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Номер 9.13, страница 48 - гдз по физике 8 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2010 - 2026
Цвет обложки: фиолетовый
ISBN: 978-5-09-046040-8
Популярные ГДЗ в 8 классе
IX. Основы динамики - номер 9.13, страница 48.
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[] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => 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] #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 {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1460052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "IX. 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Массы тел одинаковы и равны 7 кг. Определите значения результирующих сил, действующих на эти тела.</p><p>Рис. 38</p>" "img" => array:2 [ 0 => array:5 [ "name" => "13-1.jpg" "alt" => null "width" => "878" "height" => 478 "path" => "/media/fizika_08/artemenkov-zd/0-09/13-1.webp?ts=1760701801" ] 1 => array:5 [ "name" => "13-2.jpg" "alt" => null "width" => "894" "height" => 809 "path" => "/media/fizika_08/artemenkov-zd/0-09/13-2.webp?ts=1760701801" ] ] ] #original: array:7 [ "id" => 1753838 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1460340" "type" => "task" ] "text" => "<p><strong>9.13</strong> На рисунке 38 приведены графики скорости для трёх тел, движущихся прямолинейно. Массы тел одинаковы и равны 7 кг. Определите значения результирующих сил, действующих на эти тела.</p><p>Рис. 38</p>" "img" => array:2 [ 0 => array:5 [ "name" => "13-1.jpg" "alt" => null "width" => "878" "height" => 478 "path" => "/media/fizika_08/artemenkov-zd/0-09/13-1.webp?ts=1760701801" ] 1 => array:5 [ "name" => "13-2.jpg" "alt" => null "width" => "894" "height" => 809 "path" => "/media/fizika_08/artemenkov-zd/0-09/13-2.webp?ts=1760701801" ] ] ] #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 {#1098 #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" => 1821945 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Edition {#1099 #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" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1104} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1105} "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" => "1460340" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Масса каждого тела $m = 7$ кг.<br>На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех тел.</p><p><strong>Найти:</strong></p><p>$F_1, F_2, F_3$ - значения результирующих сил, действующих на тела.</p><p><strong>Решение:</strong></p><p>Согласно второму закону Ньютона, результирующая сила $\text{F}$, действующая на тело, равна произведению массы тела $\text{m}$ на его ускорение $\text{a}$:</p><p>$F = m \cdot a$</p><p>Ускорение тела можно найти по графику зависимости скорости от времени. Ускорение равно отношению изменения скорости $\Delta v$ к промежутку времени $\Delta t$, за которое это изменение произошло:</p><p>$a = \frac{\Delta v}{\Delta t} = \frac{v_к - v_н}{t_к - t_н}$</p><p>где $v_н$ и $v_к$ — начальная и конечная скорости тела за промежуток времени от $t_н$ до $t_к$.</p><p>Определим результирующую силу для каждого из трех тел.</p><p><strong>1)</strong> Для тела 1</p><p>Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 25$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 0$ м/с.</p><p>Вычислим ускорение тела 1:</p><p>$a_1 = \frac{0 \text{ м/с} - 25 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = -2,5 \text{ м/с}^2$</p><p>Знак "минус" указывает на то, что движение является равнозамедленным.</p><p>Теперь найдем результирующую силу, действующую на тело 1. Поскольку в задаче требуется найти значение силы, мы находим ее модуль:</p><p>$F_1 = m \cdot |a_1| = 7 \text{ кг} \cdot |-2,5 \text{ м/с}^2| = 17,5 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на первое тело, равна 17,5 Н.</p><p><strong>2)</strong> Для тела 2</p><p>График скорости для второго тела — это горизонтальная прямая. Это означает, что скорость тела постоянна и равна $v_2 = 20$ м/с (равномерное прямолинейное движение).</p><p>Поскольку скорость не изменяется, ускорение тела равно нулю:</p><p>$a_2 = 0 \text{ м/с}^2$</p><p>Следовательно, результирующая сила, действующая на тело 2, также равна нулю:</p><p>$F_2 = m \cdot a_2 = 7 \text{ кг} \cdot 0 \text{ м/с}^2 = 0 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на второе тело, равна 0 Н.</p><p><strong>3)</strong> Для тела 3</p><p>Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 5$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 35$ м/с.</p><p>Вычислим ускорение тела 3:</p><p>$a_3 = \frac{35 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = \frac{30 \text{ м/с}}{10 \text{ с}} = 3 \text{ м/с}^2$</p><p>Положительное значение ускорения говорит о том, что движение является равноускоренным.</p><p>Найдем результирующую силу, действующую на тело 3:</p><p>$F_3 = m \cdot a_3 = 7 \text{ кг} \cdot 3 \text{ м/с}^2 = 21 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на третье тело, равна 21 Н.</p>" ] #original: array:6 [ "id" => 1821945 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1108} "task" => array:2 [ "refs" => "1460340" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Масса каждого тела $m = 7$ кг.<br>На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех тел.</p><p><strong>Найти:</strong></p><p>$F_1, F_2, F_3$ - значения результирующих сил, действующих на тела.</p><p><strong>Решение:</strong></p><p>Согласно второму закону Ньютона, результирующая сила $\text{F}$, действующая на тело, равна произведению массы тела $\text{m}$ на его ускорение $\text{a}$:</p><p>$F = m \cdot a$</p><p>Ускорение тела можно найти по графику зависимости скорости от времени. Ускорение равно отношению изменения скорости $\Delta v$ к промежутку времени $\Delta t$, за которое это изменение произошло:</p><p>$a = \frac{\Delta v}{\Delta t} = \frac{v_к - v_н}{t_к - t_н}$</p><p>где $v_н$ и $v_к$ — начальная и конечная скорости тела за промежуток времени от $t_н$ до $t_к$.</p><p>Определим результирующую силу для каждого из трех тел.</p><p><strong>1)</strong> Для тела 1</p><p>Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 25$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 0$ м/с.</p><p>Вычислим ускорение тела 1:</p><p>$a_1 = \frac{0 \text{ м/с} - 25 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = -2,5 \text{ м/с}^2$</p><p>Знак "минус" указывает на то, что движение является равнозамедленным.</p><p>Теперь найдем результирующую силу, действующую на тело 1. Поскольку в задаче требуется найти значение силы, мы находим ее модуль:</p><p>$F_1 = m \cdot |a_1| = 7 \text{ кг} \cdot |-2,5 \text{ м/с}^2| = 17,5 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на первое тело, равна 17,5 Н.</p><p><strong>2)</strong> Для тела 2</p><p>График скорости для второго тела — это горизонтальная прямая. Это означает, что скорость тела постоянна и равна $v_2 = 20$ м/с (равномерное прямолинейное движение).</p><p>Поскольку скорость не изменяется, ускорение тела равно нулю:</p><p>$a_2 = 0 \text{ м/с}^2$</p><p>Следовательно, результирующая сила, действующая на тело 2, также равна нулю:</p><p>$F_2 = m \cdot a_2 = 7 \text{ кг} \cdot 0 \text{ м/с}^2 = 0 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на второе тело, равна 0 Н.</p><p><strong>3)</strong> Для тела 3</p><p>Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 5$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 35$ м/с.</p><p>Вычислим ускорение тела 3:</p><p>$a_3 = \frac{35 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = \frac{30 \text{ м/с}}{10 \text{ с}} = 3 \text{ м/с}^2$</p><p>Положительное значение ускорения говорит о том, что движение является равноускоренным.</p><p>Найдем результирующую силу, действующую на тело 3:</p><p>$F_3 = m \cdot a_3 = 7 \text{ кг} \cdot 3 \text{ м/с}^2 = 21 \text{ Н}$</p><p><strong>Ответ:</strong> результирующая сила, действующая на третье тело, равна 21 Н.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460341" "type" => "task" ] "previous" => array:2 [ "refs" => "1460339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1088 #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" => 1646 "created_at" => "2026-04-10 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"field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1109 #items: array:1 [ 0 => App\Models\Term {#1110 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1111 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Term {#1081} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Term {#1120 #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" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "fioletovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1075} "field_class" => Illuminate\Database\Eloquent\Collection {#1074} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079} "field_author" => Illuminate\Database\Eloquent\Collection {#1076} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1090} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1086} "field_country" => Illuminate\Database\Eloquent\Collection {#1087} "field_city" => Illuminate\Database\Eloquent\Collection {#1106} "field_series" => Illuminate\Database\Eloquent\Collection {#1109} "field_umk" => Illuminate\Database\Eloquent\Collection {#1111} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\BookPage {#1127 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1462345 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-48" "field_display_title" => "48" "field_folder" => "1" "field_image_name" => "48" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1088} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Element {#1140 #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" => 1753906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1753906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "book_page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1462346" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462344" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:9 [ 0 => App\Models\Task {#1241 #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" => 1460339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-12" "field_display_title" => "9.12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:1 [ …1] #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 {#1243 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460340" "type" => "task" ] "previous" => array:2 [ "refs" => "1460338" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-12" "field_display_title" => "9.12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242} "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 {#1243} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245} "content" => Illuminate\Database\Eloquent\Collection {#1247} "next" => array:2 [ "refs" => "1460340" "type" => "task" ] "previous" => array:2 [ "refs" => "1460338" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1253} "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1248 #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" => 1460340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-13" "field_display_title" => "9.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ …1] #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 {#1255 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1252 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460341" "type" => "task" ] "previous" => array:2 [ "refs" => "1460339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-13" "field_display_title" => "9.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246} "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 {#1255} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249} "content" => Illuminate\Database\Eloquent\Collection {#1252} "next" => array:2 [ "refs" => "1460341" "type" => "task" ] "previous" => array:2 [ "refs" => "1460339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1250} "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1260 #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" => 1460341 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-14" "field_display_title" => "9.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ …1] #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 {#1262 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460342" "type" => "task" ] "previous" => array:2 [ "refs" => "1460340" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460341 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-14" "field_display_title" => "9.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261} "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 {#1262} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264} "content" => Illuminate\Database\Eloquent\Collection {#1275} "next" => array:2 [ "refs" => "1460342" "type" => "task" ] "previous" => array:2 [ "refs" => "1460340" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1280} "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1265 #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" => 1460342 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-15" "field_display_title" => "9.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ …1] #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 {#1266 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460343" "type" => "task" ] "previous" => array:2 [ "refs" => "1460341" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460342 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-15" "field_display_title" => "9.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267} "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 {#1266} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1272} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271} "content" => Illuminate\Database\Eloquent\Collection {#1287} "next" => array:2 [ "refs" => "1460343" "type" => "task" ] "previous" => array:2 [ "refs" => "1460341" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1292} "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1270 #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" => 1460343 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-16" "field_display_title" => "9.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:1 [ …1] #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 {#1268 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460344" "type" => "task" ] "previous" => array:2 [ "refs" => "1460342" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1304 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460343 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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#attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1282 #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" => 1460344 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-17" "field_display_title" => "9.17" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:1 [ …1] #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 {#1274 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460345" "type" => "task" ] "previous" => array:2 [ "refs" => "1460343" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460344 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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#attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1279 #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" => 1460345 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-18" "field_display_title" => "9.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 #items: array:1 [ …1] #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 {#1301 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1306 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 …2} "content" => Illuminate\Database\Eloquent\Collection {#1291 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1320 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460345 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-18" "field_display_title" => "9.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294} "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 {#1301} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1306 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 …2} "content" => Illuminate\Database\Eloquent\Collection {#1291 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1320 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Task {#1315 #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" => 1460346 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-19" "field_display_title" => "9.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1302 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1322 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1318 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1316 …2} "content" => Illuminate\Database\Eloquent\Collection {#1317 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1332 …2} 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false } ] #original: array:24 [ "id" => 1460340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/09-13" "field_display_title" => "9.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1071} "content" => Illuminate\Database\Eloquent\Collection {#1083} "next" => array:2 [ "refs" => "1460341" "type" => "task" ] "previous" => array:2 [ "refs" => "1460339" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123} "page" => array:2 [ "refs" => "1462345" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№9.13 (с. 48)
Условие. №9.13 (с. 48)
скриншот условия
9.13 На рисунке 38 приведены графики скорости для трёх тел, движущихся прямолинейно. Массы тел одинаковы и равны 7 кг. Определите значения результирующих сил, действующих на эти тела.
Рис. 38
Решение. №9.13 (с. 48)
Дано:
Масса каждого тела $m = 7$ кг.
На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех тел.
Найти:
$F_1, F_2, F_3$ - значения результирующих сил, действующих на тела.
Решение:
Согласно второму закону Ньютона, результирующая сила $\text{F}$, действующая на тело, равна произведению массы тела $\text{m}$ на его ускорение $\text{a}$:
$F = m \cdot a$
Ускорение тела можно найти по графику зависимости скорости от времени. Ускорение равно отношению изменения скорости $\Delta v$ к промежутку времени $\Delta t$, за которое это изменение произошло:
$a = \frac{\Delta v}{\Delta t} = \frac{v_к - v_н}{t_к - t_н}$
где $v_н$ и $v_к$ — начальная и конечная скорости тела за промежуток времени от $t_н$ до $t_к$.
Определим результирующую силу для каждого из трех тел.
1) Для тела 1
Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 25$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 0$ м/с.
Вычислим ускорение тела 1:
$a_1 = \frac{0 \text{ м/с} - 25 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = -2,5 \text{ м/с}^2$
Знак "минус" указывает на то, что движение является равнозамедленным.
Теперь найдем результирующую силу, действующую на тело 1. Поскольку в задаче требуется найти значение силы, мы находим ее модуль:
$F_1 = m \cdot |a_1| = 7 \text{ кг} \cdot |-2,5 \text{ м/с}^2| = 17,5 \text{ Н}$
Ответ: результирующая сила, действующая на первое тело, равна 17,5 Н.
2) Для тела 2
График скорости для второго тела — это горизонтальная прямая. Это означает, что скорость тела постоянна и равна $v_2 = 20$ м/с (равномерное прямолинейное движение).
Поскольку скорость не изменяется, ускорение тела равно нулю:
$a_2 = 0 \text{ м/с}^2$
Следовательно, результирующая сила, действующая на тело 2, также равна нулю:
$F_2 = m \cdot a_2 = 7 \text{ кг} \cdot 0 \text{ м/с}^2 = 0 \text{ Н}$
Ответ: результирующая сила, действующая на второе тело, равна 0 Н.
3) Для тела 3
Из графика видно, что в начальный момент времени $t_н = 0$ с начальная скорость тела $v_н = 5$ м/с, а в момент времени $t_к = 10$ с конечная скорость $v_к = 35$ м/с.
Вычислим ускорение тела 3:
$a_3 = \frac{35 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с} - 0 \text{ с}} = \frac{30 \text{ м/с}}{10 \text{ с}} = 3 \text{ м/с}^2$
Положительное значение ускорения говорит о том, что движение является равноускоренным.
Найдем результирующую силу, действующую на тело 3:
$F_3 = m \cdot a_3 = 7 \text{ кг} \cdot 3 \text{ м/с}^2 = 21 \text{ Н}$
Ответ: результирующая сила, действующая на третье тело, равна 21 Н.
Другие задания:
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ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 8 класс, для упражнения номер 9.13 расположенного на странице 48 к задачнику серии сферы 2010 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №9.13 (с. 48), авторов: Артеменков (Денис Александрович), Ломаченков (Иван Алексеевич), Панебратцев (Юрий Анатольевич), учебного пособия издательства Просвещение.