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Номер 4.1, страница 20 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Механика. 4. Импульс, работа, энергия. Законы сохранения - номер 4.1, страница 20.
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" => 1288016 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "20" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/04-1" "field_display_title" => "4.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:3 [ 0 => App\Models\Branch {#1074 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Book {#1078 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …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 {#1111 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1075} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111} ] #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 {#1112 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Book {#1115 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …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 {#1148 #items: array:1 [ 0 => App\Models\Branch {#1149 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150 …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 {#1151 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152 …2} ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150 …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 {#1151 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152 …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" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113} "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 {#1114} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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 {#1153 #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" => 1287871 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Импульс, работа, энергия. Законы сохранения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "20" "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 {#1155 #items: array:1 [ 0 => App\Models\Book {#1156 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1157 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1159 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1166 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1187 …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 {#1189 #items: array:1 [ 0 => App\Models\Branch {#1190 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1191 …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 {#1192 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1193 …2} ] #original: array:24 [ "id" => 1287867 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1191 …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 {#1192 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1193 …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" => 1287871 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "4. Импульс, работа, энергия. Законы сохранения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154} "field_page_start" => "20" "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 {#1155} "branch_parent" => 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 } "content" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:3 [ 0 => App\Models\Element {#1243 #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" => 1477791 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1252 #items: array:1 [ 0 => App\Models\Edition {#1244 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1246 …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 {#1247 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1248 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1249 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1246 …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 {#1247 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1248 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1249 …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" => "1288016" "type" => "task" ] "text" => "<p><strong>4.1.</strong> Мяч массой $m = 300 \text{ г}$ упал с высоты $H = 1,23 \text{ м}$ на асфальт и подскочил на ту же высоту. Продолжительность удара об асфальт $t = 0,1 \text{ с}$. Найдите среднюю силу удара $F_{\text{cp}}$. Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом $\alpha = 30^{\circ}$ к горизонту? Какой будет $F_{\text{cp}}$, если в обоих случаях мяч заменить пластилиновым шаром той же массы? Продолжительность удара считайте той же.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1431" "height" => 449 "path" => "/media/fizika_08/gelfgat-u/0-04/1-1.webp?ts=1756049683" ] ] ] #original: array:7 [ "id" => 1477791 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1252} "task" => array:2 [ "refs" => "1288016" "type" => "task" ] "text" => "<p><strong>4.1.</strong> Мяч массой $m = 300 \text{ г}$ упал с высоты $H = 1,23 \text{ м}$ на асфальт и подскочил на ту же высоту. Продолжительность удара об асфальт $t = 0,1 \text{ с}$. Найдите среднюю силу удара $F_{\text{cp}}$. Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом $\alpha = 30^{\circ}$ к горизонту? Какой будет $F_{\text{cp}}$, если в обоих случаях мяч заменить пластилиновым шаром той же массы? Продолжительность удара считайте той же.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1431" "height" => 449 "path" => "/media/fizika_08/gelfgat-u/0-04/1-1.webp?ts=1756049683" ] ] ] #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 {#1250 #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" => 1478164 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Edition {#1251 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1254 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1255 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1257 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1254 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1255 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1257 …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" => "1288016" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1487" "height" => 1090 "path" => "/media/fizika_08/gelfgat-u/1-04/1-1.webp?ts=1756049746" ] ] ] #original: array:6 [ "id" => 1478164 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1260} "task" => array:2 [ "refs" => "1288016" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1487" "height" => 1090 "path" => "/media/fizika_08/gelfgat-u/1-04/1-1.webp?ts=1756049746" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1258 #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" => 1737709 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:1 [ 0 => App\Models\Edition {#1259 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1262 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1263 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1264 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1265 …2} "field_content_source" => null ] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288016" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 300 г<br>H = 1,23 м<br>t = 0,1 с<br>α = 30°<br>g ≈ 9,8 м/с²</p><p>Перевод в систему СИ:<br>m = 0,3 кг</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Fср при ударе об асфальт.<br>2. Как изменится Fср при ударе о наклонную поверхность.<br>3. Fср для пластилинового шара в обоих случаях.</p><p><strong>Решение:</strong></p><p>Для всех случаев сначала найдем скорость мяча непосредственно перед ударом о поверхность. Используя закон сохранения энергии, потенциальная энергия на высоте $\text{H}$ переходит в кинетическую энергию перед ударом:</p><p>$m g H = \frac{1}{2} m v^2$</p><p>Отсюда скорость $\text{v}$ равна:</p><p>$v = \sqrt{2 g H} = \sqrt{2 \cdot 9,8 \, \text{м/с}^2 \cdot 1,23 \, \text{м}} = \sqrt{24,108} \, \text{м/с} \approx 4,91 \, \text{м/с}$</p><p>Средняя сила удара $F_{ср}$ (сила реакции опоры) связана с изменением импульса $\Delta p$ через второй закон Ньютона в импульсной форме. В течение времени удара $\text{t}$ на мяч действуют сила реакции опоры $F_{ср}$ (направлена от поверхности) и сила тяжести $m\vec{g}$. Выберем ось, направленную перпендикулярно поверхности (нормаль), и спроецируем на нее силы и изменение импульса:</p><p>$(F_{ср} - F_{g \perp}) \cdot t = \Delta p_\perp$</p><p>где $F_{g \perp}$ — проекция силы тяжести на нормаль к поверхности, а $\Delta p_\perp$ — изменение проекции импульса на эту нормаль.</p><p><strong>1.</strong> Найдите среднюю силу удара Fср.</p><p>В данном случае мяч падает на горизонтальную поверхность (асфальт) и подпрыгивает на ту же высоту. Это означает, что удар упругий, и скорость после удара $v'$ равна по модулю скорости до удара $\text{v}$, но направлена в противоположную сторону. Ось направим вертикально вверх.</p><p>Начальный импульс (перед ударом): $p_1 = -mv$.</p><p>Конечный импульс (после удара): $p_2 = mv$.</p><p>Изменение импульса: $\Delta p = p_2 - p_1 = mv - (-mv) = 2mv$.</p><p>Сила тяжести направлена против оси, ее проекция на нормаль (вертикальную ось) $F_{g \perp} = mg$.</p><p>Подставляем в формулу:</p><p>$(F_{ср} - mg) \cdot t = 2mv$</p><p>$F_{ср} = \frac{2mv}{t} + mg$</p><p>Выполним расчет:</p><p>$F_{ср} = \frac{2 \cdot 0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 29,46 \, \text{Н} + 2,94 \, \text{Н} = 32,4 \, \text{Н}$</p><p><strong>Ответ:</strong> Средняя сила удара равна 32,4 Н.</p><p><strong>2.</strong> Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом α = 30° к горизонту?</p><p>При ударе о наклонную поверхность сила реакции опоры $F_{ср}$ направлена перпендикулярно (нормально) к этой поверхности. Рассмотрим изменение импульса и силы в направлении этой нормали. Скорость $\text{v}$ перед ударом направлена вертикально вниз. Ее проекция на нормаль к наклонной поверхности равна $v_\perp = v \cos \alpha$.</p><p>Поскольку удар упругий, нормальная составляющая скорости после удара меняет направление на противоположное, оставаясь равной по модулю. Изменение импульса в направлении нормали:</p><p>$\Delta p_\perp = m v_\perp - (-m v_\perp) = 2mv_\perp = 2mv \cos \alpha$</p><p>Проекция силы тяжести на нормаль к поверхности равна $F_{g \perp} = mg \cos \alpha$.</p><p>Импульсная форма второго закона Ньютона для нормального направления:</p><p>$(F_{ср}' - mg \cos \alpha) \cdot t = 2mv \cos \alpha$</p><p>$F_{ср}' = \frac{2mv \cos \alpha}{t} + mg \cos \alpha = (\frac{2mv}{t} + mg) \cos \alpha$</p><p>Видно, что новая сила удара $F_{ср}'$ связана с силой из первого пункта $F_{ср}$ соотношением $F_{ср}' = F_{ср} \cos \alpha$.</p><p>Поскольку $\cos(30°) = \frac{\sqrt{3}}{2} \approx 0,866$, что меньше единицы, сила удара уменьшится.</p><p>Рассчитаем ее значение:</p><p>$F_{ср}' = 32,4 \, \text{Н} \cdot \cos(30°) \approx 32,4 \, \text{Н} \cdot 0,866 \approx 28,1 \, \text{Н}$</p><p><strong>Ответ:</strong> Сила уменьшится в $\cos(30°) \approx 0,866$ раз и станет равной примерно 28,1 Н.</p><p><strong>3.</strong> Какой будет Fср, если в обоих случаях мяч заменить пластилиновым шаром той же массы?</p><p>Удар пластилинового шара о поверхность является абсолютно неупругим. Это означает, что после удара шар останавливается, его конечная скорость равна нулю.</p><p><em>Случай 1: Удар о горизонтальную поверхность.</em></p><p>Начальный импульс $p_1 = -mv$, конечный импульс $p_2 = 0$.</p><p>Изменение импульса: $\Delta p = p_2 - p_1 = 0 - (-mv) = mv$.</p><p>Сила удара:</p><p>$(F_{ср} - mg) \cdot t = mv$</p><p>$F_{ср} = \frac{mv}{t} + mg$</p><p>Выполним расчет:</p><p>$F_{ср} = \frac{0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 14,73 \, \text{Н} + 2,94 \, \text{Н} = 17,67 \, \text{Н} \approx 17,7 \, \text{Н}$</p><p><em>Случай 2: Удар о наклонную поверхность.</em></p><p>При неупругом ударе о наклонную поверхность нормальная составляющая скорости становится равной нулю (шар "прилипает"). Рассматриваем силу реакции опоры (нормальную силу).</p><p>Изменение импульса в направлении нормали: $\Delta p_\perp = 0 - (-mv_\perp) = mv_\perp = mv \cos \alpha$.</p><p>Проекция силы тяжести на нормаль: $F_{g \perp} = mg \cos \alpha$.</p><p>Сила удара:</p><p>$(F_{ср}' - mg \cos \alpha) \cdot t = mv \cos \alpha$</p><p>$F_{ср}' = \frac{mv \cos \alpha}{t} + mg \cos \alpha = (\frac{mv}{t} + mg) \cos \alpha$</p><p>Сила удара для пластилинового шара на наклонной поверхности также в $\cos \alpha$ раз меньше, чем на горизонтальной.</p><p>$F_{ср}' = 17,67 \, \text{Н} \cdot \cos(30°) \approx 17,67 \, \text{Н} \cdot 0,866 \approx 15,3 \, \text{Н}$</p><p><strong>Ответ:</strong> Для пластилинового шара средняя сила удара о горизонтальную поверхность составит 17,7 Н, а о наклонную — 15,3 Н.</p>" ] #original: array:6 [ "id" => 1737709 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1268} "task" => array:2 [ "refs" => "1288016" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>m = 300 г<br>H = 1,23 м<br>t = 0,1 с<br>α = 30°<br>g ≈ 9,8 м/с²</p><p>Перевод в систему СИ:<br>m = 0,3 кг</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Fср при ударе об асфальт.<br>2. Как изменится Fср при ударе о наклонную поверхность.<br>3. Fср для пластилинового шара в обоих случаях.</p><p><strong>Решение:</strong></p><p>Для всех случаев сначала найдем скорость мяча непосредственно перед ударом о поверхность. Используя закон сохранения энергии, потенциальная энергия на высоте $\text{H}$ переходит в кинетическую энергию перед ударом:</p><p>$m g H = \frac{1}{2} m v^2$</p><p>Отсюда скорость $\text{v}$ равна:</p><p>$v = \sqrt{2 g H} = \sqrt{2 \cdot 9,8 \, \text{м/с}^2 \cdot 1,23 \, \text{м}} = \sqrt{24,108} \, \text{м/с} \approx 4,91 \, \text{м/с}$</p><p>Средняя сила удара $F_{ср}$ (сила реакции опоры) связана с изменением импульса $\Delta p$ через второй закон Ньютона в импульсной форме. В течение времени удара $\text{t}$ на мяч действуют сила реакции опоры $F_{ср}$ (направлена от поверхности) и сила тяжести $m\vec{g}$. Выберем ось, направленную перпендикулярно поверхности (нормаль), и спроецируем на нее силы и изменение импульса:</p><p>$(F_{ср} - F_{g \perp}) \cdot t = \Delta p_\perp$</p><p>где $F_{g \perp}$ — проекция силы тяжести на нормаль к поверхности, а $\Delta p_\perp$ — изменение проекции импульса на эту нормаль.</p><p><strong>1.</strong> Найдите среднюю силу удара Fср.</p><p>В данном случае мяч падает на горизонтальную поверхность (асфальт) и подпрыгивает на ту же высоту. Это означает, что удар упругий, и скорость после удара $v'$ равна по модулю скорости до удара $\text{v}$, но направлена в противоположную сторону. Ось направим вертикально вверх.</p><p>Начальный импульс (перед ударом): $p_1 = -mv$.</p><p>Конечный импульс (после удара): $p_2 = mv$.</p><p>Изменение импульса: $\Delta p = p_2 - p_1 = mv - (-mv) = 2mv$.</p><p>Сила тяжести направлена против оси, ее проекция на нормаль (вертикальную ось) $F_{g \perp} = mg$.</p><p>Подставляем в формулу:</p><p>$(F_{ср} - mg) \cdot t = 2mv$</p><p>$F_{ср} = \frac{2mv}{t} + mg$</p><p>Выполним расчет:</p><p>$F_{ср} = \frac{2 \cdot 0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 29,46 \, \text{Н} + 2,94 \, \text{Н} = 32,4 \, \text{Н}$</p><p><strong>Ответ:</strong> Средняя сила удара равна 32,4 Н.</p><p><strong>2.</strong> Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом α = 30° к горизонту?</p><p>При ударе о наклонную поверхность сила реакции опоры $F_{ср}$ направлена перпендикулярно (нормально) к этой поверхности. Рассмотрим изменение импульса и силы в направлении этой нормали. Скорость $\text{v}$ перед ударом направлена вертикально вниз. Ее проекция на нормаль к наклонной поверхности равна $v_\perp = v \cos \alpha$.</p><p>Поскольку удар упругий, нормальная составляющая скорости после удара меняет направление на противоположное, оставаясь равной по модулю. Изменение импульса в направлении нормали:</p><p>$\Delta p_\perp = m v_\perp - (-m v_\perp) = 2mv_\perp = 2mv \cos \alpha$</p><p>Проекция силы тяжести на нормаль к поверхности равна $F_{g \perp} = mg \cos \alpha$.</p><p>Импульсная форма второго закона Ньютона для нормального направления:</p><p>$(F_{ср}' - mg \cos \alpha) \cdot t = 2mv \cos \alpha$</p><p>$F_{ср}' = \frac{2mv \cos \alpha}{t} + mg \cos \alpha = (\frac{2mv}{t} + mg) \cos \alpha$</p><p>Видно, что новая сила удара $F_{ср}'$ связана с силой из первого пункта $F_{ср}$ соотношением $F_{ср}' = F_{ср} \cos \alpha$.</p><p>Поскольку $\cos(30°) = \frac{\sqrt{3}}{2} \approx 0,866$, что меньше единицы, сила удара уменьшится.</p><p>Рассчитаем ее значение:</p><p>$F_{ср}' = 32,4 \, \text{Н} \cdot \cos(30°) \approx 32,4 \, \text{Н} \cdot 0,866 \approx 28,1 \, \text{Н}$</p><p><strong>Ответ:</strong> Сила уменьшится в $\cos(30°) \approx 0,866$ раз и станет равной примерно 28,1 Н.</p><p><strong>3.</strong> Какой будет Fср, если в обоих случаях мяч заменить пластилиновым шаром той же массы?</p><p>Удар пластилинового шара о поверхность является абсолютно неупругим. Это означает, что после удара шар останавливается, его конечная скорость равна нулю.</p><p><em>Случай 1: Удар о горизонтальную поверхность.</em></p><p>Начальный импульс $p_1 = -mv$, конечный импульс $p_2 = 0$.</p><p>Изменение импульса: $\Delta p = p_2 - p_1 = 0 - (-mv) = mv$.</p><p>Сила удара:</p><p>$(F_{ср} - mg) \cdot t = mv$</p><p>$F_{ср} = \frac{mv}{t} + mg$</p><p>Выполним расчет:</p><p>$F_{ср} = \frac{0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 14,73 \, \text{Н} + 2,94 \, \text{Н} = 17,67 \, \text{Н} \approx 17,7 \, \text{Н}$</p><p><em>Случай 2: Удар о наклонную поверхность.</em></p><p>При неупругом ударе о наклонную поверхность нормальная составляющая скорости становится равной нулю (шар "прилипает"). Рассматриваем силу реакции опоры (нормальную силу).</p><p>Изменение импульса в направлении нормали: $\Delta p_\perp = 0 - (-mv_\perp) = mv_\perp = mv \cos \alpha$.</p><p>Проекция силы тяжести на нормаль: $F_{g \perp} = mg \cos \alpha$.</p><p>Сила удара:</p><p>$(F_{ср}' - mg \cos \alpha) \cdot t = mv \cos \alpha$</p><p>$F_{ср}' = \frac{mv \cos \alpha}{t} + mg \cos \alpha = (\frac{mv}{t} + mg) \cos \alpha$</p><p>Сила удара для пластилинового шара на наклонной поверхности также в $\cos \alpha$ раз меньше, чем на горизонтальной.</p><p>$F_{ср}' = 17,67 \, \text{Н} \cdot \cos(30°) \approx 17,67 \, \text{Н} \cdot 0,866 \approx 15,3 \, \text{Н}$</p><p><strong>Ответ:</strong> Для пластилинового шара средняя сила удара о горизонтальную поверхность составит 17,7 Н, а о наклонную — 15,3 Н.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: 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№4.1 (с. 20)
Условие. №4.1 (с. 20)
скриншот условия
4.1. Мяч массой $m = 300 \text{ г}$ упал с высоты $H = 1,23 \text{ м}$ на асфальт и подскочил на ту же высоту. Продолжительность удара об асфальт $t = 0,1 \text{ с}$. Найдите среднюю силу удара $F_{\text{cp}}$. Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом $\alpha = 30^{\circ}$ к горизонту? Какой будет $F_{\text{cp}}$, если в обоих случаях мяч заменить пластилиновым шаром той же массы? Продолжительность удара считайте той же.
Решение. №4.1 (с. 20)
Решение 2. №4.1 (с. 20)
Дано:
m = 300 г
H = 1,23 м
t = 0,1 с
α = 30°
g ≈ 9,8 м/с²
Перевод в систему СИ:
m = 0,3 кг
Найти:
1. Fср при ударе об асфальт.
2. Как изменится Fср при ударе о наклонную поверхность.
3. Fср для пластилинового шара в обоих случаях.
Решение:
Для всех случаев сначала найдем скорость мяча непосредственно перед ударом о поверхность. Используя закон сохранения энергии, потенциальная энергия на высоте $\text{H}$ переходит в кинетическую энергию перед ударом:
$m g H = \frac{1}{2} m v^2$
Отсюда скорость $\text{v}$ равна:
$v = \sqrt{2 g H} = \sqrt{2 \cdot 9,8 \, \text{м/с}^2 \cdot 1,23 \, \text{м}} = \sqrt{24,108} \, \text{м/с} \approx 4,91 \, \text{м/с}$
Средняя сила удара $F_{ср}$ (сила реакции опоры) связана с изменением импульса $\Delta p$ через второй закон Ньютона в импульсной форме. В течение времени удара $\text{t}$ на мяч действуют сила реакции опоры $F_{ср}$ (направлена от поверхности) и сила тяжести $m\vec{g}$. Выберем ось, направленную перпендикулярно поверхности (нормаль), и спроецируем на нее силы и изменение импульса:
$(F_{ср} - F_{g \perp}) \cdot t = \Delta p_\perp$
где $F_{g \perp}$ — проекция силы тяжести на нормаль к поверхности, а $\Delta p_\perp$ — изменение проекции импульса на эту нормаль.
1. Найдите среднюю силу удара Fср.
В данном случае мяч падает на горизонтальную поверхность (асфальт) и подпрыгивает на ту же высоту. Это означает, что удар упругий, и скорость после удара $v'$ равна по модулю скорости до удара $\text{v}$, но направлена в противоположную сторону. Ось направим вертикально вверх.
Начальный импульс (перед ударом): $p_1 = -mv$.
Конечный импульс (после удара): $p_2 = mv$.
Изменение импульса: $\Delta p = p_2 - p_1 = mv - (-mv) = 2mv$.
Сила тяжести направлена против оси, ее проекция на нормаль (вертикальную ось) $F_{g \perp} = mg$.
Подставляем в формулу:
$(F_{ср} - mg) \cdot t = 2mv$
$F_{ср} = \frac{2mv}{t} + mg$
Выполним расчет:
$F_{ср} = \frac{2 \cdot 0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 29,46 \, \text{Н} + 2,94 \, \text{Н} = 32,4 \, \text{Н}$
Ответ: Средняя сила удара равна 32,4 Н.
2. Как изменится эта сила, если мяч ударится о твердую поверхность, наклоненную под углом α = 30° к горизонту?
При ударе о наклонную поверхность сила реакции опоры $F_{ср}$ направлена перпендикулярно (нормально) к этой поверхности. Рассмотрим изменение импульса и силы в направлении этой нормали. Скорость $\text{v}$ перед ударом направлена вертикально вниз. Ее проекция на нормаль к наклонной поверхности равна $v_\perp = v \cos \alpha$.
Поскольку удар упругий, нормальная составляющая скорости после удара меняет направление на противоположное, оставаясь равной по модулю. Изменение импульса в направлении нормали:
$\Delta p_\perp = m v_\perp - (-m v_\perp) = 2mv_\perp = 2mv \cos \alpha$
Проекция силы тяжести на нормаль к поверхности равна $F_{g \perp} = mg \cos \alpha$.
Импульсная форма второго закона Ньютона для нормального направления:
$(F_{ср}' - mg \cos \alpha) \cdot t = 2mv \cos \alpha$
$F_{ср}' = \frac{2mv \cos \alpha}{t} + mg \cos \alpha = (\frac{2mv}{t} + mg) \cos \alpha$
Видно, что новая сила удара $F_{ср}'$ связана с силой из первого пункта $F_{ср}$ соотношением $F_{ср}' = F_{ср} \cos \alpha$.
Поскольку $\cos(30°) = \frac{\sqrt{3}}{2} \approx 0,866$, что меньше единицы, сила удара уменьшится.
Рассчитаем ее значение:
$F_{ср}' = 32,4 \, \text{Н} \cdot \cos(30°) \approx 32,4 \, \text{Н} \cdot 0,866 \approx 28,1 \, \text{Н}$
Ответ: Сила уменьшится в $\cos(30°) \approx 0,866$ раз и станет равной примерно 28,1 Н.
3. Какой будет Fср, если в обоих случаях мяч заменить пластилиновым шаром той же массы?
Удар пластилинового шара о поверхность является абсолютно неупругим. Это означает, что после удара шар останавливается, его конечная скорость равна нулю.
Случай 1: Удар о горизонтальную поверхность.
Начальный импульс $p_1 = -mv$, конечный импульс $p_2 = 0$.
Изменение импульса: $\Delta p = p_2 - p_1 = 0 - (-mv) = mv$.
Сила удара:
$(F_{ср} - mg) \cdot t = mv$
$F_{ср} = \frac{mv}{t} + mg$
Выполним расчет:
$F_{ср} = \frac{0,3 \, \text{кг} \cdot 4,91 \, \text{м/с}}{0,1 \, \text{с}} + 0,3 \, \text{кг} \cdot 9,8 \, \text{м/с}^2 = 14,73 \, \text{Н} + 2,94 \, \text{Н} = 17,67 \, \text{Н} \approx 17,7 \, \text{Н}$
Случай 2: Удар о наклонную поверхность.
При неупругом ударе о наклонную поверхность нормальная составляющая скорости становится равной нулю (шар "прилипает"). Рассматриваем силу реакции опоры (нормальную силу).
Изменение импульса в направлении нормали: $\Delta p_\perp = 0 - (-mv_\perp) = mv_\perp = mv \cos \alpha$.
Проекция силы тяжести на нормаль: $F_{g \perp} = mg \cos \alpha$.
Сила удара:
$(F_{ср}' - mg \cos \alpha) \cdot t = mv \cos \alpha$
$F_{ср}' = \frac{mv \cos \alpha}{t} + mg \cos \alpha = (\frac{mv}{t} + mg) \cos \alpha$
Сила удара для пластилинового шара на наклонной поверхности также в $\cos \alpha$ раз меньше, чем на горизонтальной.
$F_{ср}' = 17,67 \, \text{Н} \cdot \cos(30°) \approx 17,67 \, \text{Н} \cdot 0,866 \approx 15,3 \, \text{Н}$
Ответ: Для пластилинового шара средняя сила удара о горизонтальную поверхность составит 17,7 Н, а о наклонную — 15,3 Н.
Другие задания:
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