Номер 1, страница 54 - гдз по физике 8 класс учебник Пёрышкин

Глава 1. Тепловые явления. Параграф 14. Закон сохранения и превращения энергии в механических и тепловых процессах. Обсуди с товарищем - номер 1, страница 54.

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App\Models\Task {#1024 // resources/views/models/task/default.blade.php
  #connection: "mysql"
  #table: "tasks"
  #primaryKey: "id"
  #keyType: "int"
  +incrementing: true
  #with: []
  #withCount: []
  +preventsLazyLoading: false
  #perPage: 15
  +exists: true
  +wasRecentlyCreated: false
  #escapeWhenCastingToString: false
  #attributes: array:24 [
    "id" => 598929
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "54"
    "field_page_end" => null
    "field_url" => "/8-klass/fizika/peryshkin-uchebnik/14-2-1"
    "field_display_title" => "1"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#331
      #items: array:1 [
        0 => App\Models\Term {#1029
          #connection: "mysql"
          #table: "terms"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: false
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => "№"
          ]
          #original: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => "№"
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
    "field_description_top" => null
    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026
      #items: []
      #escapeWhenCastingToString: false
    }
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342
      #items: array:1 [
        0 => App\Models\Branch {#1023
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 598563
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Тепловые явления"
            "field_branch_order" => "1"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333
              #items: array:1 [
                0 => App\Models\Term {#1033
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "3"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1030
              #items: array:1 [
                0 => App\Models\Book {#1032
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 51
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1034
                      #items: array:1 [
                        0 => App\Models\Term {#1035
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [ …10]
                          #original: array:10 [ …10]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1036
                      #items: array:1 [
                        0 => App\Models\Term {#1037
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038
                      #items: array:1 [
                        0 => App\Models\Term {#1039
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1040
                      #items: array:1 [
                        0 => App\Models\Term {#1041
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043
                      #items: array:1 [
                        0 => App\Models\Term {#1044
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [ …10]
                          #original: array:10 [ …10]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1045
                      #items: array:1 [
                        0 => App\Models\Term {#1046
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1047
                      #items: array:1 [
                        0 => App\Models\Term {#1048
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1049
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1050
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051
                      #items: array:1 [
                        0 => App\Models\Term {#1052
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053
                      #items: array:1 [
                        0 => App\Models\Term {#1054
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [ …10]
                          #original: array:10 [ …10]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "3"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055
                      #items: array:1 [
                        0 => App\Models\Term {#1056
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "с градусником"
                    "field_publication_year" => "2023"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => null
                    "field_allowed" => "Допущено Министерством просвещения Российской Федерации"
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "706"
                    "field_priority" => "2"
                    "field_default_folder" => "/fizika_08/Peryshkin-u23/"
                    "field_isbn" => "978-5-09-102555-2"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_08/Peryshkin-u23/covers/cover1.webp?ts=1737917825"
                        "alt" => ""
                        "width" => "1350"
                        "height" => "1772"
                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1058
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1059
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1060
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/8-klass/fizika/peryshkin-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1061
                      #items: array:1 [
                        0 => App\Models\Term {#1062
                          #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 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "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" => 51
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1034}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1036}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1040}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1045}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1047}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1049}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1050}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053}
                    "field_publication_number" => "3"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "с градусником"
                    "field_publication_year" => "2023"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => null
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    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1064
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        0 => App\Models\Branch {#1065
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                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1094 …2}
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                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1097 …2}
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        }
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          #primaryKey: "id"
          #keyType: "int"
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                  #attributes: array:7 [
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                    "created_at" => "2026-04-10 13:58:26"
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                    "updated_at" => null
                    "name" => "Параграф"
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            "book" => Illuminate\Database\Eloquent\Collection {#1103
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                0 => App\Models\Book {#1104
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                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1113 …2}
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                    "field_part" => ""
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                    "field_second_foreign_language" => null
                    "field_for_whom" => null
                    "field_allowed" => "Допущено Министерством просвещения Российской Федерации"
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "706"
                    "field_priority" => "2"
                    "field_default_folder" => "/fizika_08/Peryshkin-u23/"
                    "field_isbn" => "978-5-09-102555-2"
                    "field_cover" => array:1 [ …1]
                    "field_cover_alts" => array:1 [ …1]
                    "field_covers" => array:1 [ …1]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2}
                    "field_url" => "/8-klass/fizika/peryshkin-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …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: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134
              #items: array:1 [
                0 => App\Models\Branch {#1135
                  #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" => 598563
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Тепловые явления"
                    "field_branch_order" => "1"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1136 …2}
                    "field_page_start" => "3"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1138 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1169 …2}
                  ]
                  #original: array:24 [
                    "id" => 598563
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Тепловые явления"
                    "field_branch_order" => "1"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1136 …2}
                    "field_page_start" => "3"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1138 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1169 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598610
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Закон сохранения и превращения энергии в механических и тепловых процессах"
            "field_branch_order" => "14"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1101}
            "field_page_start" => "52"
            "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 {#1103}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1134}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
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          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1170
          #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" => 598612
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Обсуди с товарищем"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "54"
            "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 {#1172
              #items: array:1 [
                0 => App\Models\Book {#1173
                  #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" => 51
                    "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 {#1174 …2}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1176 …2}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 …2}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1180 …2}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1182 …2}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1183 …2}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1185 …2}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1187 …2}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1189 …2}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1190 …2}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1191 …2}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1193 …2}
                    "field_publication_number" => "3"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1195 …2}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1197 …2}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "с градусником"
                    "field_publication_year" => "2023"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => null
                    "field_allowed" => "Допущено Министерством просвещения Российской Федерации"
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "706"
                    "field_priority" => "2"
                    "field_default_folder" => "/fizika_08/Peryshkin-u23/"
                     …16
                  ]
                  #original: array:50 [ …50]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
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                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1203
              #items: array:1 [
                0 => App\Models\Branch {#1204
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
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                  #attributeCastCache: []
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598612
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Обсуди с товарищем"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1171}
            "field_page_start" => "54"
            "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 {#1172}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1203}
          ]
          #changes: []
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          #attributeCastCache: []
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          #hidden: []
          #visible: []
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          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1214
      #items: array:5 [
        0 => App\Models\Element {#1215
          #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" => 745277
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1216
              #items: array:1 [
                0 => App\Models\Edition {#1217
                  #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 [ …21]
                  #original: array:21 [ …21]
                  #changes: []
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                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "598929"
              "type" => "task"
            ]
            "text" => "<p> <b>1.</b> Газ, находящийся в цилиндре под поршнем, сжимают. Подумайте, положительную или отрицательную работу совершает при этом сила, действующая на поршень со стороны газа. </p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.png"
                "alt" => null
                "width" => "716"
                "height" => 118
                "path" => "/media/fizika_08/Peryshkin-u23/0-14-2/1-1.webp?ts=1738080832"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 745277
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1216}
            "task" => array:2 [
              "refs" => "598929"
              "type" => "task"
            ]
            "text" => "<p> <b>1.</b> Газ, находящийся в цилиндре под поршнем, сжимают. Подумайте, положительную или отрицательную работу совершает при этом сила, действующая на поршень со стороны газа. </p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.png"
                "alt" => null
                "width" => "716"
                "height" => 118
                "path" => "/media/fizika_08/Peryshkin-u23/0-14-2/1-1.webp?ts=1738080832"
              ]
            ]
          ]
          #changes: []
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          #attributeCastCache: []
          #dateFormat: null
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          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1223
          #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" => 745468
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1224
              #items: array:1 [
                0 => App\Models\Edition {#1225
                  #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 [ …21]
                  #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" => "598929"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.jpg"
                "alt" => null
                "width" => "1741"
                "height" => 345
                "path" => "/media/fizika_08/Peryshkin-u23/1-14-2/1-1.webp?ts=1738080862"
              ]
            ]
          ]
          #original: array:6 [
            "id" => 745468
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1224}
            "task" => array:2 [
              "refs" => "598929"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.jpg"
                "alt" => null
                "width" => "1741"
                "height" => 345
                "path" => "/media/fizika_08/Peryshkin-u23/1-14-2/1-1.webp?ts=1738080862"
              ]
            ]
          ]
          #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 {#1231
          #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" => 746383
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1232
              #items: array:1 [
                0 => App\Models\Edition {#1233
                  #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 [ …21]
                  #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" => "598929"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.png"
                "alt" => null
                "width" => "700"
                "height" => 698
                "path" => "/media/fizika_08/Peryshkin-u23/3-14-2/1-1.webp?ts=1738080922"
              ]
            ]
          ]
          #original: array:6 [
            "id" => 746383
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1232}
            "task" => array:2 [
              "refs" => "598929"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.png"
                "alt" => null
                "width" => "700"
                "height" => 698
                "path" => "/media/fizika_08/Peryshkin-u23/3-14-2/1-1.webp?ts=1738080922"
              ]
            ]
          ]
          #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\Element {#1239
          #connection: "mysql"
          #table: "elements"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1240
              #items: array:1 [
                0 => App\Models\Edition {#1241
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            "edition" => Illuminate\Database\Eloquent\Collection {#1240}
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        4 => App\Models\Element {#1247
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            "created_at" => "2026-04-10 13:58:26"
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            "edition" => Illuminate\Database\Eloquent\Collection {#1248
              #items: array:1 [
                0 => App\Models\Edition {#1249
                  #connection: "mysql"
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              #escapeWhenCastingToString: false
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            "task" => array:2 [
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              "type" => "task"
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            "text" => "<p><strong>Дано:</strong></p><p>Процесс - сжатие газа в цилиндре под поршнем.</p><p><strong>Найти:</strong></p><p>Знак работы $A_{газа}$, совершаемой силой, действующей на поршень со стороны газа.</p><p><strong>Решение:</strong></p><p>Механическая работа $A$ определяется как скалярное произведение вектора силы $\vec{F}$ на вектор перемещения $\vec{s}$ и вычисляется по формуле:</p><p>$A = F \cdot s \cdot \cos\alpha$</p><p>где $F$ – модуль силы, $s$ – модуль перемещения точки приложения силы, а $\alpha$ – угол между векторами силы и перемещения.</p><p>Проанализируем направления векторов для нашего случая:</p><p><strong>1.</strong> <span><em>Направление силы.</em> Газ, находящийся в цилиндре, давит на все стенки, включая поршень. Сила давления газа на поршень ($\vec{F}_{газа}$) всегда направлена в сторону увеличения объема, то есть наружу из цилиндра.</span></p><p><strong>2.</strong> <span><em>Направление перемещения.</em> По условию задачи, газ сжимают. Это означает, что поршень движется внутрь цилиндра, уменьшая его объем. Следовательно, вектор перемещения поршня $\vec{s}$ направлен внутрь цилиндра.</span></p><p>Таким образом, вектор силы, с которой газ действует на поршень, $\vec{F}_{газа}$, и вектор перемещения поршня, $\vec{s}$, направлены в противоположные стороны. Угол $\alpha$ между ними равен $180^\circ$.</p><p>Косинус угла $180^\circ$ равен -1:</p><p>$\cos(180^\circ) = -1$</p><p>Подставим это значение в формулу для работы, совершаемой силой газа:</p><p>$A_{газа} = F_{газа} \cdot s \cdot \cos(180^\circ) = F_{газа} \cdot s \cdot (-1) = -F_{газа} \cdot s$</p><p>Поскольку модуль силы $F_{газа}$ и модуль перемещения $s$ являются положительными величинами, их произведение $F_{газа} \cdot s$ также положительно. Следовательно, работа $A_{газа}$ будет отрицательной.</p><p>К этому же выводу можно прийти, используя формулу для работы газа в термодинамике:</p><p>$A_{газа} = \int_{V_1}^{V_2} p \, dV$</p><p>При сжатии конечный объем газа $V_2$ меньше начального $V_1$ ($V_2 &lt; V_1$), поэтому изменение объема $\Delta V = V_2 - V_1$ отрицательно. Так как давление $p$ — величина положительная, то и работа газа при сжатии всегда отрицательна.</p><p><strong>Ответ:</strong><span>сила, действующая на поршень со стороны газа, совершает отрицательную работу.</span></p>"
          ]
          #original: array:6 [
            "id" => 1466734
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1248}
            "task" => array:2 [
              "refs" => "598929"
              "type" => "task"
            ]
            "text" => "<p><strong>Дано:</strong></p><p>Процесс - сжатие газа в цилиндре под поршнем.</p><p><strong>Найти:</strong></p><p>Знак работы $A_{газа}$, совершаемой силой, действующей на поршень со стороны газа.</p><p><strong>Решение:</strong></p><p>Механическая работа $A$ определяется как скалярное произведение вектора силы $\vec{F}$ на вектор перемещения $\vec{s}$ и вычисляется по формуле:</p><p>$A = F \cdot s \cdot \cos\alpha$</p><p>где $F$ – модуль силы, $s$ – модуль перемещения точки приложения силы, а $\alpha$ – угол между векторами силы и перемещения.</p><p>Проанализируем направления векторов для нашего случая:</p><p><strong>1.</strong> <span><em>Направление силы.</em> Газ, находящийся в цилиндре, давит на все стенки, включая поршень. Сила давления газа на поршень ($\vec{F}_{газа}$) всегда направлена в сторону увеличения объема, то есть наружу из цилиндра.</span></p><p><strong>2.</strong> <span><em>Направление перемещения.</em> По условию задачи, газ сжимают. Это означает, что поршень движется внутрь цилиндра, уменьшая его объем. Следовательно, вектор перемещения поршня $\vec{s}$ направлен внутрь цилиндра.</span></p><p>Таким образом, вектор силы, с которой газ действует на поршень, $\vec{F}_{газа}$, и вектор перемещения поршня, $\vec{s}$, направлены в противоположные стороны. Угол $\alpha$ между ними равен $180^\circ$.</p><p>Косинус угла $180^\circ$ равен -1:</p><p>$\cos(180^\circ) = -1$</p><p>Подставим это значение в формулу для работы, совершаемой силой газа:</p><p>$A_{газа} = F_{газа} \cdot s \cdot \cos(180^\circ) = F_{газа} \cdot s \cdot (-1) = -F_{газа} \cdot s$</p><p>Поскольку модуль силы $F_{газа}$ и модуль перемещения $s$ являются положительными величинами, их произведение $F_{газа} \cdot s$ также положительно. Следовательно, работа $A_{газа}$ будет отрицательной.</p><p>К этому же выводу можно прийти, используя формулу для работы газа в термодинамике:</p><p>$A_{газа} = \int_{V_1}^{V_2} p \, dV$</p><p>При сжатии конечный объем газа $V_2$ меньше начального $V_1$ ($V_2 &lt; V_1$), поэтому изменение объема $\Delta V = V_2 - V_1$ отрицательно. Так как давление $p$ — величина положительная, то и работа газа при сжатии всегда отрицательна.</p><p><strong>Ответ:</strong><span>сила, действующая на поршень со стороны газа, совершает отрицательную работу.</span></p>"
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    "book" => Illuminate\Database\Eloquent\Collection {#1255
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        0 => App\Models\BookPage {#1269
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            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1304
              #items: array:1 [
                0 => App\Models\Book {#1272
                  #connection: "mysql"
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                  #primaryKey: "id"
                  #keyType: "int"
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                  #attributes: array:50 [ …50]
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            "field_metatags_title" => null
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            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1302
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            "content" => Illuminate\Database\Eloquent\Collection {#1313
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                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [ …6]
                  #original: array:6 [ …6]
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                  #guarded: array:1 [ …1]
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            "next" => array:2 [
              "refs" => "991419"
              "type" => "book_page"
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            "previous" => array:2 [
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            "tasks" => Illuminate\Database\Eloquent\Collection {#2805
              #items: array:10 [
                0 => App\Models\Task {#2821
                  #connection: "mysql"
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                  #keyType: "int"
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                  #perPage: 15
                  +exists: true
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                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
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                  #guarded: array:1 [ …1]
                }
                1 => App\Models\Task {#2867
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
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                  #attributes: array:24 [ …24]
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                }
                2 => App\Models\Task {#2954
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
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                  +preventsLazyLoading: false
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                  +exists: true
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                  #guarded: array:1 [ …1]
                }
                3 => App\Models\Task {#2993
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
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                  #attributes: array:24 [ …24]
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                  #guarded: array:1 [ …1]
                }
                4 => App\Models\Task {#3039
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
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                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                5 => App\Models\Task {#3235
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
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                  +timestamps: true
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                  #hidden: []
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                  #guarded: array:1 [ …1]
                }
                6 => App\Models\Task {#3282
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
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                  +exists: true
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                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
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                  +timestamps: true
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                  #hidden: []
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                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                7 => App\Models\Task {#3531
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
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                  +exists: true
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                  #attributes: array:24 [ …24]
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                }
                8 => App\Models\Task {#3577
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
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                  #perPage: 15
                  +exists: true
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                  #attributes: array:24 [ …24]
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                  +timestamps: true
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                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                9 => App\Models\Task {#3624
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
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№1 (с. 54)

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Условие. №1 (с. 54)

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скриншот условия

1. Газ, находящийся в цилиндре под поршнем, сжимают. Подумайте, положительную или отрицательную работу совершает при этом сила, действующая на поршень со стороны газа.

Решение 1. №1 (с. 54)

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Решение 2. №1 (с. 54)

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Решение 3. №1 (с. 54)

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Решение 4. №1 (с. 54)

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Дано:

Процесс - сжатие газа в цилиндре под поршнем.

Найти:

Знак работы $A_{газа}$, совершаемой силой, действующей на поршень со стороны газа.

Решение:

Механическая работа $A$ определяется как скалярное произведение вектора силы $\vec{F}$ на вектор перемещения $\vec{s}$ и вычисляется по формуле:

$A = F \cdot s \cdot \cos\alpha$

где $F$ – модуль силы, $s$ – модуль перемещения точки приложения силы, а $\alpha$ – угол между векторами силы и перемещения.

Проанализируем направления векторов для нашего случая:

1. Направление силы. Газ, находящийся в цилиндре, давит на все стенки, включая поршень. Сила давления газа на поршень ($\vec{F}_{газа}$) всегда направлена в сторону увеличения объема, то есть наружу из цилиндра.

2. Направление перемещения. По условию задачи, газ сжимают. Это означает, что поршень движется внутрь цилиндра, уменьшая его объем. Следовательно, вектор перемещения поршня $\vec{s}$ направлен внутрь цилиндра.

Таким образом, вектор силы, с которой газ действует на поршень, $\vec{F}_{газа}$, и вектор перемещения поршня, $\vec{s}$, направлены в противоположные стороны. Угол $\alpha$ между ними равен $180^\circ$.

Косинус угла $180^\circ$ равен -1:

$\cos(180^\circ) = -1$

Подставим это значение в формулу для работы, совершаемой силой газа:

$A_{газа} = F_{газа} \cdot s \cdot \cos(180^\circ) = F_{газа} \cdot s \cdot (-1) = -F_{газа} \cdot s$

Поскольку модуль силы $F_{газа}$ и модуль перемещения $s$ являются положительными величинами, их произведение $F_{газа} \cdot s$ также положительно. Следовательно, работа $A_{газа}$ будет отрицательной.

К этому же выводу можно прийти, используя формулу для работы газа в термодинамике:

$A_{газа} = \int_{V_1}^{V_2} p \, dV$

При сжатии конечный объем газа $V_2$ меньше начального $V_1$ ($V_2 < V_1$), поэтому изменение объема $\Delta V = V_2 - V_1$ отрицательно. Так как давление $p$ — величина положительная, то и работа газа при сжатии всегда отрицательна.

Ответ:сила, действующая на поршень со стороны газа, совершает отрицательную работу.