>$F_{1} = G \frac{m_{1} m_{2}}{r^2}$</p><p>После замены одного из тел на тело с массой втрое большей (например, $m_{1}$ заменяется на $m'_{1} = 3m_{1}$), новая сила притяжения ($F_{2}$) будет равна:</p><p>$F_{2} = G \frac{m'_{1} m_{2}}{r^2} = G \frac{(3m_{1}) m_{2}}{r^2}$</p><p>Чтобы определить, как изменилась сила, найдем отношение новой силы $F_{2}$ к первоначальной $F_{1}$:</p><p>$\frac{F_{2}}{F_{1}} = \frac{G \frac{3m_{1} m_{2}}{r^2}}{G \frac{m_{1} m_{2}}{r^2}}$</p><p>Сокращая одинаковые множители в числителе и знаменателе ($G, m_{1}, m_{2}, r^2$), получаем:</p><p>$\frac{F_{2}}{F_{1}} = 3$</p><p>Таким образом, сила притяжения прямо пропорциональна произведению масс тел. Если масса одного из тел увеличивается в 3 раза, то и сила их взаимного притяжения увеличивается в 3 раза.</p><p><strong>Ответ:</strong> Сила притяжения увеличится в 3 раза.</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" => "1436963" "type" => "task" ] "previous" => array:2 [ "refs" => "1436961" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1105 #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" => 1436641 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-82" "field_display_title" => "82" "field_folder" => "1" "field_image_name" => "82" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1085 #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 {#1083 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1112 #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" => 1702717 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Edition {#1098} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "82-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/82-1.webp?ts=1759449091" ] ] ] #original: array:6 [ "id" => 1702717 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110} "book_page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "82-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/shahmaev-u/0-1/82-1.webp?ts=1759449091" ] ] ] #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" => "1436642" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436640" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:4 [ 0 => 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 [ "id" => 1436961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1198 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:2 [ 0 => App\Models\Element {#1211 #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" => 1702382 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> От каких физических величин зависит сила всемирного тяготения?</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702382 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1212 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> От каких физических величин зависит сила всемирного тяготения?</p>" "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 => "*" ] } 1 => App\Models\Element {#1213 #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" => 1732303 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> От каких физических величин зависит сила всемирного тяготения?</p><p>Сила всемирного тяготения зависит от масс взаимодействующих тел и от расстояния между ними. Эта зависимость описывается законом всемирного тяготения, который был открыт Исааком Ньютоном. Формула закона выглядит следующим образом:</p><p>$F = G \frac{m_1 m_2}{r^2}$</p><p>где:</p><p>$\text{F}$ – сила всемирного тяготения,<br>$m_1$ и $m_2$ – массы двух тел,<br>$\text{r}$ – расстояние между центрами масс этих тел,<br>$\text{G}$ – гравитационная постоянная, фундаментальная физическая константа, равная приблизительно $6.674 \times 10^{-11} \text{ Н} \cdot \text{м}^2/\text{кг}^2$.</p><p>Из формулы следует, что сила тяготения прямо пропорциональна произведению масс тел (чем больше массы, тем больше сила) и обратно пропорциональна квадрату расстояния между ними (чем больше расстояние, тем слабее сила).</p><p><strong>Ответ:</strong> Сила всемирного тяготения зависит от масс двух взаимодействующих тел и расстояния между ними.</p><p><strong>2.</strong> Как изменится сила притяжения между двумя телами, если одно из н...</p><p>Вопрос в изображении представлен не полностью, поэтому дать на него однозначный ответ невозможно. Однако можно рассмотреть, как изменяется сила притяжения в наиболее распространенных случаях, исходя из закона всемирного тяготения: $F = G \frac{m_1 m_2}{r^2}$.</p><p><strong>Если изменяется масса одного из тел.</strong><br>Сила притяжения прямо пропорциональна массе каждого из тел. Если массу одного из тел (например, $m_1$) увеличить в $\text{k}$ раз, то и сила притяжения увеличится в $\text{k}$ раз:<br>$F_{новая} = G \frac{(k \cdot m_1) m_2}{r^2} = k \cdot (G \frac{m_1 m_2}{r^2}) = k \cdot F_{начальная}$<br>Например, при увеличении массы одного из тел в 3 раза сила притяжения также увеличится в 3 раза.</p><p><strong>Если изменяется расстояние между телами.</strong><br>Сила притяжения обратно пропорциональна квадрату расстояния между телами. Если расстояние $\text{r}$ увеличить в $\text{n}$ раз, то сила притяжения уменьшится в $n^2$ раз:<br>$F_{новая} = G \frac{m_1 m_2}{(n \cdot r)^2} = G \frac{m_1 m_2}{n^2 r^2} = \frac{1}{n^2} \cdot (G \frac{m_1 m_2}{r^2}) = \frac{F_{начальная}}{n^2}$<br>Например, при увеличении расстояния в 2 раза сила притяжения уменьшится в $2^2 = 4$ раза.</p><p><strong>Ответ:</strong> Так как вопрос неполон, точного ответа дать нельзя. Сила притяжения прямо пропорциональна произведению масс тел и обратно пропорциональна квадрату расстояния между ними. Для получения точного ответа необходимо полное условие задачи.</p>" ] #original: array:6 [ "id" => 1732303 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "task" => array:2 [ …2] "text" => "<p><strong>1.</strong> От каких физических величин зависит сила всемирного тяготения?</p><p>Сила всемирного тяготения зависит от масс взаимодействующих тел и от расстояния между ними. Эта зависимость описывается законом всемирного тяготения, который был открыт Исааком Ньютоном. Формула закона выглядит следующим образом:</p><p>$F = G \frac{m_1 m_2}{r^2}$</p><p>где:</p><p>$\text{F}$ – сила всемирного тяготения,<br>$m_1$ и $m_2$ – массы двух тел,<br>$\text{r}$ – расстояние между центрами масс этих тел,<br>$\text{G}$ – гравитационная постоянная, фундаментальная физическая константа, равная приблизительно $6.674 \times 10^{-11} \text{ Н} \cdot \text{м}^2/\text{кг}^2$.</p><p>Из формулы следует, что сила тяготения прямо пропорциональна произведению масс тел (чем больше массы, тем больше сила) и обратно пропорциональна квадрату расстояния между ними (чем больше расстояние, тем слабее сила).</p><p><strong>Ответ:</strong> Сила всемирного тяготения зависит от масс двух взаимодействующих тел и расстояния между ними.</p><p><strong>2.</strong> Как изменится сила притяжения между двумя телами, если одно из н...</p><p>Вопрос в изображении представлен не полностью, поэтому дать на него однозначный ответ невозможно. Однако можно рассмотреть, как изменяется сила притяжения в наиболее распространенных случаях, исходя из закона всемирного тяготения: $F = G \frac{m_1 m_2}{r^2}$.</p><p><strong>Если изменяется масса одного из тел.</strong><br>Сила притяжения прямо пропорциональна массе каждого из тел. Если массу одного из тел (например, $m_1$) увеличить в $\text{k}$ раз, то и сила притяжения увеличится в $\text{k}$ раз:<br>$F_{новая} = G \frac{(k \cdot m_1) m_2}{r^2} = k \cdot (G \frac{m_1 m_2}{r^2}) = k \cdot F_{начальная}$<br>Например, при увеличении массы одного из тел в 3 раза сила притяжения также увеличится в 3 раза.</p><p><strong>Если изменяется расстояние между телами.</strong><br>Сила притяжения обратно пропорциональна квадрату расстояния между телами. Если расстояние $\text{r}$ увеличить в $\text{n}$ раз, то сила притяжения уменьшится в $n^2$ раз:<br>$F_{новая} = G \frac{m_1 m_2}{(n \cdot r)^2} = G \frac{m_1 m_2}{n^2 r^2} = \frac{1}{n^2} \cdot (G \frac{m_1 m_2}{r^2}) = \frac{F_{начальная}}{n^2}$<br>Например, при увеличении расстояния в 2 раза сила притяжения уменьшится в $2^2 = 4$ раза.</p><p><strong>Ответ:</strong> Так как вопрос неполон, точного ответа дать нельзя. Сила притяжения прямо пропорциональна произведению масс тел и обратно пропорциональна квадрату расстояния между ними. Для получения точного ответа необходимо полное условие задачи.</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" => "1436962" "type" => "task" ] "previous" => array:2 [ "refs" => "1436960" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #original: array:24 [ "id" => 1436961 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1197} "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 {#1198} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1199} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200} "content" => Illuminate\Database\Eloquent\Collection {#1202} "next" => array:2 [ "refs" => "1436962" "type" => "task" ] "previous" => array:2 [ "refs" => "1436960" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1208} "page" => array:2 [ "refs" => "1436641" "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 => "*" ] } 1 => App\Models\Task {#1203 #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" => 1436962 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1210 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:2 [ 0 => App\Models\Element {#1100} 1 => App\Models\Element {#1092} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1436963" "type" => "task" ] "previous" => array:2 [ "refs" => "1436961" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #original: array:24 [ "id" => 1436962 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1201} "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 {#1210} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1206} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1204} "content" => Illuminate\Database\Eloquent\Collection {#1207} "next" => array:2 [ "refs" => "1436963" "type" => "task" ] "previous" => array:2 [ "refs" => "1436961" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1205} "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1215 #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" => 1436963 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1217 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:2 [ 0 => App\Models\Element {#1230 #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" => 1702384 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1231 …2} "task" => array:2 [ …2] "text" => "<p><strong>3.</strong> Как изменится сила притяжения между двумя шарами, если расстояние между их центрами увеличить в три раза?</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702384 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1231 …2} "task" => array:2 [ …2] "text" => "<p><strong>3.</strong> Как изменится сила притяжения между двумя шарами, если расстояние между их центрами увеличить в три раза?</p>" "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 => "*" ] } 1 => App\Models\Element {#1232 #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" => 1732305 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1233 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>$m_1$, $m_2$ - массы шаров (остаются неизменными)</p><p>$r_1$ - начальное расстояние между центрами шаров</p><p>$r_2 = 3r_1$ - конечное расстояние между центрами шаров</p><p><strong>Найти:</strong></p><p>Отношение начальной силы притяжения к конечной, то есть $\frac{F_1}{F_2}$.</p><p><strong>Решение:</strong></p><p>Сила гравитационного притяжения между двумя телами описывается законом всемирного тяготения Ньютона:</p><p>$F = G \frac{m_1 m_2}{r^2}$</p><p>где $\text{G}$ — гравитационная постоянная, $m_1$ и $m_2$ — массы тел, а $\text{r}$ — расстояние между их центрами.</p><p>Сила притяжения в начальном состоянии, когда расстояние между центрами шаров равно $r_1$, составляет:</p><p>$F_1 = G \frac{m_1 m_2}{r_1^2}$</p><p>По условию задачи, расстояние между центрами шаров увеличили в три раза. Новое расстояние $r_2$ равно $3r_1$. Сила притяжения в конечном состоянии $F_2$ будет равна:</p><p>$F_2 = G \frac{m_1 m_2}{r_2^2} = G \frac{m_1 m_2}{(3r_1)^2} = G \frac{m_1 m_2}{9r_1^2}$</p><p>Чтобы определить, как изменилась сила притяжения, найдем отношение $F_1$ к $F_2$:</p><p>$\frac{F_1}{F_2} = \frac{G \frac{m_1 m_2}{r_1^2}}{G \frac{m_1 m_2}{9r_1^2}}$</p><p>Сократив одинаковые множители ($G, m_1, m_2, r_1^2$), получим:</p><p>$\frac{F_1}{F_2} = \frac{1}{1/9} = 9$</p><p>Из этого соотношения следует, что $F_2 = \frac{F_1}{9}$.</p><p>Таким образом, при увеличении расстояния между центрами шаров в три раза сила их взаимного притяжения уменьшится в девять раз.</p><p><strong>Ответ:</strong> Сила притяжения уменьшится в 9 раз.</p>" ] #original: array:6 [ "id" => 1732305 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1233 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>$m_1$, $m_2$ - массы шаров (остаются неизменными)</p><p>$r_1$ - начальное расстояние между центрами шаров</p><p>$r_2 = 3r_1$ - конечное расстояние между центрами шаров</p><p><strong>Найти:</strong></p><p>Отношение начальной силы притяжения к конечной, то есть $\frac{F_1}{F_2}$.</p><p><strong>Решение:</strong></p><p>Сила гравитационного притяжения между двумя телами описывается законом всемирного тяготения Ньютона:</p><p>$F = G \frac{m_1 m_2}{r^2}$</p><p>где $\text{G}$ — гравитационная постоянная, $m_1$ и $m_2$ — массы тел, а $\text{r}$ — расстояние между их центрами.</p><p>Сила притяжения в начальном состоянии, когда расстояние между центрами шаров равно $r_1$, составляет:</p><p>$F_1 = G \frac{m_1 m_2}{r_1^2}$</p><p>По условию задачи, расстояние между центрами шаров увеличили в три раза. Новое расстояние $r_2$ равно $3r_1$. Сила притяжения в конечном состоянии $F_2$ будет равна:</p><p>$F_2 = G \frac{m_1 m_2}{r_2^2} = G \frac{m_1 m_2}{(3r_1)^2} = G \frac{m_1 m_2}{9r_1^2}$</p><p>Чтобы определить, как изменилась сила притяжения, найдем отношение $F_1$ к $F_2$:</p><p>$\frac{F_1}{F_2} = \frac{G \frac{m_1 m_2}{r_1^2}}{G \frac{m_1 m_2}{9r_1^2}}$</p><p>Сократив одинаковые множители ($G, m_1, m_2, r_1^2$), получим:</p><p>$\frac{F_1}{F_2} = \frac{1}{1/9} = 9$</p><p>Из этого соотношения следует, что $F_2 = \frac{F_1}{9}$.</p><p>Таким образом, при увеличении расстояния между центрами шаров в три раза сила их взаимного притяжения уменьшится в девять раз.</p><p><strong>Ответ:</strong> Сила притяжения уменьшится в 9 раз.</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" => "1436964" "type" => "task" ] "previous" => array:2 [ "refs" => "1436962" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #original: array:24 [ "id" => 1436963 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1216} "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 {#1217} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219} "content" => Illuminate\Database\Eloquent\Collection {#1221} "next" => array:2 [ "refs" => "1436964" "type" => "task" ] "previous" => array:2 [ "refs" => "1436962" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1227} "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1222 #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" => 1436964 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1229 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:2 [ 0 => App\Models\Branch {#1117} 1 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:2 [ 0 => App\Models\Element {#1242 #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" => 1702385 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1243 …2} "task" => array:2 [ …2] "text" => "<p><strong>4.</strong> Вычислите силу притяжения Луны к Земле. Масса Луны равна $7,4 \cdot 10^{22}$ кг, масса Земли — $6,0 \cdot 10^{24}$ кг, расстояние между центрами этих тел составляет $3,8 \cdot 10^8$ м.</p>" "img" => array:1 [ …1] ] #original: array:7 [ "id" => 1702385 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1243 …2} "task" => array:2 [ …2] "text" => "<p><strong>4.</strong> Вычислите силу притяжения Луны к Земле. Масса Луны равна $7,4 \cdot 10^{22}$ кг, масса Земли — $6,0 \cdot 10^{24}$ кг, расстояние между центрами этих тел составляет $3,8 \cdot 10^8$ м.</p>" "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 => "*" ] } 1 => App\Models\Element {#1244 #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" => 1732306 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1245 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Масса Луны $m_Л = 7.4 \cdot 10^{22}$ кг</p><p>Масса Земли $m_З = 6.0 \cdot 10^{24}$ кг</p><p>Расстояние между центрами $r = 3.8 \cdot 10^8$ м</p><p>Гравитационная постоянная $G \approx 6.67 \cdot 10^{-11} \frac{Н \cdot м^2}{кг^2}$</p><p><em>Все данные представлены в системе СИ.</em></p><p><strong>Найти:</strong></p><p>Силу притяжения $\text{F}$</p><p><strong>Решение:</strong></p><p>Для вычисления силы притяжения между Луной и Землей воспользуемся законом всемирного тяготения Ньютона:</p><p>$F = G \frac{m_Л \cdot m_З}{r^2}$</p><p>где $\text{F}$ — сила притяжения, $\text{G}$ — гравитационная постоянная, $m_Л$ и $m_З$ — массы Луны и Земли соответственно, а $\text{r}$ — расстояние между их центрами.</p><p>Подставим известные значения в формулу:</p><p>$F = 6.67 \cdot 10^{-11} \frac{Н \cdot м^2}{кг^2} \cdot \frac{(7.4 \cdot 10^{22} кг) \cdot (6.0 \cdot 10^{24} кг)}{(3.8 \cdot 10^8 м)^2}$</p><p>Сгруппируем числовые коэффициенты и степени десяти для удобства вычислений:</p><p>$F = \frac{6.67 \cdot 7.4 \cdot 6.0}{3.8^2} \cdot \frac{10^{-11} \cdot 10^{22} \cdot 10^{24}}{(10^8)^2}$</p><p>Выполним вычисления:</p><p>$F = \frac{296.148}{14.44} \cdot 10^{(-11 + 22 + 24 - 16)} Н$</p><p>$F \approx 20.51 \cdot 10^{19}$ Н</p><p>Представим результат в стандартном виде (с одной значащей цифрой до запятой) и округлим его до двух значащих цифр, так как исходные данные имеют такую же точность:</p><p>$F \approx 2.1 \cdot 10^{20}$ Н</p><p><strong>Ответ:</strong> сила притяжения Луны к Земле составляет примерно $2.1 \cdot 10^{20}$ Н.</p>" ] #original: array:6 [ "id" => 1732306 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1245 …2} "task" => array:2 [ …2] "text" => "<p><strong>Дано:</strong></p><p>Масса Луны $m_Л = 7.4 \cdot 10^{22}$ кг</p><p>Масса Земли $m_З = 6.0 \cdot 10^{24}$ кг</p><p>Расстояние между центрами $r = 3.8 \cdot 10^8$ м</p><p>Гравитационная постоянная $G \approx 6.67 \cdot 10^{-11} \frac{Н \cdot м^2}{кг^2}$</p><p><em>Все данные представлены в системе СИ.</em></p><p><strong>Найти:</strong></p><p>Силу притяжения $\text{F}$</p><p><strong>Решение:</strong></p><p>Для вычисления силы притяжения между Луной и Землей воспользуемся законом всемирного тяготения Ньютона:</p><p>$F = G \frac{m_Л \cdot m_З}{r^2}$</p><p>где $\text{F}$ — сила притяжения, $\text{G}$ — гравитационная постоянная, $m_Л$ и $m_З$ — массы Луны и Земли соответственно, а $\text{r}$ — расстояние между их центрами.</p><p>Подставим известные значения в формулу:</p><p>$F = 6.67 \cdot 10^{-11} \frac{Н \cdot м^2}{кг^2} \cdot \frac{(7.4 \cdot 10^{22} кг) \cdot (6.0 \cdot 10^{24} кг)}{(3.8 \cdot 10^8 м)^2}$</p><p>Сгруппируем числовые коэффициенты и степени десяти для удобства вычислений:</p><p>$F = \frac{6.67 \cdot 7.4 \cdot 6.0}{3.8^2} \cdot \frac{10^{-11} \cdot 10^{22} \cdot 10^{24}}{(10^8)^2}$</p><p>Выполним вычисления:</p><p>$F = \frac{296.148}{14.44} \cdot 10^{(-11 + 22 + 24 - 16)} Н$</p><p>$F \approx 20.51 \cdot 10^{19}$ Н</p><p>Представим результат в стандартном виде (с одной значащей цифрой до запятой) и округлим его до двух значащих цифр, так как исходные данные имеют такую же точность:</p><p>$F \approx 2.1 \cdot 10^{20}$ Н</p><p><strong>Ответ:</strong> сила притяжения Луны к Земле составляет примерно $2.1 \cdot 10^{20}$ Н.</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" => "1436965" "type" => "task" ] "previous" => array:2 [ "refs" => "1436963" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #original: array:24 [ "id" => 1436964 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1220} "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 {#1229} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1225} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1223} "content" => Illuminate\Database\Eloquent\Collection {#1224} "next" => array:2 [ "refs" => "1436965" "type" => "task" ] "previous" => array:2 [ "refs" => "1436963" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1239} "page" => array:2 [ "refs" => "1436641" "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" => 1436641 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_url" => "/9-klass/fizika/shahmaev-uchebnik/page-82" "field_display_title" => "82" "field_folder" => "1" "field_image_name" => "82" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1086} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1085} "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 {#1083} "content" => Illuminate\Database\Eloquent\Collection {#1112} "next" => array:2 [ "refs" => "1436642" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1436640" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186} ] #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" => 1436962 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "82" "field_page_end" => null "field_url" => "/9-klass/fizika/shahmaev-uchebnik/19-2" "field_display_title" => "2" "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 {#1109} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1436963" "type" => "task" ] "previous" => array:2 [ "refs" => "1436961" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103} "page" => array:2 [ "refs" => "1436641" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№2 (с. 82)
Условие. №2 (с. 82)
скриншот условия
2. Как изменится сила притяжения между двумя телами, если одно из них заменить другим, масса которого втрое больше?
Решение. №2 (с. 82)
Дано:
$m_{1}, m_{2}$ - начальные массы тел
$m'_{1} = 3m_{1}$ - новая масса первого тела
$\text{r}$ - расстояние между телами (постоянное)
Найти:
Во сколько раз изменится сила притяжения, т.е. найти отношение $\frac{F_{2}}{F_{1}}$
Решение:
Сила гравитационного притяжения между двумя телами описывается законом всемирного тяготения:
$F = G \frac{m_{1} m_{2}}{r^2}$
где $\text{G}$ - гравитационная постоянная, $m_{1}$ и $m_{2}$ - массы взаимодействующих тел, а $\text{r}$ - расстояние между их центрами.
Изначальная сила притяжения ($F_{1}$) между двумя телами с массами $m_{1}$ и $m_{2}$ равна:
$F_{1} = G \frac{m_{1} m_{2}}{r^2}$
После замены одного из тел на тело с массой втрое большей (например, $m_{1}$ заменяется на $m'_{1} = 3m_{1}$), новая сила притяжения ($F_{2}$) будет равна:
$F_{2} = G \frac{m'_{1} m_{2}}{r^2} = G \frac{(3m_{1}) m_{2}}{r^2}$
Чтобы определить, как изменилась сила, найдем отношение новой силы $F_{2}$ к первоначальной $F_{1}$:
$\frac{F_{2}}{F_{1}} = \frac{G \frac{3m_{1} m_{2}}{r^2}}{G \frac{m_{1} m_{2}}{r^2}}$
Сокращая одинаковые множители в числителе и знаменателе ($G, m_{1}, m_{2}, r^2$), получаем:
$\frac{F_{2}}{F_{1}} = 3$
Таким образом, сила притяжения прямо пропорциональна произведению масс тел. Если масса одного из тел увеличивается в 3 раза, то и сила их взаимного притяжения увеличивается в 3 раза.
Ответ: Сила притяжения увеличится в 3 раза.
Другие задания:
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