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Номер 6, страница 62 - гдз по физике 9 класс учебник Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю.
Тип: Учебник
Серия: алгоритм успеха
Издательство: Вентана-граф
Год издания: 2012 - 2026
Цвет обложки: синий изображено здание и радуга
ISBN: 978-5-360-07412-0
Популярные ГДЗ в 9 классе
Глава 1. Кинематика. Параграф 10. Равномерное движение по окружности. Угловая скорость. Период и частота вращения. Упражнения - номер 6, страница 62.
App\Models\Task {#1024 // 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" => 1438124 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10upr-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1437875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #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" => "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 1202 "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 {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #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 {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 #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" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #original: array:6 [ "id" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #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 {#1040 #items: array:3 [ 0 => App\Models\Term {#1041 #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" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1042 #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" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "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 {#1043 #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" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 {#1044 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #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 {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1049 #items: array:1 [ 0 => App\Models\Term {#1050 #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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #original: array:8 [ "id" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #original: array:6 [ "id" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #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 {#1059 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #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" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1202 "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 {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1044} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1045} "field_country" => Illuminate\Database\Eloquent\Collection {#1047} "field_city" => Illuminate\Database\Eloquent\Collection {#1049} "field_series" => Illuminate\Database\Eloquent\Collection {#1051} "field_umk" => Illuminate\Database\Eloquent\Collection {#1053} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063} "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 {#1065 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065} ] #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 {#1066 #items: array:3 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1067 #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" => 1437899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" => "55" "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 {#1070 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1072 #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" => 1437875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1073 …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 {#1074 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 …2} ] #original: array:24 [ "id" => 1437875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1073 …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 {#1074 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 …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" => 1437899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068} "field_page_start" => "55" "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 {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #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 {#1076 #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" => 1437901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "62" "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 {#1078 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Branch {#1080 #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" => 1437899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_page_start" => "55" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1082 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1083 …2} ] #original: array:24 [ "id" => 1437899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Равномерное движение по окружности. Угловая скорость. Период и частота вращения" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_page_start" => "55" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1082 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1083 …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" => 1437901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_page_start" => "62" "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 {#1078} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #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 {#1121 #items: array:2 [ 0 => App\Models\Element {#1122 #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" => 1705003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Edition {#1124 #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" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 …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 {#1127 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 …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 {#1127 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …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" => "1438124" "type" => "task" ] "text" => "<p><strong>6.</strong> Выберите прямолинейный участок дороги и измерьте его длину.</p><p>Прокатитесь по очереди на велосипеде по этому участку, измеряя каждый раз время движения. Оцените среднюю скорость движения каждого из учеников. Проведите все необходимые измерения для того, чтобы определить в каждом случае среднюю частоту вращения: а) колеса велосипеда; б) ведомой звёздочки; в) ведущей звёздочки. Сравните полученные результаты и сформулируйте выводы. Оцените погрешности результатов.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "482" "height" => 195 "path" => "/media/fizika_09/grachev-u/0-10upr/6-1.webp?ts=1759503102" ] ] ] #original: array:7 [ "id" => 1705003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123} "task" => array:2 [ "refs" => "1438124" "type" => "task" ] "text" => "<p><strong>6.</strong> Выберите прямолинейный участок дороги и измерьте его длину.</p><p>Прокатитесь по очереди на велосипеде по этому участку, измеряя каждый раз время движения. Оцените среднюю скорость движения каждого из учеников. Проведите все необходимые измерения для того, чтобы определить в каждом случае среднюю частоту вращения: а) колеса велосипеда; б) ведомой звёздочки; в) ведущей звёздочки. Сравните полученные результаты и сформулируйте выводы. Оцените погрешности результатов.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "482" "height" => 195 "path" => "/media/fizika_09/grachev-u/0-10upr/6-1.webp?ts=1759503102" ] ] ] #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 {#1130 #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" => 1812687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Edition {#1132 #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" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …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 {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …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 {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …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" => "1438124" "type" => "task" ] "text" => "<p>Поскольку данная задача является практической, для её решения приведём примерные данные, которые могли бы быть получены в ходе эксперимента.</p><p><strong>Дано:</strong></p><p>Длина прямолинейного участка дороги: $s = 100 \text{ м}$</p><p>Время движения по участку: $t = 25 \text{ с}$</p><p>Диаметр колеса велосипеда: $D_{кол} = 70 \text{ см}$</p><p>Число зубьев на ведущей звёздочке: $Z_{вед} = 48$</p><p>Число зубьев на ведомой звёздочке: $Z_{ведом} = 16$</p><p>Перевод в систему СИ:</p><p>$s = 100 \text{ м}$</p><p>$t = 25 \text{ с}$</p><p>Радиус колеса: $R_{кол} = \frac{D_{кол}}{2} = \frac{70 \text{ см}}{2} = 35 \text{ см} = 0.35 \text{ м}$</p><p><strong>Найти:</strong></p><p>$v_{ср}$ — средняя скорость движения</p><p>$\nu_{кол}$ — средняя частота вращения колеса</p><p>$\nu_{ведом}$ — средняя частота вращения ведомой звёздочки</p><p>$\nu_{вед}$ — средняя частота вращения ведущей звёздочки</p><p><strong>Решение:</strong></p><p>Сначала оценим среднюю скорость движения ученика. Средняя скорость — это отношение пройденного пути ко времени, за которое этот путь пройден.</p><p>$v_{ср} = \frac{s}{t}$</p><p>$v_{ср} = \frac{100 \text{ м}}{25 \text{ с}} = 4 \text{ м/с}$</p><p><strong>Ответ:</strong> Средняя скорость движения составляет 4 м/с.</p><p>Теперь определим средние частоты вращения.</p><p><strong>а) колеса велосипеда</strong></p><p>Линейная скорость движения велосипеда связана с частотой вращения его колеса формулой:</p><p>$v_{ср} = 2\pi R_{кол} \nu_{кол}$</p><p>Отсюда выразим частоту вращения колеса:</p><p>$\nu_{кол} = \frac{v_{ср}}{2\pi R_{кол}}$</p><p>$\nu_{кол} = \frac{4 \text{ м/с}}{2 \cdot 3.14 \cdot 0.35 \text{ м}} \approx 1.82 \text{ об/с} = 1.82 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения колеса велосипеда $\nu_{кол} \approx 1.82 \text{ Гц}$.</p><p><strong>б) ведомой звёздочки</strong></p><p>Ведомая (задняя) звёздочка установлена на оси заднего колеса и вращается вместе с ним. Следовательно, их угловые скорости и частоты вращения равны.</p><p>$\nu_{ведом} = \nu_{кол} \approx 1.82 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения ведомой звёздочки $\nu_{ведом} \approx 1.82 \text{ Гц}$.</p><p><strong>в) ведущей звёздочки</strong></p><p>Ведущая (передняя) и ведомая (задняя) звёздочки соединены цепью. Линейная скорость движения цепи одинакова для обеих звёздочек. Линейная скорость точек на окружности звёздочки связана с её частотой вращения и радиусом ($v = 2\pi R \nu$). Радиус звёздочки пропорционален числу зубьев ($R \propto Z$). Таким образом, можно записать соотношение:</p><p>$v_{цепи} = 2\pi R_{вед} \nu_{вед} = 2\pi R_{ведом} \nu_{ведом}$</p><p>Учитывая пропорциональность радиуса числу зубьев, получаем:</p><p>$Z_{вед} \nu_{вед} = Z_{ведом} \nu_{ведом}$</p><p>Отсюда выразим частоту вращения ведущей звёздочки:</p><p>$\nu_{вед} = \nu_{ведом} \frac{Z_{ведом}}{Z_{вед}}$</p><p>$\nu_{вед} = 1.82 \text{ Гц} \cdot \frac{16}{48} = 1.82 \text{ Гц} \cdot \frac{1}{3} \approx 0.61 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения ведущей звёздочки $\nu_{вед} \approx 0.61 \text{ Гц}$.</p><p><strong>Сравнение результатов и выводы</strong></p><p>Сравним полученные частоты:</p><p>$\nu_{кол} = \nu_{ведом} \approx 1.82 \text{ Гц}$</p><p>$\nu_{вед} \approx 0.61 \text{ Гц}$</p><p>Видно, что $\nu_{кол} = \nu_{ведом} > \nu_{вед}$.</p><p><strong>Выводы:</strong></p><p><strong>1.</strong> Частота вращения колеса и ведомой звёздочки одинаковы, так как они жёстко соединены и вращаются как единое целое.</p><p><strong>2.</strong> Частота вращения ведущей звёздочки (частота вращения педалей) в 3 раза меньше частоты вращения заднего колеса. Это означает, что за один оборот педалей колесо совершает три оборота. Такая трансмиссия называется повышающей и позволяет развивать высокую скорость движения.</p><p><strong>3.</strong> Отношение частот вращения звёздочек обратно пропорционально отношению чисел их зубьев: $\frac{\nu_{ведом}}{\nu_{вед}} = \frac{Z_{вед}}{Z_{ведом}}$.</p><p><strong>Оценка погрешностей результатов</strong></p><p>Основными источниками погрешности являются измерения длины, времени и радиуса колеса. Примем абсолютные погрешности измерений: $\Delta s = 0.5 \text{ м}$ (измерение рулеткой), $\Delta t = 0.5 \text{ с}$ (реакция при использовании секундомера), $\Delta R_{кол} = 0.005 \text{ м}$ (измерение линейкой). Число зубьев является точной величиной.</p><p>Относительная погрешность измерения скорости: $\varepsilon_v = \frac{\Delta s}{s} + \frac{\Delta t}{t} = \frac{0.5}{100} + \frac{0.5}{25} = 0.005 + 0.02 = 0.025 = 2.5\%$.</p><p>Абсолютная погрешность скорости: $\Delta v_{ср} = v_{ср} \cdot \varepsilon_v = 4 \text{ м/с} \cdot 0.025 = 0.1 \text{ м/с}$.</p><p>Результат измерения скорости: $v_{ср} = (4.0 \pm 0.1) \text{ м/с}$.</p><p>Относительная погрешность измерения частоты вращения колеса: $\varepsilon_{\nu_{кол}} = \varepsilon_v + \frac{\Delta R_{кол}}{R_{кол}} = 0.025 + \frac{0.005}{0.35} \approx 0.025 + 0.014 = 0.039 = 3.9\%$.</p><p>Абсолютная погрешность частоты вращения колеса: $\Delta \nu_{кол} = \nu_{кол} \cdot \varepsilon_{\nu_{кол}} = 1.82 \text{ Гц} \cdot 0.039 \approx 0.07 \text{ Гц}$.</p><p>Результаты измерений частот с учётом погрешностей:</p><p>$\nu_{кол} = \nu_{ведом} = (1.82 \pm 0.07) \text{ Гц}$.</p><p>$\nu_{вед} = (0.61 \pm 0.02) \text{ Гц}$ (абсолютная погрешность $\Delta \nu_{вед} = 0.61 \cdot 0.039 \approx 0.024 \text{ Гц}$).</p>" ] #original: array:6 [ "id" => 1812687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131} "task" => array:2 [ "refs" => "1438124" "type" => "task" ] "text" => "<p>Поскольку данная задача является практической, для её решения приведём примерные данные, которые могли бы быть получены в ходе эксперимента.</p><p><strong>Дано:</strong></p><p>Длина прямолинейного участка дороги: $s = 100 \text{ м}$</p><p>Время движения по участку: $t = 25 \text{ с}$</p><p>Диаметр колеса велосипеда: $D_{кол} = 70 \text{ см}$</p><p>Число зубьев на ведущей звёздочке: $Z_{вед} = 48$</p><p>Число зубьев на ведомой звёздочке: $Z_{ведом} = 16$</p><p>Перевод в систему СИ:</p><p>$s = 100 \text{ м}$</p><p>$t = 25 \text{ с}$</p><p>Радиус колеса: $R_{кол} = \frac{D_{кол}}{2} = \frac{70 \text{ см}}{2} = 35 \text{ см} = 0.35 \text{ м}$</p><p><strong>Найти:</strong></p><p>$v_{ср}$ — средняя скорость движения</p><p>$\nu_{кол}$ — средняя частота вращения колеса</p><p>$\nu_{ведом}$ — средняя частота вращения ведомой звёздочки</p><p>$\nu_{вед}$ — средняя частота вращения ведущей звёздочки</p><p><strong>Решение:</strong></p><p>Сначала оценим среднюю скорость движения ученика. Средняя скорость — это отношение пройденного пути ко времени, за которое этот путь пройден.</p><p>$v_{ср} = \frac{s}{t}$</p><p>$v_{ср} = \frac{100 \text{ м}}{25 \text{ с}} = 4 \text{ м/с}$</p><p><strong>Ответ:</strong> Средняя скорость движения составляет 4 м/с.</p><p>Теперь определим средние частоты вращения.</p><p><strong>а) колеса велосипеда</strong></p><p>Линейная скорость движения велосипеда связана с частотой вращения его колеса формулой:</p><p>$v_{ср} = 2\pi R_{кол} \nu_{кол}$</p><p>Отсюда выразим частоту вращения колеса:</p><p>$\nu_{кол} = \frac{v_{ср}}{2\pi R_{кол}}$</p><p>$\nu_{кол} = \frac{4 \text{ м/с}}{2 \cdot 3.14 \cdot 0.35 \text{ м}} \approx 1.82 \text{ об/с} = 1.82 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения колеса велосипеда $\nu_{кол} \approx 1.82 \text{ Гц}$.</p><p><strong>б) ведомой звёздочки</strong></p><p>Ведомая (задняя) звёздочка установлена на оси заднего колеса и вращается вместе с ним. Следовательно, их угловые скорости и частоты вращения равны.</p><p>$\nu_{ведом} = \nu_{кол} \approx 1.82 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения ведомой звёздочки $\nu_{ведом} \approx 1.82 \text{ Гц}$.</p><p><strong>в) ведущей звёздочки</strong></p><p>Ведущая (передняя) и ведомая (задняя) звёздочки соединены цепью. Линейная скорость движения цепи одинакова для обеих звёздочек. Линейная скорость точек на окружности звёздочки связана с её частотой вращения и радиусом ($v = 2\pi R \nu$). Радиус звёздочки пропорционален числу зубьев ($R \propto Z$). Таким образом, можно записать соотношение:</p><p>$v_{цепи} = 2\pi R_{вед} \nu_{вед} = 2\pi R_{ведом} \nu_{ведом}$</p><p>Учитывая пропорциональность радиуса числу зубьев, получаем:</p><p>$Z_{вед} \nu_{вед} = Z_{ведом} \nu_{ведом}$</p><p>Отсюда выразим частоту вращения ведущей звёздочки:</p><p>$\nu_{вед} = \nu_{ведом} \frac{Z_{ведом}}{Z_{вед}}$</p><p>$\nu_{вед} = 1.82 \text{ Гц} \cdot \frac{16}{48} = 1.82 \text{ Гц} \cdot \frac{1}{3} \approx 0.61 \text{ Гц}$</p><p><strong>Ответ:</strong> Средняя частота вращения ведущей звёздочки $\nu_{вед} \approx 0.61 \text{ Гц}$.</p><p><strong>Сравнение результатов и выводы</strong></p><p>Сравним полученные частоты:</p><p>$\nu_{кол} = \nu_{ведом} \approx 1.82 \text{ Гц}$</p><p>$\nu_{вед} \approx 0.61 \text{ Гц}$</p><p>Видно, что $\nu_{кол} = \nu_{ведом} > \nu_{вед}$.</p><p><strong>Выводы:</strong></p><p><strong>1.</strong> Частота вращения колеса и ведомой звёздочки одинаковы, так как они жёстко соединены и вращаются как единое целое.</p><p><strong>2.</strong> Частота вращения ведущей звёздочки (частота вращения педалей) в 3 раза меньше частоты вращения заднего колеса. Это означает, что за один оборот педалей колесо совершает три оборота. Такая трансмиссия называется повышающей и позволяет развивать высокую скорость движения.</p><p><strong>3.</strong> Отношение частот вращения звёздочек обратно пропорционально отношению чисел их зубьев: $\frac{\nu_{ведом}}{\nu_{вед}} = \frac{Z_{вед}}{Z_{ведом}}$.</p><p><strong>Оценка погрешностей результатов</strong></p><p>Основными источниками погрешности являются измерения длины, времени и радиуса колеса. Примем абсолютные погрешности измерений: $\Delta s = 0.5 \text{ м}$ (измерение рулеткой), $\Delta t = 0.5 \text{ с}$ (реакция при использовании секундомера), $\Delta R_{кол} = 0.005 \text{ м}$ (измерение линейкой). Число зубьев является точной величиной.</p><p>Относительная погрешность измерения скорости: $\varepsilon_v = \frac{\Delta s}{s} + \frac{\Delta t}{t} = \frac{0.5}{100} + \frac{0.5}{25} = 0.005 + 0.02 = 0.025 = 2.5\%$.</p><p>Абсолютная погрешность скорости: $\Delta v_{ср} = v_{ср} \cdot \varepsilon_v = 4 \text{ м/с} \cdot 0.025 = 0.1 \text{ м/с}$.</p><p>Результат измерения скорости: $v_{ср} = (4.0 \pm 0.1) \text{ м/с}$.</p><p>Относительная погрешность измерения частоты вращения колеса: $\varepsilon_{\nu_{кол}} = \varepsilon_v + \frac{\Delta R_{кол}}{R_{кол}} = 0.025 + \frac{0.005}{0.35} \approx 0.025 + 0.014 = 0.039 = 3.9\%$.</p><p>Абсолютная погрешность частоты вращения колеса: $\Delta \nu_{кол} = \nu_{кол} \cdot \varepsilon_{\nu_{кол}} = 1.82 \text{ Гц} \cdot 0.039 \approx 0.07 \text{ Гц}$.</p><p>Результаты измерений частот с учётом погрешностей:</p><p>$\nu_{кол} = \nu_{ведом} = (1.82 \pm 0.07) \text{ Гц}$.</p><p>$\nu_{вед} = (0.61 \pm 0.02) \text{ Гц}$ (абсолютная погрешность $\Delta \nu_{вед} = 0.61 \cdot 0.039 \approx 0.024 \text{ Гц}$).</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" => "1438125" "type" => "task" ] "previous" => array:2 [ "refs" => "1438123" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1409 #items: array:1 [ 0 => App\Models\BookPage {#1142 #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" => 1437568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-62" "field_display_title" => "62" "field_folder" => "1" "field_image_name" => "62" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Book {#1147 #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" => 1202 "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 {#1148 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1158 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "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 {#1174 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1177 …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" => 1202 "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 {#1148 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1154 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1158 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1168 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "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 {#1174 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1177 …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 } "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 {#1179 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\Element {#1181 #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" => 1705564 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1182 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1705564 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1182 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1437569" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437567" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:13 [ 0 => App\Models\Task {#1190 #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" => 1438112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1193 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1194 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1262 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1193 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1194 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1262 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1263 #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" => 1438113 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1273 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438113 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1264 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1266 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1267 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1273 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1274 #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" => 1438114 "created_at" => "2026-04-10 13:58:26" …22 ] #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 {#1285 #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 {#1296 #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] } 5 => App\Models\Task {#1307 #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] } 6 => App\Models\Task {#1318 #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] } 7 => App\Models\Task {#1329 #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] } 8 => App\Models\Task {#1352 #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] } 9 => App\Models\Task {#1363 #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] } 10 => App\Models\Task {#1374 #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] } 11 => App\Models\Task {#1385 #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] } 12 => App\Models\Task {#1396 #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" => 1437568 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-62" "field_display_title" => "62" "field_folder" => "1" "field_image_name" => "62" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1146} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1145} "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 {#1179} "content" => Illuminate\Database\Eloquent\Collection {#1180} "next" => array:2 [ "refs" => "1437569" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437567" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1189} ] #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" => 1438124 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "62" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/10upr-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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 {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1066} "content" => Illuminate\Database\Eloquent\Collection {#1121} "next" => array:2 [ "refs" => "1438125" "type" => "task" ] "previous" => array:2 [ "refs" => "1438123" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1138} "page" => array:2 [ "refs" => "1437568" "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 => "*" ] }
№6 (с. 62)
Условие. №6 (с. 62)
скриншот условия
6. Выберите прямолинейный участок дороги и измерьте его длину.
Прокатитесь по очереди на велосипеде по этому участку, измеряя каждый раз время движения. Оцените среднюю скорость движения каждого из учеников. Проведите все необходимые измерения для того, чтобы определить в каждом случае среднюю частоту вращения: а) колеса велосипеда; б) ведомой звёздочки; в) ведущей звёздочки. Сравните полученные результаты и сформулируйте выводы. Оцените погрешности результатов.
Решение. №6 (с. 62)
Поскольку данная задача является практической, для её решения приведём примерные данные, которые могли бы быть получены в ходе эксперимента.
Дано:
Длина прямолинейного участка дороги: $s = 100 \text{ м}$
Время движения по участку: $t = 25 \text{ с}$
Диаметр колеса велосипеда: $D_{кол} = 70 \text{ см}$
Число зубьев на ведущей звёздочке: $Z_{вед} = 48$
Число зубьев на ведомой звёздочке: $Z_{ведом} = 16$
Перевод в систему СИ:
$s = 100 \text{ м}$
$t = 25 \text{ с}$
Радиус колеса: $R_{кол} = \frac{D_{кол}}{2} = \frac{70 \text{ см}}{2} = 35 \text{ см} = 0.35 \text{ м}$
Найти:
$v_{ср}$ — средняя скорость движения
$\nu_{кол}$ — средняя частота вращения колеса
$\nu_{ведом}$ — средняя частота вращения ведомой звёздочки
$\nu_{вед}$ — средняя частота вращения ведущей звёздочки
Решение:
Сначала оценим среднюю скорость движения ученика. Средняя скорость — это отношение пройденного пути ко времени, за которое этот путь пройден.
$v_{ср} = \frac{s}{t}$
$v_{ср} = \frac{100 \text{ м}}{25 \text{ с}} = 4 \text{ м/с}$
Ответ: Средняя скорость движения составляет 4 м/с.
Теперь определим средние частоты вращения.
а) колеса велосипеда
Линейная скорость движения велосипеда связана с частотой вращения его колеса формулой:
$v_{ср} = 2\pi R_{кол} \nu_{кол}$
Отсюда выразим частоту вращения колеса:
$\nu_{кол} = \frac{v_{ср}}{2\pi R_{кол}}$
$\nu_{кол} = \frac{4 \text{ м/с}}{2 \cdot 3.14 \cdot 0.35 \text{ м}} \approx 1.82 \text{ об/с} = 1.82 \text{ Гц}$
Ответ: Средняя частота вращения колеса велосипеда $\nu_{кол} \approx 1.82 \text{ Гц}$.
б) ведомой звёздочки
Ведомая (задняя) звёздочка установлена на оси заднего колеса и вращается вместе с ним. Следовательно, их угловые скорости и частоты вращения равны.
$\nu_{ведом} = \nu_{кол} \approx 1.82 \text{ Гц}$
Ответ: Средняя частота вращения ведомой звёздочки $\nu_{ведом} \approx 1.82 \text{ Гц}$.
в) ведущей звёздочки
Ведущая (передняя) и ведомая (задняя) звёздочки соединены цепью. Линейная скорость движения цепи одинакова для обеих звёздочек. Линейная скорость точек на окружности звёздочки связана с её частотой вращения и радиусом ($v = 2\pi R \nu$). Радиус звёздочки пропорционален числу зубьев ($R \propto Z$). Таким образом, можно записать соотношение:
$v_{цепи} = 2\pi R_{вед} \nu_{вед} = 2\pi R_{ведом} \nu_{ведом}$
Учитывая пропорциональность радиуса числу зубьев, получаем:
$Z_{вед} \nu_{вед} = Z_{ведом} \nu_{ведом}$
Отсюда выразим частоту вращения ведущей звёздочки:
$\nu_{вед} = \nu_{ведом} \frac{Z_{ведом}}{Z_{вед}}$
$\nu_{вед} = 1.82 \text{ Гц} \cdot \frac{16}{48} = 1.82 \text{ Гц} \cdot \frac{1}{3} \approx 0.61 \text{ Гц}$
Ответ: Средняя частота вращения ведущей звёздочки $\nu_{вед} \approx 0.61 \text{ Гц}$.
Сравнение результатов и выводы
Сравним полученные частоты:
$\nu_{кол} = \nu_{ведом} \approx 1.82 \text{ Гц}$
$\nu_{вед} \approx 0.61 \text{ Гц}$
Видно, что $\nu_{кол} = \nu_{ведом} > \nu_{вед}$.
Выводы:
1. Частота вращения колеса и ведомой звёздочки одинаковы, так как они жёстко соединены и вращаются как единое целое.
2. Частота вращения ведущей звёздочки (частота вращения педалей) в 3 раза меньше частоты вращения заднего колеса. Это означает, что за один оборот педалей колесо совершает три оборота. Такая трансмиссия называется повышающей и позволяет развивать высокую скорость движения.
3. Отношение частот вращения звёздочек обратно пропорционально отношению чисел их зубьев: $\frac{\nu_{ведом}}{\nu_{вед}} = \frac{Z_{вед}}{Z_{ведом}}$.
Оценка погрешностей результатов
Основными источниками погрешности являются измерения длины, времени и радиуса колеса. Примем абсолютные погрешности измерений: $\Delta s = 0.5 \text{ м}$ (измерение рулеткой), $\Delta t = 0.5 \text{ с}$ (реакция при использовании секундомера), $\Delta R_{кол} = 0.005 \text{ м}$ (измерение линейкой). Число зубьев является точной величиной.
Относительная погрешность измерения скорости: $\varepsilon_v = \frac{\Delta s}{s} + \frac{\Delta t}{t} = \frac{0.5}{100} + \frac{0.5}{25} = 0.005 + 0.02 = 0.025 = 2.5\%$.
Абсолютная погрешность скорости: $\Delta v_{ср} = v_{ср} \cdot \varepsilon_v = 4 \text{ м/с} \cdot 0.025 = 0.1 \text{ м/с}$.
Результат измерения скорости: $v_{ср} = (4.0 \pm 0.1) \text{ м/с}$.
Относительная погрешность измерения частоты вращения колеса: $\varepsilon_{\nu_{кол}} = \varepsilon_v + \frac{\Delta R_{кол}}{R_{кол}} = 0.025 + \frac{0.005}{0.35} \approx 0.025 + 0.014 = 0.039 = 3.9\%$.
Абсолютная погрешность частоты вращения колеса: $\Delta \nu_{кол} = \nu_{кол} \cdot \varepsilon_{\nu_{кол}} = 1.82 \text{ Гц} \cdot 0.039 \approx 0.07 \text{ Гц}$.
Результаты измерений частот с учётом погрешностей:
$\nu_{кол} = \nu_{ведом} = (1.82 \pm 0.07) \text{ Гц}$.
$\nu_{вед} = (0.61 \pm 0.02) \text{ Гц}$ (абсолютная погрешность $\Delta \nu_{вед} = 0.61 \cdot 0.039 \approx 0.024 \text{ Гц}$).
Другие задания:
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