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Номер 8, страница 29, часть 2 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 2
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 2. Глава 4. Механическая работа. Механическая энергия. Закон сохранения механической энергии. Параграф 27. Потенциальная энергия - номер 8, страница 29.
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" => 1435090 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "29" "field_page_end" => "30" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/27-8" "field_display_title" => "8" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #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" => "3" "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" => 1203 "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 {#1063 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 1203 "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 {#1063 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "3" "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 {#1073} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:3 [ 0 => App\Models\Branch {#1165 #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" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 #items: array:1 [ 0 => App\Models\Term {#1166 #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" => "3" "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 {#1202 #items: array:1 [ 0 => App\Models\Book {#1168 #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" => 1203 "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 {#1170 #items: array:1 [ 0 => App\Models\Term {#1167 #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 {#1171 #items: array:1 [ 0 => App\Models\Term {#1172 #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 {#1173 #items: array:1 [ 0 => App\Models\Term {#1174 #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 {#1175 #items: array:4 [ 0 => App\Models\Term {#1176 #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 {#1177 #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 {#1178 #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 => "*" ] } 3 => App\Models\Term {#1179 #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" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1180 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Term {#1182 #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" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1183 #items: array:1 [ 0 => App\Models\Term {#1184 #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 {#1185 #items: array:1 [ 0 => App\Models\Term {#1186 #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 {#1187 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1188 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190 #items: array:1 [ 0 => App\Models\Term {#1191 #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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192 #items: array:1 [ 0 => App\Models\Term {#1193 #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 {#1194 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198 #items: array:1 [ 0 => App\Models\Term {#1199 #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" => 1203 "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 {#1170} "field_class" => Illuminate\Database\Eloquent\Collection {#1171} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173} "field_author" => Illuminate\Database\Eloquent\Collection {#1175} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1180} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1181} "field_country" => Illuminate\Database\Eloquent\Collection {#1183} "field_city" => Illuminate\Database\Eloquent\Collection {#1185} "field_series" => Illuminate\Database\Eloquent\Collection {#1187} "field_umk" => Illuminate\Database\Eloquent\Collection {#1188} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1194} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198} "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 {#1200 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434829 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169} "field_page_start" => "3" "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 {#1202} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1200} ] #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 {#1201 #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" => 1434833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механическая работа. Механическая энергия. Закон сохранения механической энергии" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1203 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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" => "17" "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 {#1205 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механическая работа. Механическая энергия. 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Механическая энергия. Закон сохранения механической энергии" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_page_start" => "17" "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 {#1214 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 …2} ] #original: array:24 [ "id" => 1434833 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механическая работа. Механическая энергия. Закон сохранения механической энергии" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_page_start" => "17" "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 {#1214 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 …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" => 1434836 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Потенциальная энергия" "field_branch_order" => "27" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "26" "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 {#1210} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1255} ] #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 {#1112 #items: array:2 [ 0 => App\Models\Element {#1144 #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" => 1698478 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ 0 => App\Models\Edition {#1143 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …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" => "1435090" "type" => "task" ] "text" => "<p><strong>8*.</strong> На рис. 12, а показана лёгкая пружина жёсткостью $k = 100 \text{ Н/м}$, подвешенная к потолку комнаты. Изобразите, соблюдая масштабы, эту пружину на рис. 12, б с подвешенным на ней к потолку комнаты грузом массой 2 кг, а на рис. 12, в эту пружину, прикреплённую нижним концом к полу, с лежащим на ней грузом массой 2 кг. Ось пружины при этом расположена вертикально.</p><p>Puc. 12</p><p>Заполните таблицу, определив неизвестные величины. Считайте, что потенциальная энергия системы «груз — Земля» в исходном состоянии (рис. 12, а) равна нулю.</p><p><strong>Величины</strong> | <strong>Пружина с подвешенным к ней грузом (рис. 12, б)</strong> | <strong>Пружина с лежащим на ней грузом (рис. 12, в)</strong></p><p>Потенциальная энергия деформированной пружины | |</p><p>Потенциальная энергия системы «груз — Земля» | |</p><p>Потенциальная энергия системы «груз — пружина — Земля» | |</p>" "img" => array:2 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "2002" "height" => 1306 "path" => "/media/fizika_09/grachev-rt/0-27/8-1.webp?ts=1759402754" ] 1 => array:5 [ "name" => "8-2.jpg" "alt" => null "width" => "1995" "height" => 899 "path" => "/media/fizika_09/grachev-rt/0-27/8-2.webp?ts=1759402754" ] ] ] #original: array:7 [ "id" => 1698478 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1135} "task" => array:2 [ "refs" => "1435090" "type" => "task" ] "text" => "<p><strong>8*.</strong> На рис. 12, а показана лёгкая пружина жёсткостью $k = 100 \text{ Н/м}$, подвешенная к потолку комнаты. Изобразите, соблюдая масштабы, эту пружину на рис. 12, б с подвешенным на ней к потолку комнаты грузом массой 2 кг, а на рис. 12, в эту пружину, прикреплённую нижним концом к полу, с лежащим на ней грузом массой 2 кг. Ось пружины при этом расположена вертикально.</p><p>Puc. 12</p><p>Заполните таблицу, определив неизвестные величины. Считайте, что потенциальная энергия системы «груз — Земля» в исходном состоянии (рис. 12, а) равна нулю.</p><p><strong>Величины</strong> | <strong>Пружина с подвешенным к ней грузом (рис. 12, б)</strong> | <strong>Пружина с лежащим на ней грузом (рис. 12, в)</strong></p><p>Потенциальная энергия деформированной пружины | |</p><p>Потенциальная энергия системы «груз — Земля» | |</p><p>Потенциальная энергия системы «груз — пружина — Земля» | |</p>" "img" => array:2 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "2002" "height" => 1306 "path" => "/media/fizika_09/grachev-rt/0-27/8-1.webp?ts=1759402754" ] 1 => array:5 [ "name" => "8-2.jpg" "alt" => null "width" => "1995" "height" => 899 "path" => "/media/fizika_09/grachev-rt/0-27/8-2.webp?ts=1759402754" ] ] ] #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 {#1137 #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" => 1734464 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Edition {#1136 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132 …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" => "1435090" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Жёсткость пружины, $k = 100 \text{ Н/м}$</p> <p>Масса груза, $m = 2 \text{ кг}$</p> <p>Длина недеформированной пружины (из рис. 12, а), $l_0 = 20 \text{ см}$</p> <p>Ускорение свободного падения, $g \approx 10 \text{ м/с}^2$</p> <p>Потенциальная энергия системы «груз – Земля» в исходном состоянии равна нулю (нулевой уровень на полу).</p> <p> $l_0 = 20 \text{ см} = 0.2 \text{ м}$ </p> <p><strong>Найти:</strong></p> <p>Потенциальную энергию деформированной пружины, потенциальную энергию системы «груз – Земля» и общую потенциальную энергию системы «груз – пружина – Земля» для случаев, изображенных на рис. 12, б и 12, в.</p> <p><strong>Решение:</strong></p> <p>Сначала найдём величину деформации пружины под действием веса груза. В обоих случаях (подвешенный груз и лежащий на пружине груз) система находится в равновесии. Это означает, что сила упругости пружины $F_{упр}$ уравновешивает силу тяжести $F_g$, действующую на груз.</p> <p>Сила тяжести: $F_g = mg = 2 \text{ кг} \cdot 10 \text{ м/с}^2 = 20 \text{ Н}$.</p> <p>По закону Гука, $F_{упр} = k \Delta x$. Так как $F_{упр} = F_g$, то деформация пружины (растяжение или сжатие) $\Delta x$ равна:</p> <p>$\Delta x = \frac{F_g}{k} = \frac{20 \text{ Н}}{100 \text{ Н/м}} = 0.2 \text{ м}$.</p> <p>Теперь, зная деформацию, мы можем рассчитать потенциальные энергии для каждого случая.</p> <p><strong>Пружина с подвешенным к ней грузом (рис. 12, б)</strong></p> <p>1. <i>Потенциальная энергия деформированной пружины.</i></p> <p>Пружина растянута на $\Delta x = 0.2 \text{ м}$. Её потенциальная энергия рассчитывается по формуле:</p> <p>$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = \frac{100 \text{ Н/м} \cdot (0.2 \text{ м})^2}{2} = \frac{100 \cdot 0.04}{2} = 2 \text{ Дж}$.</p> <p>2. <i>Потенциальная энергия системы «груз – Земля».</i></p> <p>Для определения этой энергии нужно найти высоту $h_б$ груза над полом. Из рисунка 12, а видно, что длина недеформированной пружины $l_0 = 20 \text{ см} = 0.2 \text{ м}$. Масштаб на стене показывает, что высота комнаты от пола до потолка $H$ вдвое больше длины пружины: $H = 2 \cdot l_0 = 2 \cdot 0.2 \text{ м} = 0.4 \text{ м}$.</p> <p>В растянутом состоянии длина пружины $l_б = l_0 + \Delta x = 0.2 \text{ м} + 0.2 \text{ м} = 0.4 \text{ м}$.</p> <p>Поскольку пружина подвешена к потолку, высота груза над полом будет: $h_б = H - l_б = 0.4 \text{ м} - 0.4 \text{ м} = 0 \text{ м}$.</p> <p>Следовательно, потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_б = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.</p> <p>3. <i>Потенциальная энергия системы «груз – пружина – Земля».</i></p> <p>Это полная потенциальная энергия системы, равная сумме энергий пружины и груза:</p> <p>$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.</p> <p><strong>Ответ:</strong> Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.</p> <p><strong>Пружина с лежащим на ней грузом (рис. 12, в)</strong></p> <p>1. <i>Потенциальная энергия деформированной пружины.</i></p> <p>Пружина сжата на ту же величину $\Delta x = 0.2 \text{ м}$. Поэтому её потенциальная энергия такая же, как и в предыдущем случае:</p> <p>$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = 2 \text{ Дж}$.</p> <p>2. <i>Потенциальная энергия системы «груз – Земля».</i></p> <p>В этом случае пружина стоит на полу. Её высота в сжатом состоянии: $l_в = l_0 - \Delta x = 0.2 \text{ м} - 0.2 \text{ м} = 0 \text{ м}$.</p> <p>Груз лежит на пружине, поэтому его высота над полом $h_в = l_в = 0 \text{ м}$.</p> <p>Потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_в = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.</p> <p>3. <i>Потенциальная энергия системы «груз – пружина – Земля».</i></p> <p>Полная потенциальная энергия системы:</p> <p>$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.</p> <p><strong>Ответ:</strong> Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.</p> <p>Итоговая таблица:</p> <div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"> <thead> <tr> <th style="border: 1px solid rgb(0, 0, 0);">Величины</th> <th style="border: 1px solid rgb(0, 0, 0);">Пружина с подвешенным к ней грузом (рис. 12, б)</th> <th style="border: 1px solid rgb(0, 0, 0);">Пружина с лежащим на ней грузом (рис. 12, в)</th> </tr> </thead> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия деформированной пружины</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия системы «груз – Земля»</td> <td style="border: 1px solid rgb(0, 0, 0);">0 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">0 Дж</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия системы «груз – пружина – Земля»</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> </tr> </tbody> </table></div>" ] #original: array:6 [ "id" => 1734464 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123} "task" => array:2 [ "refs" => "1435090" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Жёсткость пружины, $k = 100 \text{ Н/м}$</p> <p>Масса груза, $m = 2 \text{ кг}$</p> <p>Длина недеформированной пружины (из рис. 12, а), $l_0 = 20 \text{ см}$</p> <p>Ускорение свободного падения, $g \approx 10 \text{ м/с}^2$</p> <p>Потенциальная энергия системы «груз – Земля» в исходном состоянии равна нулю (нулевой уровень на полу).</p> <p> $l_0 = 20 \text{ см} = 0.2 \text{ м}$ </p> <p><strong>Найти:</strong></p> <p>Потенциальную энергию деформированной пружины, потенциальную энергию системы «груз – Земля» и общую потенциальную энергию системы «груз – пружина – Земля» для случаев, изображенных на рис. 12, б и 12, в.</p> <p><strong>Решение:</strong></p> <p>Сначала найдём величину деформации пружины под действием веса груза. В обоих случаях (подвешенный груз и лежащий на пружине груз) система находится в равновесии. Это означает, что сила упругости пружины $F_{упр}$ уравновешивает силу тяжести $F_g$, действующую на груз.</p> <p>Сила тяжести: $F_g = mg = 2 \text{ кг} \cdot 10 \text{ м/с}^2 = 20 \text{ Н}$.</p> <p>По закону Гука, $F_{упр} = k \Delta x$. Так как $F_{упр} = F_g$, то деформация пружины (растяжение или сжатие) $\Delta x$ равна:</p> <p>$\Delta x = \frac{F_g}{k} = \frac{20 \text{ Н}}{100 \text{ Н/м}} = 0.2 \text{ м}$.</p> <p>Теперь, зная деформацию, мы можем рассчитать потенциальные энергии для каждого случая.</p> <p><strong>Пружина с подвешенным к ней грузом (рис. 12, б)</strong></p> <p>1. <i>Потенциальная энергия деформированной пружины.</i></p> <p>Пружина растянута на $\Delta x = 0.2 \text{ м}$. Её потенциальная энергия рассчитывается по формуле:</p> <p>$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = \frac{100 \text{ Н/м} \cdot (0.2 \text{ м})^2}{2} = \frac{100 \cdot 0.04}{2} = 2 \text{ Дж}$.</p> <p>2. <i>Потенциальная энергия системы «груз – Земля».</i></p> <p>Для определения этой энергии нужно найти высоту $h_б$ груза над полом. Из рисунка 12, а видно, что длина недеформированной пружины $l_0 = 20 \text{ см} = 0.2 \text{ м}$. Масштаб на стене показывает, что высота комнаты от пола до потолка $H$ вдвое больше длины пружины: $H = 2 \cdot l_0 = 2 \cdot 0.2 \text{ м} = 0.4 \text{ м}$.</p> <p>В растянутом состоянии длина пружины $l_б = l_0 + \Delta x = 0.2 \text{ м} + 0.2 \text{ м} = 0.4 \text{ м}$.</p> <p>Поскольку пружина подвешена к потолку, высота груза над полом будет: $h_б = H - l_б = 0.4 \text{ м} - 0.4 \text{ м} = 0 \text{ м}$.</p> <p>Следовательно, потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_б = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.</p> <p>3. <i>Потенциальная энергия системы «груз – пружина – Земля».</i></p> <p>Это полная потенциальная энергия системы, равная сумме энергий пружины и груза:</p> <p>$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.</p> <p><strong>Ответ:</strong> Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.</p> <p><strong>Пружина с лежащим на ней грузом (рис. 12, в)</strong></p> <p>1. <i>Потенциальная энергия деформированной пружины.</i></p> <p>Пружина сжата на ту же величину $\Delta x = 0.2 \text{ м}$. Поэтому её потенциальная энергия такая же, как и в предыдущем случае:</p> <p>$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = 2 \text{ Дж}$.</p> <p>2. <i>Потенциальная энергия системы «груз – Земля».</i></p> <p>В этом случае пружина стоит на полу. Её высота в сжатом состоянии: $l_в = l_0 - \Delta x = 0.2 \text{ м} - 0.2 \text{ м} = 0 \text{ м}$.</p> <p>Груз лежит на пружине, поэтому его высота над полом $h_в = l_в = 0 \text{ м}$.</p> <p>Потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_в = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.</p> <p>3. <i>Потенциальная энергия системы «груз – пружина – Земля».</i></p> <p>Полная потенциальная энергия системы:</p> <p>$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.</p> <p><strong>Ответ:</strong> Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.</p> <p>Итоговая таблица:</p> <div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"> <thead> <tr> <th style="border: 1px solid rgb(0, 0, 0);">Величины</th> <th style="border: 1px solid rgb(0, 0, 0);">Пружина с подвешенным к ней грузом (рис. 12, б)</th> <th style="border: 1px solid rgb(0, 0, 0);">Пружина с лежащим на ней грузом (рис. 12, в)</th> </tr> </thead> <tbody> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия деформированной пружины</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия системы «груз – Земля»</td> <td style="border: 1px solid rgb(0, 0, 0);">0 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">0 Дж</td> </tr> <tr> <td style="border: 1px solid rgb(0, 0, 0);">Потенциальная энергия системы «груз – пружина – Земля»</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> <td style="border: 1px solid rgb(0, 0, 0);">2 Дж</td> </tr> </tbody> </table></div>" ] #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" => "1435091" "type" => "task" ] "previous" => array:2 [ "refs" => "1435089" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\BookPage {#1116 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: 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№8 (с. 29)
Условие. №8 (с. 29)
скриншот условия
8*. На рис. 12, а показана лёгкая пружина жёсткостью $k = 100 \text{ Н/м}$, подвешенная к потолку комнаты. Изобразите, соблюдая масштабы, эту пружину на рис. 12, б с подвешенным на ней к потолку комнаты грузом массой 2 кг, а на рис. 12, в эту пружину, прикреплённую нижним концом к полу, с лежащим на ней грузом массой 2 кг. Ось пружины при этом расположена вертикально.
Puc. 12
Заполните таблицу, определив неизвестные величины. Считайте, что потенциальная энергия системы «груз — Земля» в исходном состоянии (рис. 12, а) равна нулю.
Величины | Пружина с подвешенным к ней грузом (рис. 12, б) | Пружина с лежащим на ней грузом (рис. 12, в)
Потенциальная энергия деформированной пружины | |
Потенциальная энергия системы «груз — Земля» | |
Потенциальная энергия системы «груз — пружина — Земля» | |
Решение. №8 (с. 29)
Дано:
Жёсткость пружины, $k = 100 \text{ Н/м}$
Масса груза, $m = 2 \text{ кг}$
Длина недеформированной пружины (из рис. 12, а), $l_0 = 20 \text{ см}$
Ускорение свободного падения, $g \approx 10 \text{ м/с}^2$
Потенциальная энергия системы «груз – Земля» в исходном состоянии равна нулю (нулевой уровень на полу).
$l_0 = 20 \text{ см} = 0.2 \text{ м}$
Найти:
Потенциальную энергию деформированной пружины, потенциальную энергию системы «груз – Земля» и общую потенциальную энергию системы «груз – пружина – Земля» для случаев, изображенных на рис. 12, б и 12, в.
Решение:
Сначала найдём величину деформации пружины под действием веса груза. В обоих случаях (подвешенный груз и лежащий на пружине груз) система находится в равновесии. Это означает, что сила упругости пружины $F_{упр}$ уравновешивает силу тяжести $F_g$, действующую на груз.
Сила тяжести: $F_g = mg = 2 \text{ кг} \cdot 10 \text{ м/с}^2 = 20 \text{ Н}$.
По закону Гука, $F_{упр} = k \Delta x$. Так как $F_{упр} = F_g$, то деформация пружины (растяжение или сжатие) $\Delta x$ равна:
$\Delta x = \frac{F_g}{k} = \frac{20 \text{ Н}}{100 \text{ Н/м}} = 0.2 \text{ м}$.
Теперь, зная деформацию, мы можем рассчитать потенциальные энергии для каждого случая.
Пружина с подвешенным к ней грузом (рис. 12, б)
1. Потенциальная энергия деформированной пружины.
Пружина растянута на $\Delta x = 0.2 \text{ м}$. Её потенциальная энергия рассчитывается по формуле:
$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = \frac{100 \text{ Н/м} \cdot (0.2 \text{ м})^2}{2} = \frac{100 \cdot 0.04}{2} = 2 \text{ Дж}$.
2. Потенциальная энергия системы «груз – Земля».
Для определения этой энергии нужно найти высоту $h_б$ груза над полом. Из рисунка 12, а видно, что длина недеформированной пружины $l_0 = 20 \text{ см} = 0.2 \text{ м}$. Масштаб на стене показывает, что высота комнаты от пола до потолка $H$ вдвое больше длины пружины: $H = 2 \cdot l_0 = 2 \cdot 0.2 \text{ м} = 0.4 \text{ м}$.
В растянутом состоянии длина пружины $l_б = l_0 + \Delta x = 0.2 \text{ м} + 0.2 \text{ м} = 0.4 \text{ м}$.
Поскольку пружина подвешена к потолку, высота груза над полом будет: $h_б = H - l_б = 0.4 \text{ м} - 0.4 \text{ м} = 0 \text{ м}$.
Следовательно, потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_б = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.
3. Потенциальная энергия системы «груз – пружина – Земля».
Это полная потенциальная энергия системы, равная сумме энергий пружины и груза:
$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.
Ответ: Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.
Пружина с лежащим на ней грузом (рис. 12, в)
1. Потенциальная энергия деформированной пружины.
Пружина сжата на ту же величину $\Delta x = 0.2 \text{ м}$. Поэтому её потенциальная энергия такая же, как и в предыдущем случае:
$E_{p, \text{пружины}} = \frac{k (\Delta x)^2}{2} = 2 \text{ Дж}$.
2. Потенциальная энергия системы «груз – Земля».
В этом случае пружина стоит на полу. Её высота в сжатом состоянии: $l_в = l_0 - \Delta x = 0.2 \text{ м} - 0.2 \text{ м} = 0 \text{ м}$.
Груз лежит на пружине, поэтому его высота над полом $h_в = l_в = 0 \text{ м}$.
Потенциальная энергия системы «груз – Земля»: $E_{p, \text{груз-Земля}} = mgh_в = 2 \cdot 10 \cdot 0 = 0 \text{ Дж}$.
3. Потенциальная энергия системы «груз – пружина – Земля».
Полная потенциальная энергия системы:
$E_{p, \text{общая}} = E_{p, \text{пружины}} + E_{p, \text{груз-Земля}} = 2 \text{ Дж} + 0 \text{ Дж} = 2 \text{ Дж}$.
Ответ: Потенциальная энергия деформированной пружины равна 2 Дж. Потенциальная энергия системы «груз – Земля» равна 0 Дж. Потенциальная энергия системы «груз – пружина – Земля» равна 2 Дж.
Итоговая таблица:
| Величины | Пружина с подвешенным к ней грузом (рис. 12, б) | Пружина с лежащим на ней грузом (рис. 12, в) |
|---|---|---|
| Потенциальная энергия деформированной пружины | 2 Дж | 2 Дж |
| Потенциальная энергия системы «груз – Земля» | 0 Дж | 0 Дж |
| Потенциальная энергия системы «груз – пружина – Земля» | 2 Дж | 2 Дж |
Другие задания:
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