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Номер 5, страница 162, часть 1 - гдз по физике 9 класс учебник Белага, Воронцова
Авторы: Белага В. В., Воронцова Н. И., Ломаченков И. А., Панебратцев Ю. А.
Тип: Учебник
Издательство: Просвещение
Год издания: 2024 - 2026
Уровень обучения: углублённый
Часть: 1
Цвет обложки: голубой
ISBN: 978-5-09-121759-9
Популярные ГДЗ в 9 классе
Часть 1. Глава 4. Механика жидкостей и газов. Параграф 38. Исследовательские работы. Темы исследовательских и проектных работ - номер 5, страница 162.
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" => 1506387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "162" "field_page_end" => null "field_url" => "/9-klass/fizika/belaga-uchebnik/38temy-5" "field_display_title" => "5" "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 {#1077 #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" => 1505744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "6" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 1652 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2024" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "919" "field_priority" => null "field_default_folder" => "/fizika_09/belaga-u/" "field_isbn" => "978-5-09-121759-9" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_url" => "/9-klass/fizika/belaga-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1072 …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" => 1652 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2024" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "919" "field_priority" => null "field_default_folder" => "/fizika_09/belaga-u/" "field_isbn" => "978-5-09-121759-9" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_url" => "/9-klass/fizika/belaga-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1072 …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 {#1074 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1505744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "6" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1074} ] #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 {#1207 #items: array:4 [ 0 => App\Models\Branch {#1217 #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" => 1505744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Term {#1218 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "6" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ 0 => App\Models\Book {#1220 #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" => 1652 "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 {#1222 #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: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 {#1223 #items: array:1 [ 0 => App\Models\Term {#1224 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ 0 => App\Models\Term {#1226 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:4 [ 0 => App\Models\Term {#1228 #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" => 3824 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Белага" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Виктория" "field_patronymic" => "Владимировна" "field_surname_rp" => null ] #original: array:12 [ "id" => 3824 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Белага" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Виктория" "field_patronymic" => "Владимировна" "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 {#1229 #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" => 4049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Воронцова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Наталия" "field_patronymic" => "Игоревна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Воронцова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Наталия" "field_patronymic" => "Игоревна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1230 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => 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:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1232 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:1 [ 0 => App\Models\Term {#1234 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ 0 => App\Models\Term {#1236 #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 {#1237 #items: array:1 [ 0 => App\Models\Term {#1238 #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 {#1239 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1240 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Term {#1242 #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" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #original: array:6 [ "id" => 39 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "углублённый" "field_cases" => array:6 [ …6] "field_translit" => "uglublennyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Term {#1244 #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" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ …6] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ …6] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #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_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ 0 => App\Models\Term {#1246 #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 [ …6] "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 [ …6] "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 {#1247 #items: array:1 [ 0 => App\Models\Term {#1231} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2024" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "919" "field_priority" => null "field_default_folder" => "/fizika_09/belaga-u/" "field_isbn" => "978-5-09-121759-9" "field_cover" => array:2 [ 0 => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721" 1 => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721" "alt" => "" "width" => "2322" "height" => "3039" ] 1 => array:4 [ "path" => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721" "alt" => "" "width" => "2308" "height" => "3035" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1248 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1249 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1250 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/belaga-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ 0 => App\Models\Term {#1252 #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 [ …6] "field_translit" => "goluboy" ] #original: array:6 [ "id" => 52 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "голубой" …2 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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" => 1652 "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 {#1222} "field_class" => Illuminate\Database\Eloquent\Collection {#1223} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1225} "field_author" => Illuminate\Database\Eloquent\Collection {#1227} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1232} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1233} "field_country" => Illuminate\Database\Eloquent\Collection {#1235} "field_city" => Illuminate\Database\Eloquent\Collection {#1237} "field_series" => Illuminate\Database\Eloquent\Collection {#1239} "field_umk" => Illuminate\Database\Eloquent\Collection {#1240} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1241} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1243} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1245} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1247} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2024" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "919" "field_priority" => null "field_default_folder" => "/fizika_09/belaga-u/" "field_isbn" => "978-5-09-121759-9" "field_cover" => array:2 [ 0 => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721" 1 => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/belaga-u/covers/cover1.webp?ts=1761256721" "alt" => "" "width" => "2322" "height" => "3039" ] 1 => array:4 [ "path" => "/media/fizika_09/belaga-u/covers/cover2.webp?ts=1761256721" "alt" => "" "width" => "2308" "height" => "3035" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1248} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1249} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1250} "field_url" => "/9-klass/fizika/belaga-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1251} "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 {#1253 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1505744 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1221} "field_page_start" => "6" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1255} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1253} ] #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 {#1254 #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" => 1505843 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика жидкостей и газов" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:1 [ 0 => App\Models\Term {#1256 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "142" "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 {#1258 #items: array:1 [ 0 => App\Models\Book {#1220} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1505843 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика жидкостей и газов" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1259} "field_page_start" => "142" "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 {#1258} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1257} ] #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 {#1260 #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" => 1505856 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Исследовательские работы" "field_branch_order" => "38" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ 0 => App\Models\Term {#1261 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "159" "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 {#1263 #items: array:1 [ 0 => App\Models\Book {#1220} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1309 #items: array:1 [ 0 => App\Models\Branch {#1262 #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" => 1505843 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика жидкостей и газов" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_page_start" => "142" "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 {#1267 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1301 …2} ] #original: array:24 [ "id" => 1505843 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика жидкостей и газов" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1266 …2} "field_page_start" => "142" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" 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"field_page_start" => "159" "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 {#1263} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1309} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Branch {#1307 #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" => 1505859 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Темы исследовательских и проектных работ" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1308 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "162" "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 {#1310 #items: array:1 [ 0 => App\Models\Book {#1220} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1361 #items: array:1 [ 0 => App\Models\Branch {#1311 #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" => 1505856 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Исследовательские работы" "field_branch_order" => "38" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1313 …2} "field_page_start" => "159" "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 {#1314 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1348 …2} ] #original: array:24 [ "id" => 1505856 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Исследовательские работы" "field_branch_order" => "38" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1313 …2} "field_page_start" => "159" "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 {#1314 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1348 …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" => 1505859 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Темы исследовательских и проектных работ" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1308} "field_page_start" => "162" "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 {#1310} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1361} ] #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 {#1157 #items: array:2 [ 0 => App\Models\Element {#1193 #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" => 1803357 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\Edition {#1191 #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" => 6617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1186 …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" => "1506387" "type" => "task" ] "text" => "<p>• Аэродинамика в спорте.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "681" "height" => 131 "path" => "/media/fizika_09/belaga-u/0-38temy/5-1.webp?ts=1762277274" ] ] ] #original: array:7 [ "id" => 1803357 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1185} "task" => array:2 [ "refs" => "1506387" "type" => "task" ] "text" => "<p>• Аэродинамика в спорте.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "681" "height" => 131 "path" => "/media/fizika_09/belaga-u/0-38temy/5-1.webp?ts=1762277274" ] ] ] #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 {#1187 #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" => 1855984 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Edition {#1184 #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" => 7180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_content_source" => null ] #original: array:21 [ "id" => 7180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1178 …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" => "1506387" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p><strong>Аэродинамика в спорте</strong></p><p>Аэродинамика — это раздел гидроаэромеханики, изучающий движение воздуха и его взаимодействие с движущимися в нем телами. В современном спорте высоких достижений, где результат могут определять сотые и даже тысячные доли секунды, понимание и использование аэродинамических принципов играет решающую роль. Основные цели применения аэродинамики в спорте сводятся к двум задачам: минимизации силы сопротивления воздуха для достижения максимальной скорости и использованию подъемной (или прижимной) силы для управления траекторией, дальностью полета или устойчивостью.</p><p>Две ключевые аэродинамические силы, влияющие на спортсменов и спортивные снаряды, — это сила лобового сопротивления и подъемная сила. <strong>Сила лобового сопротивления</strong> (аэродинамическое сопротивление) направлена против движения и замедляет объект. Ее величина описывается формулой: $F_D = \frac{1}{2} \rho v^2 C_d A$, где $\rho$ — плотность воздуха, $\text{v}$ — скорость объекта, $C_d$ — коэффициент лобового сопротивления (зависит от формы тела и гладкости его поверхности), а $\text{A}$ — площадь поперечного сечения тела. <strong>Подъемная сила</strong> перпендикулярна направлению движения и может быть использована как для "подъема" объекта (например, лыжника-прыгуна), так и для "прижимания" его к поверхности (например, гоночного болида).</p><p>Рассмотрим применение этих принципов на примерах конкретных видов спорта:</p><p><strong>Велоспорт.</strong> Для уменьшения сопротивления воздуха велогонщики принимают низкую, сгруппированную позу, что уменьшает площадь поперечного сечения $\text{A}$. Используются аэродинамические шлемы каплевидной формы, облегающие костюмы из специальной ткани и велосипеды с рамами и колесами, профиль которых спроектирован для плавного обтекания воздушным потоком (уменьшение $C_d$). Также широко применяется тактика "драфтинга", когда один гонщик едет в "воздушном мешке" за другим, экономя до 40% усилий.</p><p><strong>Автогонки (Формула-1).</strong> Здесь аэродинамика используется в первую очередь для создания прижимной силы — подъемной силы, направленной вниз. Она вдавливает болид в трассу, увеличивая сцепление шин с дорогой и позволяя проходить повороты на более высоких скоростях. Для этого служат передние и задние антикрылья, а также сложная форма днища и диффузора, которые работают как перевернутое крыло самолета.</p><p><strong>Прыжки на лыжах с трамплина.</strong> Лыжник после отрыва от стола разводит лыжи в V-образное положение. Это позволяет значительно увеличить площадь опоры на воздух и создать большую подъемную силу, что, в свою очередь, увеличивает дальность полета. Специальные комбинезоны также имеют регламентированную воздухопроницаемость для оптимизации аэродинамических характеристик.</p><p><strong>Игровые виды спорта с мячом (гольф, теннис, футбол, бейсбол).</strong> Вращение мяча или шара в полете создает эффект Магнуса, приводящий к возникновению боковой силы, которая искривляет траекторию полета. Это позволяет выполнять "крученые" удары. Ямочки на мяче для гольфа — классический пример аэродинамического инжиниринга: они создают турбулентный пограничный слой вокруг мяча, который уменьшает общее сопротивление и позволяет мячу лететь почти в два раза дальше, чем гладкому мячу тех же размеров и массы.</p><p><strong>Плавание.</strong> Хотя это гидродинамика, принципы аналогичны. Пловцы стремятся к максимально обтекаемому положению тела для снижения сопротивления воды. Бритые тела, плавательные шапочки и высокотехнологичные костюмы, снижающие трение, служат той же цели.</p><p>Таким образом, аэродинамика является неотъемлемой частью современного спорта, где технологии и научный подход помогают атлетам расширять границы человеческих возможностей.</p><p><strong>Ответ:</strong> Аэродинамика в спорте — это применение законов движения воздуха для улучшения результатов. Основные цели: снижение силы лобового сопротивления для увеличения скорости (велоспорт, бег, плавание) и использование подъемной или прижимной силы для контроля траектории и устойчивости (прыжки с трамплина, автогонки). Технологии, такие как обтекаемая форма экипировки и инвентаря (шлемы, костюмы, рамы велосипедов), а также специальные техники (V-стиль у лыжников, драфтинг у велосипедистов) и конструктивные особенности снарядов (ямочки на мяче для гольфа), напрямую используют аэродинамические принципы для достижения превосходства.</p>" ] #original: array:6 [ "id" => 1855984 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1177} "task" => array:2 [ "refs" => "1506387" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p><strong>Аэродинамика в спорте</strong></p><p>Аэродинамика — это раздел гидроаэромеханики, изучающий движение воздуха и его взаимодействие с движущимися в нем телами. В современном спорте высоких достижений, где результат могут определять сотые и даже тысячные доли секунды, понимание и использование аэродинамических принципов играет решающую роль. Основные цели применения аэродинамики в спорте сводятся к двум задачам: минимизации силы сопротивления воздуха для достижения максимальной скорости и использованию подъемной (или прижимной) силы для управления траекторией, дальностью полета или устойчивостью.</p><p>Две ключевые аэродинамические силы, влияющие на спортсменов и спортивные снаряды, — это сила лобового сопротивления и подъемная сила. <strong>Сила лобового сопротивления</strong> (аэродинамическое сопротивление) направлена против движения и замедляет объект. Ее величина описывается формулой: $F_D = \frac{1}{2} \rho v^2 C_d A$, где $\rho$ — плотность воздуха, $\text{v}$ — скорость объекта, $C_d$ — коэффициент лобового сопротивления (зависит от формы тела и гладкости его поверхности), а $\text{A}$ — площадь поперечного сечения тела. <strong>Подъемная сила</strong> перпендикулярна направлению движения и может быть использована как для "подъема" объекта (например, лыжника-прыгуна), так и для "прижимания" его к поверхности (например, гоночного болида).</p><p>Рассмотрим применение этих принципов на примерах конкретных видов спорта:</p><p><strong>Велоспорт.</strong> Для уменьшения сопротивления воздуха велогонщики принимают низкую, сгруппированную позу, что уменьшает площадь поперечного сечения $\text{A}$. Используются аэродинамические шлемы каплевидной формы, облегающие костюмы из специальной ткани и велосипеды с рамами и колесами, профиль которых спроектирован для плавного обтекания воздушным потоком (уменьшение $C_d$). Также широко применяется тактика "драфтинга", когда один гонщик едет в "воздушном мешке" за другим, экономя до 40% усилий.</p><p><strong>Автогонки (Формула-1).</strong> Здесь аэродинамика используется в первую очередь для создания прижимной силы — подъемной силы, направленной вниз. Она вдавливает болид в трассу, увеличивая сцепление шин с дорогой и позволяя проходить повороты на более высоких скоростях. Для этого служат передние и задние антикрылья, а также сложная форма днища и диффузора, которые работают как перевернутое крыло самолета.</p><p><strong>Прыжки на лыжах с трамплина.</strong> Лыжник после отрыва от стола разводит лыжи в V-образное положение. Это позволяет значительно увеличить площадь опоры на воздух и создать большую подъемную силу, что, в свою очередь, увеличивает дальность полета. Специальные комбинезоны также имеют регламентированную воздухопроницаемость для оптимизации аэродинамических характеристик.</p><p><strong>Игровые виды спорта с мячом (гольф, теннис, футбол, бейсбол).</strong> Вращение мяча или шара в полете создает эффект Магнуса, приводящий к возникновению боковой силы, которая искривляет траекторию полета. Это позволяет выполнять "крученые" удары. Ямочки на мяче для гольфа — классический пример аэродинамического инжиниринга: они создают турбулентный пограничный слой вокруг мяча, который уменьшает общее сопротивление и позволяет мячу лететь почти в два раза дальше, чем гладкому мячу тех же размеров и массы.</p><p><strong>Плавание.</strong> Хотя это гидродинамика, принципы аналогичны. Пловцы стремятся к максимально обтекаемому положению тела для снижения сопротивления воды. Бритые тела, плавательные шапочки и высокотехнологичные костюмы, снижающие трение, служат той же цели.</p><p>Таким образом, аэродинамика является неотъемлемой частью современного спорта, где технологии и научный подход помогают атлетам расширять границы человеческих возможностей.</p><p><strong>Ответ:</strong> Аэродинамика в спорте — это применение законов движения воздуха для улучшения результатов. Основные цели: снижение силы лобового сопротивления для увеличения скорости (велоспорт, бег, плавание) и использование подъемной или прижимной силы для контроля траектории и устойчивости (прыжки с трамплина, автогонки). Технологии, такие как обтекаемая форма экипировки и инвентаря (шлемы, костюмы, рамы велосипедов), а также специальные техники (V-стиль у лыжников, драфтинг у велосипедистов) и конструктивные особенности снарядов (ямочки на мяче для гольфа), напрямую используют аэродинамические принципы для достижения превосходства.</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" => "1506388" "type" => "task" ] "previous" => array:2 [ "refs" => "1506386" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1203 #items: array:1 [ 0 => App\Models\Book {#1220} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\BookPage {#1204 #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" => 1507431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "162" "field_url" => "/9-klass/fizika/belaga-uchebnik/page-2-162" "field_display_title" => "162" "field_folder" => "2" "field_image_name" => "162" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Branch {#1179 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Book {#1220} ] #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 {#1142 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Element {#1132 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1507432" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1507430" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1659 #items: array:5 [ 0 => App\Models\Task {#1671 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1766 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1754 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1741 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1724 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1507431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "162" "field_url" => "/9-klass/fizika/belaga-uchebnik/page-2-162" "field_display_title" => "162" "field_folder" => "2" "field_image_name" => "162" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1139} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1141} "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 {#1142} "content" => Illuminate\Database\Eloquent\Collection {#1130} "next" => array:2 [ "refs" => "1507432" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1507430" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1659} ] #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" => 1506387 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "162" "field_page_end" => null "field_url" => "/9-klass/fizika/belaga-uchebnik/38temy-5" "field_display_title" => "5" "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 {#1077} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1207} "content" => Illuminate\Database\Eloquent\Collection {#1157} "next" => array:2 [ "refs" => "1506388" "type" => "task" ] "previous" => array:2 [ "refs" => "1506386" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1203} "page" => array:2 [ "refs" => "1507431" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№5 (с. 162)
Условие. №5 (с. 162)
скриншот условия
• Аэродинамика в спорте.
Решение. №5 (с. 162)
Решение
Аэродинамика в спорте
Аэродинамика — это раздел гидроаэромеханики, изучающий движение воздуха и его взаимодействие с движущимися в нем телами. В современном спорте высоких достижений, где результат могут определять сотые и даже тысячные доли секунды, понимание и использование аэродинамических принципов играет решающую роль. Основные цели применения аэродинамики в спорте сводятся к двум задачам: минимизации силы сопротивления воздуха для достижения максимальной скорости и использованию подъемной (или прижимной) силы для управления траекторией, дальностью полета или устойчивостью.
Две ключевые аэродинамические силы, влияющие на спортсменов и спортивные снаряды, — это сила лобового сопротивления и подъемная сила. Сила лобового сопротивления (аэродинамическое сопротивление) направлена против движения и замедляет объект. Ее величина описывается формулой: $F_D = \frac{1}{2} \rho v^2 C_d A$, где $\rho$ — плотность воздуха, $\text{v}$ — скорость объекта, $C_d$ — коэффициент лобового сопротивления (зависит от формы тела и гладкости его поверхности), а $\text{A}$ — площадь поперечного сечения тела. Подъемная сила перпендикулярна направлению движения и может быть использована как для "подъема" объекта (например, лыжника-прыгуна), так и для "прижимания" его к поверхности (например, гоночного болида).
Рассмотрим применение этих принципов на примерах конкретных видов спорта:
Велоспорт. Для уменьшения сопротивления воздуха велогонщики принимают низкую, сгруппированную позу, что уменьшает площадь поперечного сечения $\text{A}$. Используются аэродинамические шлемы каплевидной формы, облегающие костюмы из специальной ткани и велосипеды с рамами и колесами, профиль которых спроектирован для плавного обтекания воздушным потоком (уменьшение $C_d$). Также широко применяется тактика "драфтинга", когда один гонщик едет в "воздушном мешке" за другим, экономя до 40% усилий.
Автогонки (Формула-1). Здесь аэродинамика используется в первую очередь для создания прижимной силы — подъемной силы, направленной вниз. Она вдавливает болид в трассу, увеличивая сцепление шин с дорогой и позволяя проходить повороты на более высоких скоростях. Для этого служат передние и задние антикрылья, а также сложная форма днища и диффузора, которые работают как перевернутое крыло самолета.
Прыжки на лыжах с трамплина. Лыжник после отрыва от стола разводит лыжи в V-образное положение. Это позволяет значительно увеличить площадь опоры на воздух и создать большую подъемную силу, что, в свою очередь, увеличивает дальность полета. Специальные комбинезоны также имеют регламентированную воздухопроницаемость для оптимизации аэродинамических характеристик.
Игровые виды спорта с мячом (гольф, теннис, футбол, бейсбол). Вращение мяча или шара в полете создает эффект Магнуса, приводящий к возникновению боковой силы, которая искривляет траекторию полета. Это позволяет выполнять "крученые" удары. Ямочки на мяче для гольфа — классический пример аэродинамического инжиниринга: они создают турбулентный пограничный слой вокруг мяча, который уменьшает общее сопротивление и позволяет мячу лететь почти в два раза дальше, чем гладкому мячу тех же размеров и массы.
Плавание. Хотя это гидродинамика, принципы аналогичны. Пловцы стремятся к максимально обтекаемому положению тела для снижения сопротивления воды. Бритые тела, плавательные шапочки и высокотехнологичные костюмы, снижающие трение, служат той же цели.
Таким образом, аэродинамика является неотъемлемой частью современного спорта, где технологии и научный подход помогают атлетам расширять границы человеческих возможностей.
Ответ: Аэродинамика в спорте — это применение законов движения воздуха для улучшения результатов. Основные цели: снижение силы лобового сопротивления для увеличения скорости (велоспорт, бег, плавание) и использование подъемной или прижимной силы для контроля траектории и устойчивости (прыжки с трамплина, автогонки). Технологии, такие как обтекаемая форма экипировки и инвентаря (шлемы, костюмы, рамы велосипедов), а также специальные техники (V-стиль у лыжников, драфтинг у велосипедистов) и конструктивные особенности снарядов (ямочки на мяче для гольфа), напрямую используют аэродинамические принципы для достижения превосходства.
Другие задания:
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