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Номер 8.37, страница 48 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Механика. 8. Комбинированные задачи по механике - номер 8.37, страница 48.
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" => 1288223 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/08-37" "field_display_title" => "8.37" "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 {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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" => 5401 "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 {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "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 {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "5" "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 {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} ] #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 {#1187 #items: array:3 [ 0 => App\Models\Branch {#1197 #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" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1198 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1234 #items: array:1 [ 0 => App\Models\Book {#1199 #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" => 5401 "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 {#1201 #items: array:1 [ 0 => App\Models\Term {#1200 #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 {#1202 #items: array:4 [ 0 => App\Models\Term {#1203 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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 {#1204 #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 => "*" ] } 2 => App\Models\Term {#1205 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1206 #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" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #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 {#1207 #items: array:1 [ 0 => App\Models\Term {#1208 #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" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #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 {#1209 #items: array:3 [ 0 => App\Models\Term {#1210 #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" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "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 {#1211 #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 => "*" ] } 2 => App\Models\Term {#1212 #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" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "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 {#1213 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Term {#1215 #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" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "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, zadachnik" ] #original: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "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, zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Term {#1217 #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 {#1218 #items: array:1 [ 0 => App\Models\Term {#1219 #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 {#1220 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1221 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1222 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1223 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ 0 => App\Models\Term {#1225 #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" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #original: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #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 {#1226 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1227 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1228 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1229 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Term {#1231 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 5401 "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 {#1201} "field_class" => Illuminate\Database\Eloquent\Collection {#1202} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1207} "field_author" => Illuminate\Database\Eloquent\Collection {#1209} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1213} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1214} "field_country" => Illuminate\Database\Eloquent\Collection {#1216} "field_city" => Illuminate\Database\Eloquent\Collection {#1218} "field_series" => Illuminate\Database\Eloquent\Collection {#1220} "field_umk" => Illuminate\Database\Eloquent\Collection {#1221} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1222} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1223} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1224} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1226} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "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" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1227} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1228} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1229} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1230} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 {#1232 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1198} "field_page_start" => "5" "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 {#1234} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1232} ] #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 {#1233 #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" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1235 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1236 #items: array:1 [ 0 => App\Models\Book {#1199} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1235} "field_page_start" => "5" "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 {#1236} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1237} ] #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 {#1238 #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" => 1287875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8. Комбинированные задачи по механике" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1239 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "43" "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 {#1240 #items: array:1 [ 0 => App\Models\Book {#1199} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1317 #items: array:1 [ 0 => App\Models\Branch {#1241 #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" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1243 …2} "field_page_start" => "5" "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 {#1242 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277 …2} ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1243 …2} "field_page_start" => "5" "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 {#1242 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277 …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" => 1287875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "8. Комбинированные задачи по механике" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1239} "field_page_start" => "43" "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 {#1240} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1317} ] #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 {#1148 #items: array:3 [ 0 => App\Models\Element {#1180 #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" => 1478052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Edition {#1179 #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" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 …2} "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 {#1176 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 …2} "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 {#1176 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1174 …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" => "1288223" "type" => "task" ] "text" => "<p><strong>8.37**</strong>. В одном из своих путешествий я открыл неизвестную планету Солнечной системы. Она, как и наша Земля, имеет радиус $r = 6400 \text{ км}$, причем радиус ее круговой орбиты составляет тоже 150 миллионов километров. Однако эта планета, в отличие от Земли, движется вокруг Солнца <em>поступательно</em>, то есть у нее отсутствует суточное вращение. Гуляя, я обошел с чувствительным динамометром всю планету и с удивлением обнаружил, что ускорение свободного падения $\text{g}$ не всюду одинаково! Сможете ли вы объяснить это явление? Заодно подсчитайте, на сколько максимальное значение $\text{g}$ на этой планете отличается от минимального. Для расчетов примите, что планета представляет собой однородный шар.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "37-1.jpg" "alt" => null "width" => "1402" "height" => 677 "path" => "/media/fizika_08/gelfgat-u/0-08/37-1.webp?ts=1756049811" ] ] ] #original: array:7 [ "id" => 1478052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172} "task" => array:2 [ "refs" => "1288223" "type" => "task" ] "text" => "<p><strong>8.37**</strong>. В одном из своих путешествий я открыл неизвестную планету Солнечной системы. Она, как и наша Земля, имеет радиус $r = 6400 \text{ км}$, причем радиус ее круговой орбиты составляет тоже 150 миллионов километров. Однако эта планета, в отличие от Земли, движется вокруг Солнца <em>поступательно</em>, то есть у нее отсутствует суточное вращение. Гуляя, я обошел с чувствительным динамометром всю планету и с удивлением обнаружил, что ускорение свободного падения $\text{g}$ не всюду одинаково! Сможете ли вы объяснить это явление? Заодно подсчитайте, на сколько максимальное значение $\text{g}$ на этой планете отличается от минимального. Для расчетов примите, что планета представляет собой однородный шар.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "37-1.jpg" "alt" => null "width" => "1402" "height" => 677 "path" => "/media/fizika_08/gelfgat-u/0-08/37-1.webp?ts=1756049811" ] ] ] #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 {#1173 #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" => 1478577 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => App\Models\Edition {#1171 #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" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166 …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" => "1288223" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "37-1.jpg" "alt" => null "width" => "1447" "height" => 717 "path" => "/media/fizika_08/gelfgat-u/1-08/37-1.webp?ts=1756049875" ] 1 => array:5 [ "name" => "37-2.jpg" "alt" => null "width" => "1430" "height" => 2231 "path" => "/media/fizika_08/gelfgat-u/1-08/37-2.webp?ts=1756049875" ] ] ] #original: array:6 [ "id" => 1478577 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1164} "task" => array:2 [ "refs" => "1288223" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "37-1.jpg" "alt" => null "width" => "1447" "height" => 717 "path" => "/media/fizika_08/gelfgat-u/1-08/37-1.webp?ts=1756049875" ] 1 => array:5 [ "name" => "37-2.jpg" "alt" => null "width" => "1430" "height" => 2231 "path" => "/media/fizika_08/gelfgat-u/1-08/37-2.webp?ts=1756049875" ] ] ] #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\Element {#1162 #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" => 1737916 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Edition {#1165 #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" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1160 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1160 …2} "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" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1159 …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" => "1288223" "type" => "task" ] "text" => "<p><strong>Объяснение явления</strong></p><p>Ускорение свободного падения $\text{g}$, измеряемое динамометром на поверхности планеты, представляет собой эффективное ускорение. Оно является векторной суммой трех ускорений:<br>1. Гравитационного ускорения, создаваемого самой планетой ($\vec{g}_0$). Для однородного шара его модуль на поверхности постоянен и направлен к центру планеты.<br>2. Гравитационного ускорения, создаваемого Солнцем ($\vec{g}_C$). Его модуль и направление различны для разных точек на поверхности планеты, так как они находятся на разном расстоянии от Солнца.<br>3. Ускорения инерции ($\vec{a}_{in}$). Поскольку система отсчета, связанная с планетой, движется с ускорением вокруг Солнца, она является неинерциальной. Ускорение инерции равно по модулю и противоположно по направлению ускорению центра масс планеты ($\vec{a}_c$). Так как планета движется поступательно, все ее точки имеют одинаковое ускорение $\vec{a}_c$, а значит, и одинаковое ускорение инерции $\vec{a}_{in} = -\vec{a}_c$.</p><p>Эффективное ускорение свободного падения равно: $\vec{g} = \vec{g}_0 + \vec{g}_C + \vec{a}_{in}$.</p><p>Сумма ускорений, вызванных Солнцем, $\vec{a}_T = \vec{g}_C + \vec{a}_{in}$, называется приливным ускорением. Оно возникает из-за того, что гравитационное притяжение Солнца ($\vec{g}_C$) неоднородно по объему планеты, в то время как инерционная составляющая ($\vec{a}_{in}$) одинакова для всех точек. Эта разница и приводит к изменению измеряемого ускорения $\text{g}$ на поверхности.</p><p>В точках планеты, ближайшей к Солнцу (подсолнечной) и наиболее удаленной от него (противосолнечной), приливное ускорение направлено от центра планеты. В этих точках сила тяжести ослабляется, и ускорение свободного падения $\text{g}$ достигает своего минимального значения.</p><p>В точках на поверхности планеты, расположенных на окружности, плоскость которой перпендикулярна линии Солнце-планета (условный "пояс" между подсолнечной и противосолнечной точками), приливное ускорение направлено к центру планеты. Здесь оно усиливает собственную гравитацию планеты, и ускорение свободного падения $\text{g}$ достигает максимального значения.</p><p>Таким образом, именно приливное действие Солнца является причиной того, что ускорение свободного падения на этой планете не всюду одинаково.</p><p><strong>Расчет, на сколько максимальное значение g на этой планете отличается от минимального</strong></p><p><strong>Дано:</strong></p><p>Радиус планеты $r = 6400$ км</p><p>Радиус орбиты планеты $R = 150 \cdot 10^6$ км</p><p>Приведем данные к системе СИ:</p><p>$r = 6400 \cdot 10^3 \text{ м} = 6.4 \cdot 10^6 \text{ м}$</p><p>$R = 150 \cdot 10^6 \cdot 10^3 \text{ м} = 1.5 \cdot 10^{11} \text{ м}$</p><p><strong>Найти:</strong></p><p>$\Delta g = g_{max} - g_{min}$</p><p><strong>Решение:</strong></p><p>Как было показано в объяснении, разница в ускорении свободного падения вызвана приливными силами со стороны Солнца. Обозначим собственное ускорение свободного падения планеты как $g_0 = G\frac{M}{r^2}$, где $\text{M}$ - масса планеты.</p><p>В точках, наиболее близких и наиболее удаленных от Солнца, приливное ускорение направлено от центра планеты и уменьшает $g_0$. Здесь ускорение свободного падения минимально и равно:</p><p>$g_{min} = g_0 - 2G\frac{M_C r}{R^3}$</p><p>где $M_C$ — масса Солнца, $\text{G}$ — гравитационная постоянная.</p><p>В точках, находящихся на равном удалении от подсолнечной и противосолнечной точек (на "боках" планеты относительно Солнца), приливное ускорение направлено к центру планеты и увеличивает $g_0$. Здесь ускорение свободного падения максимально и равно:</p><p>$g_{max} = g_0 + G\frac{M_C r}{R^3}$</p><p>Разница между максимальным и минимальным значениями ускорения свободного падения составляет:</p><p>$\Delta g = g_{max} - g_{min} = \left(g_0 + G\frac{M_C r}{R^3}\right) - \left(g_0 - 2G\frac{M_C r}{R^3}\right) = 3G\frac{M_C r}{R^3}$</p><p>Подставим числовые значения. Используем справочные данные для массы Солнца $M_C \approx 1.99 \cdot 10^{30}$ кг и гравитационной постоянной $G \approx 6.67 \cdot 10^{-11}$ Н·м²/кг².</p><p>$\Delta g = 3 \cdot (6.67 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2}) \cdot \frac{(1.99 \cdot 10^{30} \text{ кг}) \cdot (6.4 \cdot 10^6 \text{ м})}{(1.5 \cdot 10^{11} \text{ м})^3}$</p><p>$\Delta g = \frac{3 \cdot 6.67 \cdot 1.99 \cdot 6.4}{1.5^3} \cdot \frac{10^{-11} \cdot 10^{30} \cdot 10^6}{10^{33}} \frac{\text{м}}{\text{с}^2} = \frac{254.8}{3.375} \cdot 10^{-8} \frac{\text{м}}{\text{с}^2} \approx 75.5 \cdot 10^{-8} \frac{\text{м}}{\text{с}^2}$</p><p>$\Delta g \approx 7.55 \cdot 10^{-7} \text{ м/с}^2$</p><p><strong>Ответ:</strong> максимальное значение $\text{g}$ на этой планете отличается от минимального на $7.55 \cdot 10^{-7} \text{ м/с}^2$.</p>" ] #original: array:6 [ "id" => 1737916 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1156} "task" => array:2 [ "refs" => "1288223" "type" => "task" ] "text" => "<p><strong>Объяснение явления</strong></p><p>Ускорение свободного падения $\text{g}$, измеряемое динамометром на поверхности планеты, представляет собой эффективное ускорение. Оно является векторной суммой трех ускорений:<br>1. Гравитационного ускорения, создаваемого самой планетой ($\vec{g}_0$). Для однородного шара его модуль на поверхности постоянен и направлен к центру планеты.<br>2. Гравитационного ускорения, создаваемого Солнцем ($\vec{g}_C$). Его модуль и направление различны для разных точек на поверхности планеты, так как они находятся на разном расстоянии от Солнца.<br>3. Ускорения инерции ($\vec{a}_{in}$). Поскольку система отсчета, связанная с планетой, движется с ускорением вокруг Солнца, она является неинерциальной. Ускорение инерции равно по модулю и противоположно по направлению ускорению центра масс планеты ($\vec{a}_c$). Так как планета движется поступательно, все ее точки имеют одинаковое ускорение $\vec{a}_c$, а значит, и одинаковое ускорение инерции $\vec{a}_{in} = -\vec{a}_c$.</p><p>Эффективное ускорение свободного падения равно: $\vec{g} = \vec{g}_0 + \vec{g}_C + \vec{a}_{in}$.</p><p>Сумма ускорений, вызванных Солнцем, $\vec{a}_T = \vec{g}_C + \vec{a}_{in}$, называется приливным ускорением. Оно возникает из-за того, что гравитационное притяжение Солнца ($\vec{g}_C$) неоднородно по объему планеты, в то время как инерционная составляющая ($\vec{a}_{in}$) одинакова для всех точек. Эта разница и приводит к изменению измеряемого ускорения $\text{g}$ на поверхности.</p><p>В точках планеты, ближайшей к Солнцу (подсолнечной) и наиболее удаленной от него (противосолнечной), приливное ускорение направлено от центра планеты. В этих точках сила тяжести ослабляется, и ускорение свободного падения $\text{g}$ достигает своего минимального значения.</p><p>В точках на поверхности планеты, расположенных на окружности, плоскость которой перпендикулярна линии Солнце-планета (условный "пояс" между подсолнечной и противосолнечной точками), приливное ускорение направлено к центру планеты. Здесь оно усиливает собственную гравитацию планеты, и ускорение свободного падения $\text{g}$ достигает максимального значения.</p><p>Таким образом, именно приливное действие Солнца является причиной того, что ускорение свободного падения на этой планете не всюду одинаково.</p><p><strong>Расчет, на сколько максимальное значение g на этой планете отличается от минимального</strong></p><p><strong>Дано:</strong></p><p>Радиус планеты $r = 6400$ км</p><p>Радиус орбиты планеты $R = 150 \cdot 10^6$ км</p><p>Приведем данные к системе СИ:</p><p>$r = 6400 \cdot 10^3 \text{ м} = 6.4 \cdot 10^6 \text{ м}$</p><p>$R = 150 \cdot 10^6 \cdot 10^3 \text{ м} = 1.5 \cdot 10^{11} \text{ м}$</p><p><strong>Найти:</strong></p><p>$\Delta g = g_{max} - g_{min}$</p><p><strong>Решение:</strong></p><p>Как было показано в объяснении, разница в ускорении свободного падения вызвана приливными силами со стороны Солнца. Обозначим собственное ускорение свободного падения планеты как $g_0 = G\frac{M}{r^2}$, где $\text{M}$ - масса планеты.</p><p>В точках, наиболее близких и наиболее удаленных от Солнца, приливное ускорение направлено от центра планеты и уменьшает $g_0$. Здесь ускорение свободного падения минимально и равно:</p><p>$g_{min} = g_0 - 2G\frac{M_C r}{R^3}$</p><p>где $M_C$ — масса Солнца, $\text{G}$ — гравитационная постоянная.</p><p>В точках, находящихся на равном удалении от подсолнечной и противосолнечной точек (на "боках" планеты относительно Солнца), приливное ускорение направлено к центру планеты и увеличивает $g_0$. Здесь ускорение свободного падения максимально и равно:</p><p>$g_{max} = g_0 + G\frac{M_C r}{R^3}$</p><p>Разница между максимальным и минимальным значениями ускорения свободного падения составляет:</p><p>$\Delta g = g_{max} - g_{min} = \left(g_0 + G\frac{M_C r}{R^3}\right) - \left(g_0 - 2G\frac{M_C r}{R^3}\right) = 3G\frac{M_C r}{R^3}$</p><p>Подставим числовые значения. Используем справочные данные для массы Солнца $M_C \approx 1.99 \cdot 10^{30}$ кг и гравитационной постоянной $G \approx 6.67 \cdot 10^{-11}$ Н·м²/кг².</p><p>$\Delta g = 3 \cdot (6.67 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2}) \cdot \frac{(1.99 \cdot 10^{30} \text{ кг}) \cdot (6.4 \cdot 10^6 \text{ м})}{(1.5 \cdot 10^{11} \text{ м})^3}$</p><p>$\Delta g = \frac{3 \cdot 6.67 \cdot 1.99 \cdot 6.4}{1.5^3} \cdot \frac{10^{-11} \cdot 10^{30} \cdot 10^6}{10^{33}} \frac{\text{м}}{\text{с}^2} = \frac{254.8}{3.375} \cdot 10^{-8} \frac{\text{м}}{\text{с}^2} \approx 75.5 \cdot 10^{-8} \frac{\text{м}}{\text{с}^2}$</p><p>$\Delta g \approx 7.55 \cdot 10^{-7} \text{ м/с}^2$</p><p><strong>Ответ:</strong> максимальное значение $\text{g}$ на этой планете отличается от минимального на $7.55 \cdot 10^{-7} \text{ м/с}^2$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: 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№8.37 (с. 48)
Условие. №8.37 (с. 48)
скриншот условия
8.37**. В одном из своих путешествий я открыл неизвестную планету Солнечной системы. Она, как и наша Земля, имеет радиус $r = 6400 \text{ км}$, причем радиус ее круговой орбиты составляет тоже 150 миллионов километров. Однако эта планета, в отличие от Земли, движется вокруг Солнца поступательно, то есть у нее отсутствует суточное вращение. Гуляя, я обошел с чувствительным динамометром всю планету и с удивлением обнаружил, что ускорение свободного падения $\text{g}$ не всюду одинаково! Сможете ли вы объяснить это явление? Заодно подсчитайте, на сколько максимальное значение $\text{g}$ на этой планете отличается от минимального. Для расчетов примите, что планета представляет собой однородный шар.
Решение. №8.37 (с. 48)
Решение 2. №8.37 (с. 48)
Объяснение явления
Ускорение свободного падения $\text{g}$, измеряемое динамометром на поверхности планеты, представляет собой эффективное ускорение. Оно является векторной суммой трех ускорений:
1. Гравитационного ускорения, создаваемого самой планетой ($\vec{g}_0$). Для однородного шара его модуль на поверхности постоянен и направлен к центру планеты.
2. Гравитационного ускорения, создаваемого Солнцем ($\vec{g}_C$). Его модуль и направление различны для разных точек на поверхности планеты, так как они находятся на разном расстоянии от Солнца.
3. Ускорения инерции ($\vec{a}_{in}$). Поскольку система отсчета, связанная с планетой, движется с ускорением вокруг Солнца, она является неинерциальной. Ускорение инерции равно по модулю и противоположно по направлению ускорению центра масс планеты ($\vec{a}_c$). Так как планета движется поступательно, все ее точки имеют одинаковое ускорение $\vec{a}_c$, а значит, и одинаковое ускорение инерции $\vec{a}_{in} = -\vec{a}_c$.
Эффективное ускорение свободного падения равно: $\vec{g} = \vec{g}_0 + \vec{g}_C + \vec{a}_{in}$.
Сумма ускорений, вызванных Солнцем, $\vec{a}_T = \vec{g}_C + \vec{a}_{in}$, называется приливным ускорением. Оно возникает из-за того, что гравитационное притяжение Солнца ($\vec{g}_C$) неоднородно по объему планеты, в то время как инерционная составляющая ($\vec{a}_{in}$) одинакова для всех точек. Эта разница и приводит к изменению измеряемого ускорения $\text{g}$ на поверхности.
В точках планеты, ближайшей к Солнцу (подсолнечной) и наиболее удаленной от него (противосолнечной), приливное ускорение направлено от центра планеты. В этих точках сила тяжести ослабляется, и ускорение свободного падения $\text{g}$ достигает своего минимального значения.
В точках на поверхности планеты, расположенных на окружности, плоскость которой перпендикулярна линии Солнце-планета (условный "пояс" между подсолнечной и противосолнечной точками), приливное ускорение направлено к центру планеты. Здесь оно усиливает собственную гравитацию планеты, и ускорение свободного падения $\text{g}$ достигает максимального значения.
Таким образом, именно приливное действие Солнца является причиной того, что ускорение свободного падения на этой планете не всюду одинаково.
Расчет, на сколько максимальное значение g на этой планете отличается от минимального
Дано:
Радиус планеты $r = 6400$ км
Радиус орбиты планеты $R = 150 \cdot 10^6$ км
Приведем данные к системе СИ:
$r = 6400 \cdot 10^3 \text{ м} = 6.4 \cdot 10^6 \text{ м}$
$R = 150 \cdot 10^6 \cdot 10^3 \text{ м} = 1.5 \cdot 10^{11} \text{ м}$
Найти:
$\Delta g = g_{max} - g_{min}$
Решение:
Как было показано в объяснении, разница в ускорении свободного падения вызвана приливными силами со стороны Солнца. Обозначим собственное ускорение свободного падения планеты как $g_0 = G\frac{M}{r^2}$, где $\text{M}$ - масса планеты.
В точках, наиболее близких и наиболее удаленных от Солнца, приливное ускорение направлено от центра планеты и уменьшает $g_0$. Здесь ускорение свободного падения минимально и равно:
$g_{min} = g_0 - 2G\frac{M_C r}{R^3}$
где $M_C$ — масса Солнца, $\text{G}$ — гравитационная постоянная.
В точках, находящихся на равном удалении от подсолнечной и противосолнечной точек (на "боках" планеты относительно Солнца), приливное ускорение направлено к центру планеты и увеличивает $g_0$. Здесь ускорение свободного падения максимально и равно:
$g_{max} = g_0 + G\frac{M_C r}{R^3}$
Разница между максимальным и минимальным значениями ускорения свободного падения составляет:
$\Delta g = g_{max} - g_{min} = \left(g_0 + G\frac{M_C r}{R^3}\right) - \left(g_0 - 2G\frac{M_C r}{R^3}\right) = 3G\frac{M_C r}{R^3}$
Подставим числовые значения. Используем справочные данные для массы Солнца $M_C \approx 1.99 \cdot 10^{30}$ кг и гравитационной постоянной $G \approx 6.67 \cdot 10^{-11}$ Н·м²/кг².
$\Delta g = 3 \cdot (6.67 \cdot 10^{-11} \frac{\text{Н} \cdot \text{м}^2}{\text{кг}^2}) \cdot \frac{(1.99 \cdot 10^{30} \text{ кг}) \cdot (6.4 \cdot 10^6 \text{ м})}{(1.5 \cdot 10^{11} \text{ м})^3}$
$\Delta g = \frac{3 \cdot 6.67 \cdot 1.99 \cdot 6.4}{1.5^3} \cdot \frac{10^{-11} \cdot 10^{30} \cdot 10^6}{10^{33}} \frac{\text{м}}{\text{с}^2} = \frac{254.8}{3.375} \cdot 10^{-8} \frac{\text{м}}{\text{с}^2} \approx 75.5 \cdot 10^{-8} \frac{\text{м}}{\text{с}^2}$
$\Delta g \approx 7.55 \cdot 10^{-7} \text{ м/с}^2$
Ответ: максимальное значение $\text{g}$ на этой планете отличается от минимального на $7.55 \cdot 10^{-7} \text{ м/с}^2$.
Другие задания:
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