Тренировочная работа № 4 по ФИЗИКЕ 30 апреля 2013 года 11
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Физика. 11 класс. Вариант ФИ1601 2 Инструкция по выполнению работы Тренировочная работа № 4 по ФИЗИКЕ 30 апреля 2013 года 11 класс Вариант ФИ1601 Для выполнения экзаменационной работы по физике отводится 235 минут. Работа состоит из 3 частей, включающих в себя 35 заданий. Часть 1 содержит 21 задание (А1–А21). К каждому заданию даётся четыре варианта ответа, из которых только один правильный. Часть 2 содержит 4 задания (В1–В4), на которые надо дать краткий ответ в виде последовательности цифр Часть 3 содержит 10 задач: А22–А25 с выбором одного верного ответа и С1–С6, для которых требуется дать развёрнутые решения. При вычислениях разрешается использовать непрограммируемый калькулятор. Все бланки ЕГЭ заполняются яркими чёрными чернилами. Допускается использование гелевой, капиллярной или перьевой ручек. При выполнении заданий Вы можете пользоваться черновиком. Обращаем Ваше внимание на то, что записи в черновике не будут учитываться при оценивании работы. Советуем выполнять задания в том порядке, в котором они даны Для экономии времени пропускайте задание, которое не удаётся выполнить сразу, и переходите к следующему. Если после выполнения всей работы у Вас останется время, Вы сможете вернуться к пропущенным заданиям Баллы, полученные Вами за выполненные задания, суммируются. Постарайтесь выполнить как можно больше заданий и набрать наибольшее количество баллов. Район. Город (населённый пункт) Школа. Класс. Фамилия Имя Отчество. © СтатГрад 2013 г. Желаем успеха! © СтатГрад 2013 г. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 4 ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɫɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ȼɚɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬɵ. ɷɥɟɤɬɪɨɧɚ ɩɪɨɬɨɧɚ ɧɟɣɬɪɨɧɚ Ⱦɟɫɹɬɢɱɧɵɟ ɩɪɢɫɬɚɜɤɢ Ɇɚɫɫɵ ɱɚɫɬɢɰ 9,1 · 10–31 ɤɝ § 5,5·10–4 ɚ. ɟ. ɦ. 1,673 · 10–27 ɤɝ § 1,007 ɚ. ɟ. ɦ. 1,675 · 10–27 ɤɝ § 1,008 ɚ. ɟ. ɦ. ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɝɢɝɚ Ƚ 10 9 ɫɚɧɬɢ ɫ 10–2 ɦɟɝɚ Ɇ 10 6 ɦɢɥɥɢ ɦ 10–3 ɜɨɞɵ 1000 ɤɝɦ3 ɤɢɥɨ ɤ 10 3 ɦɢɤɪɨ ɦɤ 10–6 ɞɪɟɜɟɫɢɧɵ (ɫɨɫɧɚ) ɚɥɸɦɢɧɢɹ ɝɟɤɬɨ ɝ ɧɚɧɨ ɧ 400 ɤɝɦ3 2700 ɤɝɦ3 10 2 10–9 ɞɟɰɢ ɞ 10–1 ɩɢɤɨ ɩ 10–12 ɤɟɪɨɫɢɧɚ 800 ɤɝɦ3 ɠɟɥɟɡɚ 7800 ɤɝɦ3 ɪɬɭɬɢ 13 600 ɤɝɦ3 ɉɥɨɬɧɨɫɬɶ ɩɨɞɫɨɥɧɟɱɧɨɝɨ ɦɚɫɥɚ Ʉɨɧɫɬɚɧɬɵ ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɺɦɤɨɫɬɶ ɱɢɫɥɨ ʌ ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɧɚ Ɂɟɦɥɟ ʌ = 3,14 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ G = 6,7 · 10–11 ɇÂɦ2ɤɝ2 R = 8,31 Ⱦɠ/(ɦɨɥɶÂɄ) ɩɨɫɬɨɹɧɧɚɹ Ⱥɜɨɝɚɞɪɨ NȺ = 6·1023 ɦɨɥɶ–1 ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ ɫ = 3 · 108 ɦɫ 1 k= = 9 · 109 ɇÂɦ2Ʉɥ2 ʌ İ0 ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɜ ɡɚɤɨɧɟ Ʉɭɥɨɧɚ ɦɨɞɭɥɶ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ (ɷɥɟɦɟɧɬɚɪɧɵɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɡɚɪɹɞ) ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ g = 10 ɦɫ2 k = 1,38 · 10–23 ȾɠɄ ɜɨɞɵ 4,2 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɚɥɸɦɢɧɢɹ 900 Ⱦɠ/(ɤɝÂɄ) ɥɶɞɚ 2,1 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɦɟɞɢ 380 Ⱦɠ/(ɤɝÂɄ) ɠɟɥɟɡɚ ɫɜɢɧɰɚ 640 Ⱦɠ/(ɤɝÂɄ) 130 Ⱦɠ/(ɤɝÂɄ) ɱɭɝɭɧɚ 500 Ⱦɠ/(ɤɝÂɄ) ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɹ ɜɨɞɵ 2,3 · 10 6 Ⱦɠɤɝ ɩɥɚɜɥɟɧɢɹ ɫɜɢɧɰɚ ɩɥɚɜɥɟɧɢɹ ɥɶɞɚ e = 1,6 · 10–19 Ʉɥ 1 ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ ɷɤɜɢɜɚɥɟɧɬɧɚ 1 ɷɥɟɤɬɪɨɧɜɨɥɶɬ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2,5 · 10 4 Ⱦɠɤɝ 3,3 · 10 5 Ⱦɠɤɝ ɇɨɪɦɚɥɶɧɵɟ ɭɫɥɨɜɢɹ h = 6,6 · 10–34 ȾɠÂɫ ɞɚɜɥɟɧɢɟ: 105 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ: 0 °ɋ ɋɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɟɞɢɧɢɰɚɦɢ ɬɟɦɩɟɪɚɬɭɪɚ ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ 900 ɤɝɦ3 Ɇɨɥɹɪɧɚɹ ɦɚFɫɚ ɝɟɥɢɹ 0 Ʉ = – 273 °ɋ ɚɡɨɬɚ 28 · 10–3 ɤɝɦɨɥɶ 1 ɚ. ɟ. ɦ. = 1,66 · 10–27 ɤɝ 931,5 Ɇɷȼ ɚɪɝɨɧɚ 40 · 10–3 ɤɝɦɨɥɶ ɤɢɫɥɨɪɨɞɚ 32 · 10–3 ɤɝɦɨɥɶ ɜɨɞɨɪɨɞɚ 2 · 10–3 ɤɝɦɨɥɶ ɥɢɬɢɹ 1 ɷȼ = 1,6 · 10–19 Ⱦɠ 6 · 10–3 ɤɝɦɨɥɶ ɜɨɡɞɭɯɚ 29 · 10–3 ɤɝɦɨɥɶ ɧɟɨɧɚ 20 · 10–3 ɤɝɦɨɥɶ ɜɨɞɵ 18 · 10–3 ɤɝɦɨɥɶ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ 44 · 10–3 ɤɝɦɨɥɶ © ɋɬɚɬȽɪɚɞ 2013 ɝ 4 · 10–3 ɤɝɦɨɥɶ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 5 ɑɚɫɬɶ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 A4 ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɱɚɫɬɢ 1 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ (A1–A21) ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A1 ɉɨ ɩɥɨɫɤɨɫɬɢ XY ɞɜɢɠɭɬɫɹ ɱɟɬɵɪɟ ɬɨɱɟɱɧɵɯ ɬɟɥɚ – Ⱥ, Ȼ, ȼ ɢ Ƚ, ɬɪɚɟɤɬɨɪɢɢ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫɭɧɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬ ɨɞɧɨɝɨ ɢɡ ɷɬɢɯ ɬɟɥ ɨɬ ɜɪɟɦɟɧɢ ɢɦɟɸɬ ɜɢɞ x 1 t ɢ y 2t. ɗɬɨ ɬɟɥɨ ɨɛɨɡɧɚɱɟɧɨ ɛɭɤɜɨɣ Ⱦɜɚ ɛɪɭɫɤɚ ɦɚɫɫɨɣ m ɢ 2m ɪɚɜɧɨɦɟɪɧɨ ɞɜɢɠɭɬɫɹ ɜɞɨɥɶ ɩɪɹɦɨɣ OX (ɫɦ. ɪɢɫɭɧɨɤ). ȼ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɛɪɭɫɤɨɦ 1, ɦɨɞɭɥɶ ɢɦɩɭɥɶɫɚ ɜɬɨɪɨɝɨ ɛɪɭɫɤɚ ɪɚɜɟɧ 1) 6mV A5 6 2) 4mV 3) 3mV 4) 2mV ɋɚɧɢ ɪɚɜɧɨɦɟɪɧɨ ɩɟɪɟɦɟɳɚɸɬ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɩɟɪɟɦɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɦɨɞɭɥɹ ɪɚɛɨɬɵ ɫɢɥɵ ɬɪɟɧɢɹ Aɬɪ ɨɬ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ S. Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ɧɚ ɩɪɨɣɞɟɧɧɨɦ ɩɭɬɢ ɪɚɜɧɨ 1) Ⱥ A2 2) Ȼ 3) ȼ 4) Ƚ 1) 2 Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɪɚɜɧɨɦɟɪɧɨɝɨ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ r A6 1) 2) 3) 4) A3 ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɫɩɭɬɧɢɤɚ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɫɩɭɬɧɢɤɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ A7 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 4) 8 1 ɞɥɢɧɵ ɛɚɥɤɢ (ɫɦ. ɪɢɫɭɧɨɤ). 4 Ʉɚɤɭɸ ɫɢɥɭ F ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ ɤ ɤɨɧɰɭ B ɛɚɥɤɢ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ? 1) Mg ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɬɟɥ ɨɞɢɧɚɤɨɜɵɯ ɦɚɫɫ M, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ F0, ɨɩɪɟɞɟɥɢɬɟ, ɞɥɹ ɤɚɤɨɣ ɩɚɪɵ ɬɟɥ ɫɢɥɚ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɪɚɜɧɚ 4F0. 3) 6 Ɉɞɧɨɪɨɞɧɚɹ ɫɩɥɨɲɧɚɹ ɛɚɥɤɚ ɦɚɫɫɨɣ M ɭɪɚɜɧɨɜɟɲɟɧɚ ɧɚ ɨɫɬɪɨɤɨɧɟɱɧɨɣ ɨɩɨɪɟ. Ɉɩɨɪɭ ɩɟɪɟɞɜɢɝɚɸɬ ɜɩɪɚɜɨ ɧɚ ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɱɟɬɵɪɟ ɩɚɪɵ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɬɨɱɟɱɧɵɯ ɬɟɥ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ ɧɚ ɪɚɡɧɵɯ ɪɚɫɫɬɨɹɧɢɹɯ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɷɬɢɯ ɬɟɥ. 1) 1 2) 4 2) Mg 2 3) Mg 3 4) Mg 4 Ⱦɢɦɚ ɢ Ʌɟɧɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɢɡɨɛɪɚɡɢɥɢ ɧɚ ɞɨɫɤɟ ɫɨɫɭɞ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɢɞɟɚɥɶɧɵɣ ɝɚɡ. Ɉɬɜɟɱɚɸɳɢɦ ɦɨɞɟɥɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɦɨɠɧɨ ɩɪɢɡɧɚɬɶ ɪɢɫɭɧɨɤ, ɫɞɟɥɚɧɧɵɣ Ⱥ) Ⱦɢɦɨɣ Ȼ) Ʌɟɧɨɣ 1) ɬɨɥɶɤɨ Ⱥ 2) ɬɨɥɶɤɨ Ȼ 3) ɢ Ⱥ, ɢ Ȼ 4) ɧɢ Ⱥ, ɧɢ Ȼ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 A8 7 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɢɡ ɫɨɫɬɨɹɧɢɹ Ⱥ ɜ ɫɨɫɬɨɹɧɢɟ Ȼ. A9 8 A11 Ɍɨɱɟɱɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ Q ɧɚɯɨɞɢɬɫɹ ɧɚ ɧɟɛɨɥɶɲɨɦ ɪɚɫɫɬɨɹɧɢɢ x0 ɨɬ ɩɪɨɬɹɠɺɧɧɨɣ ɧɟɩɪɨɜɨɞɹɳɟɣ ɡɚɪɹɠɟɧɧɨɣ ɩɥɚɫɬɢɧɵ, ɪɚɜɧɨɦɟɪɧɨ ɡɚɪɹɠɟɧɧɨɣ ɡɚɪɹɞɨɦ q (ɫɦ. ɪɢɫɭɧɨɤ). Ɂɚɪɹɞ Q ɧɚɱɢɧɚɸɬ ɩɟɪɟɦɟɳɚɬɶ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɚɫɬɢɧɟ, ɭɞɚɥɹɹ ɨɬ ɧɟɺ. ɇɚ ɤɚɤɨɦ ɢɡ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ ɝɪɚɮɢɤɨɜ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɫɢɥɵ F ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɞɚ Q ɫ ɩɥɚɫɬɢɧɨɣ ɨɬ ɪɚɫɫɬɨɹɧɢɹ x ɦɟɠɞɭ ɡɚɪɹɞɨɦ ɢ ɩɥɚɫɬɢɧɨɣ? ȼ ɫɨɫɬɨɹɧɢɢ Ȼ ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɝɨ ɝɚɡɚ 1) 2) 3) 4) Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 ɜ 2 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɜ 2 ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɜ 4 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ȼ ɬɚɛɥɢɰɟ ɭɤɚɡɚɧɚ ɩɥɨɬɧɨɫɬɶ ɝɚɡɨɜ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ. Ƚɚɡ ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɤɝɦ3 ɚɡɨɬ ɜɨɞɨɪɨɞ ɤɫɟɧɨɧ ɯɥɨɪ 1,25 0,09 5,9 3,2 1) 1 ɉɪɢ ɷɬɨɦ ɧɚɢɦɟɧɶɲɭɸ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɭɸ ɫɤɨɪɨɫɬɶ ɢɦɟɸɬ ɦɨɥɟɤɭɥɵ 1) ɚɡɨɬɚ 2) ɜɨɞɨɪɨɞɚ 3) ɤɫɟɧɨɧɚ 4) ɯɥɨɪɚ A10 Ⱦɜɚ ɦɨɥɹ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɜɨɞɹɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T1 ɜ ɫɨɫɬɨɹɧɢɟ 2 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T2 ɫɦ. ɪɢɫɭɧɨɤ). Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɫɨɨɛɳɟɧɨ ɝɚɡɭ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɬɨɥɛɰɭ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ, ɨɛɨɡɧɚɱɟɧɧɨɦɭ ɰɢɮɪɨɣ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 2) 2 3) 3 4) 4 A12 ɂɞɟɚɥɶɧɵɣ ɚɦɩɟɪɦɟɬɪ ɢ ɬɪɢ ɪɟɡɢɫɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ R 2 Ɉɦ, 2R ɢ 3R ɜɤɥɸɱɟɧɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɰɟɩɶ, ɫɨɞɟɪɠɚɳɭɸ ɢɫɬɨɱɧɢɤ ɫ ɗȾɋ, ɪɚɜɧɨɣ 5 ȼ, ɢ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ r = 8 Ɉɦ. ɉɨɤɚɡɚɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɪɚɜɧɵ 1) 100 Ⱥ 2) 4 Ⱥ 3) § 0,56 Ⱥ 4) 0,25 Ⱥ JG A13 ɗɥɟɤɬɪɨɧ, ɞɜɢɝɚɹɫɶ ɫɨ ɫɤɨɪɨɫɬɶɸ V , ɧɚɩɪɚɜɥɟɧɧɨɣ JGɜɞɨɥɶ ɨɫɢ X, ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɫɬɶ ɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɢɧɞɭɤɰɢɟɣ B , ɥɟɠɚɳɟɣ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ XY (ɧɚ ɪɢɫɭɧɤɟ ɷɬɚ ɩɥɨɫɤɨɫɬɶ ɩɨɤɚɡɚɧɚ ɬɨɧɢɪɨɜɤɨɣ). ɉɪɚɜɢɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɤɬɪɨɧ, ɢɡɨɛɪɚɠɟɧɨ ɜɟɤɬɨɪɨɦ ɩɨɞ ɧɨɦɟɪɨɦ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 9 A14 ɂɦɟɸɬɫɹ ɞɜɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ: ɩɟɪɜɚɹ ɞɜɢɠɟɬɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ, ɜɬɨɪɚɹ – ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ 1) 2) 3) 4) Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 10 A17 ɉɪɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦ ɢɡɭɱɟɧɢɢ ɮɨɬɨɷɮɮɟɤɬɚ ɩɨɥɭɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɡɚɩɢɪɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ Uɡ ɨɬ ɱɚɫɬɨɬɵ Ȟ ɫɜɟɬɚ, ɩɚɞɚɸɳɟɝɨ ɧɚ ɦɟɬɚɥɥɢɱɟɫɤɭɸ ɩɥɚɫɬɢɧɤɭ. ɇɚ ɤɚɤɨɦ ɪɢɫɭɧɤɟ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ? ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɩɟɪɜɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɢ ɩɟɪɜɚɹ, ɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɧɟ ɢɡɥɭɱɚɟɬ ɧɢ ɩɟɪɜɚɹ, ɧɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ A15 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɨɩɬɢɱɟɫɤɚɹ ɨɫɶ OO c ɬɨɧɤɨɣ ɫɨɛɢɪɚɸɳɟɣ ɥɢɧɡɵ, ɥɭɱ ɫɜɟɬɚ 1, ɩɚɞɚɸɳɢɣ ɧɚ ɷɬɭ ɥɢɧɡɭ, ɢ ɥɭɱ ɫɜɟɬɚ 2, ɩɪɨɲɟɞɲɢɣ ɱɟɪɟɡ ɷɬɭ ɥɢɧɡɭ. ɇɚ ɪɢɫɭɧɤɟ ɪɚɡɦɟɪ ɨɞɧɨɣ ɤɥɟɬɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ 1 ɫɦ. Ɏɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɥɢɧɡɵ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɨ 1) 1 1) 0,01 ɦ 2) 0,02 ɦ 3) 0,04 ɦ 4) 4 A18 Ɉɬɧɨɲɟɧɢɟ ɦɚɫɫɨɜɨɝɨ ɱɢɫɥɚ ɤ ɱɢɫɥɭ ɧɟɣɬɪɨɧɨɜ ɪɚɜɧɨ § 2,11 ɜ ɹɞɪɟ 1) 7Be 4 © ɋɬɚɬȽɪɚɞ 2013 ɝ 3) 3 4) 0,05 ɦ A16 ɇɚ ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɭɸ ɫɬɟɤɥɹɧɧɭɸ ɩɥɚɫɬɢɧɤɭ ɢ ɫɬɟɤɥɹɧɧɭɸ ɩɪɢɡɦɭ ɩɚɞɚɟɬ ɥɭɱ ɛɟɥɨɝɨ ɫɜɟɬɚ (ɫɦ. ɪɢɫɭɧɨɤ). Ⱦɢɫɩɟɪɫɢɹ ɫɜɟɬɚ ɜ ɜɢɞɟ ɪɚɞɭɠɧɵɯ ɩɨɥɨɫ ɧɚ ɷɤɪɚɧɟ 1) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ⱥ 2) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ȼ 3) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɢ ɜ ɫɥɭɱɚɟ Ȼ 4) ɧɟ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɧɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɧɢ ɜ ɫɥɭɱɚɟ Ȼ 2) 2 2) 20Mg 12 3) 19 N e 10 4) 35C l 17 A19 Ⱦɨɥɹ ɚɬɨɦɨɜ ɪɚɞɢɨɚɤɬɢɜɧɨɝɨ ɢɡɨɬɨɩɚ, ɧɟ ɪɚɫɩɚɜɲɢɯɫɹ ɩɨ ɩɪɨɲɟɫɬɜɢɢ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ, ɪɚɜɧɨɝɨ ɩɨɥɨɜɢɧɟ ɩɟɪɢɨɞɚ ɩɨɥɭɪɚɫɩɚɞɚ, ɨɛɨɡɧɚɱɟɧɚ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ ɰɢɮɪɨɣ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 11 A20 ɉɨɤɚɡɚɧɢɹ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɧɟɤɨɬɨɪɨɦ ɩɨɦɟɳɟɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ 20 °ɋ ɢ 15 °ɋ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ ɬɚɛɥɢɰ, ɨɩɪɟɞɟɥɢɬɟ ɚɛɫɨɥɸɬɧɭɸ ɜɥɚɠɧɨɫɬɶ ɜɨɡɞɭɯɚ ɜ ɩɨɦɟɳɟɧɢɢ, ɝɞɟ ɭɫɬɚɧɨɜɥɟɧɵ ɞɚɧɧɵɟ ɬɟɪɦɨɦɟɬɪɵ. ȼ ɩɟɪɜɨɣ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ, ɜɵɪɚɠɟɧɧɚɹ ɜ %. Ɍɟɦɩɟɪɚɬɭɪɚ ɫɭɯɨɝɨ ɬɟɪɦɨɦɟɬɪɚ, °ɋ 15 16 17 18 19 20 21 22 23 24 25 Ɋɚɡɧɨɫɬɶ ɩɨɤɚɡɚɧɢɣ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, °ɋ 3 4 5 6 71 61 52 44 71 62 54 45 72 64 55 47 73 64 56 48 74 65 58 50 74 66 59 51 75 67 60 52 76 68 61 54 76 69 61 55 77 69 62 56 77 70 63 57 Ɍɟɦɩɟɪɚɬɭɪɚ, °ɋ ɉɥɨɬɧɨɫɬɶ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɜɨɞɵ ȡ, ɝɦ3 15 16 17 18 19 20 21 22 23 24 25 12,8 13,6 14,5 15,4 16,3 17,3 18,3 19,4 20,6 21,8 23,0 1) 7,6 ɝɦ3 2) 10,2 ɝɦ3 3) 12,8 ɝɦ3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 A21 Ʉ ɢɫɬɨɱɧɢɤɭ ɬɨɤɚ ɩɨɞɤɥɸɱɟɧɵ ɪɟɨɫɬɚɬ, ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ (ɪɢɫɭɧɨɤ 1). ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɩɨɥɡɭɧɤɚ ɪɟɨɫɬɚɬɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɩɪɢɛɨɪɚɦɢ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ, ɢɡɨɛɪɚɠɺɧɧɵɟ ɧɚ ɪɢɫɭɧɤɚɯ 2 ɢ 3 (R – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɤɥɸɱɺɧɧɨɣ ɜ ɰɟɩɶ ɱɚɫɬɢ ɪɟɨɫɬɚɬɚ). ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ(-ɵɟ) ɭɬɜɟɪɠɞɟɧɢɟ(-ɹ), ɟɫɥɢ ɬɚɤɨɜɨɟ(-ɵɟ) ɢɦɟɟɬɫɹ(-ɸɬɫɹ). Ⱥ. ȼɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɨ 2 Ɉɦ. Ȼ. ɗȾɋ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɚ 30 ɦȼ. 1) ɬɨɥɶɤɨ Ⱥ 3) ɢ Ⱥ, ɢ Ȼ 4) ɧɢ Ⱥ, ɧɢ Ȼ Ɉɬɜɟɬɨɦ ɤ ɡɚɞɚɧɢɹɦ ɷɬɨɣ ɱɚɫɬɢ (ȼ1–ȼ4) ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɰɢɮɪ. ȼɩɢɲɢɬɟ ɨɬɜɟɬɵ ɫɧɚɱɚɥɚ ɜ ɬɟɤɫɬ ɪɚɛɨɬɵ, ɚ ɡɚɬɟɦ ɩɟɪɟɧɟɫɢɬɟ ɢɯ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ, ɛɟɡ ɡɚɩɹɬɵɯ, ɩɪɨɛɟɥɨɜ ɢ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɢɦɜɨɥɨɜ. Ʉɚɠɞɭɸ ɰɢɮɪɭ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɰɟɩɶ ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɗȾɋ ɫ ɧɟɤɨɬɨɪɵɦ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ, ɞɜɭɯ ɨɞɢɧɚɤɨɜɵɯ ɥɚɦɩɨɱɟɤ, ɤɥɸɱɚ, ɜɨɥɶɬɦɟɬɪɚ ɢ ɞɜɭɯ ɚɦɩɟɪɦɟɬɪɨɜ (ɫɦ. ɪɢɫɭɧɨɤ). ɂɡɦɟɪɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɵɦɢ. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɩɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɨɜ, ɟɫɥɢ ɡɚɦɤɧɭɬɶ ɤɥɸɱ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɉɈɄȺɁȺɇɂȿ ɉɊɂȻɈɊȺ Ⱥ) ɩɨɤɚɡɚɧɢɟ ɜɨɥɶɬɦɟɬɪɚ Ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ1 ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ2 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) ɬɨɥɶɤɨ Ȼ ɑɚɫɬɶ 2 B1 4) 17,3 ɝɦ3 12 © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ ȼ ȿȽɈ ɂɁɆȿɇȿɇɂȿ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 B2 13 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 Ɉɞɢɧ ɦɨɥɶ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 1. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɫɥɟɞɭɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ, ɟɫɥɢ ɡɚɦɟɧɢɬɶ ɢɫɯɨɞɧɵɣ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ ɧɚ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 2: ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɝɚɡɨɦ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ; ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ; ɄɉȾ ɰɢɤɥɚ? ɍɑȺɋɌɈɄ ȽɊȺɎɂɄȺ Ⱥ) ȺȻ Ȼ) Ȼȼ Ɉɬɜɟɬ: B4 Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɎɂɁɂɑȿɋɄɂȿ ȼȿɅɂɑɂɇɕ Ⱥ) ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɧɚɝɪɟɜɚɬɟɥɹ Ȼ) ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ ȼ) ɄɉȾ ɰɢɤɥɚ Ɉɬɜɟɬ: B3 Ⱥ Ȼ ɝɚɡɨɦ ɨɬ ɂɏ ɂɁɆȿɇȿɇɂȿ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ ȼ ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɢɥɵ ɬɨɤɚ I ɜ ɤɚɬɭɲɤɟ ɢɧɞɭɤɬɢɜɧɨɫɬɶɸ 10 ɦȽɧ ɨɬ ɜɪɟɦɟɧɢ t. 14 Ʉ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ ɩɟɪɜɨɝɨ ɫɬɨɥɛɰɚ ɩɨɞɛɟɪɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɨɡɢɰɢɸ ɜɬɨɪɨɝɨ ɫɬɨɥɛɰɚ ɢ ɡɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɩɨɞ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɛɭɤɜɚɦɢ. Ⱥ Ȼ ɆɈȾɍɅɖ ɗȾɋ ɋȺɆɈɂɇȾɍɄɐɂɂ 1) 0,625 ɦȼ 2) 0,027 ȼ 3) 0,4 ɦȼ 4) 0,1 ɦȼ 5) 0 ȼ ɇɚ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɫ ɩɟɪɢɨɞɨɦ d 0 ɧɨɪɦɚɥɶɧɨ ɩɚɞɚɟɬ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɣ ɩɭɱɨɤ ɫɜɟɬɚ, ɚ ɡɚ ɪɟɲɺɬɤɨɣ ɪɚɫɩɨɥɨɠɟɧ ɨɛɴɟɤɬɢɜ, ɜ ɮɨɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɧɚɛɥɸɞɚɸɬɫɹ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ ɫɦ. ɪɢɫɭɧɨɤ). Ɍɨɱɤɚɦɢ ɩɨɤɚɡɚɧɵ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ, ɚ ɰɢɮɪɚɦɢ ɨɛɨɡɧɚɱɟɧɵ ɢɯ ɧɨɦɟɪɚ. ɍɝɥɵ ɞɢɮɪɚɤɰɢɢ ɦɚɥɵ. ɗɬɭ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɩɨɨɱɟɪɺɞɧɨ ɡɚɦɟɧɹɸɬ ɞɪɭɝɢɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɦɢ ɪɟɲɺɬɤɚɦɢ – Ⱥ, Ȼ ɢ ȼ. ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɫɯɟɦɚɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɦɚɤɫɢɦɭɦɨɜ ɢ ɩɟɪɢɨɞɚɦɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɪɟɲɺɬɨɤ. ɋɏȿɆȺ ȾɂɎɊȺɄɐɂɈɇɇɕɏ ɆȺɄɋɂɆɍɆɈȼ Ⱥ) Ⱥ Ȼ) Ȼ ɉȿɊɂɈȾ ȾɂɎɊȺɄɐɂɈɇɇɈɃ ɊȿɒȬɌɄɂ 1) 4d 0 2) d 0 4 3) 2d 0 4) 2 d 0 3 5) 2 d 0 ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɭɱɚɫɬɤɚɦɢ ɝɪɚɮɢɤɚ ɢ ɡɧɚɱɟɧɢɹɦɢ ɦɨɞɭɥɹ ɗȾɋ ɫɚɦɨɢɧɞɭɤɰɢɢ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 15 ɑɚɫɬɶ 3 Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 3 ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɞɚɱɢ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɢɯ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ ɧɚ ɱɟɪɧɨɜɢɤɟ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ Ⱥ22–Ⱥ25 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A22 Ƚɪɭɡ ɧɚɱɢɧɚɟɬ ɫɜɨɛɨɞɧɨ ɩɚɞɚɬɶ ɫ ɧɟɤɨɬɨɪɨɣ ɜɵɫɨɬɵ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɨɥɟɬɟɜ 40 ɦ, ɝɪɭɡ ɩɪɢɨɛɪɺɥ ɫɤɨɪɨɫɬɶ 20 ɦɫ. ɇɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ ɨɬɧɨɲɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɝɪɭɡɚ ɤ ɪɚɛɨɬɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɪɚɜɧɨ 1) 1 2) 2 3) –2 4) 4 A23 ɉɨɪɲɟɧɶ ɦɨɠɟɬ ɫɜɨɛɨɞɧɨ ɛɟɡ ɬɪɟɧɢɹ ɩɟɪɟɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɬɟɧɨɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɨɫɭɞɚ. ȼ ɨɛɴɺɦɟ, ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɧɨɦ ɫɨɫɭɞɚ ɢ ɩɨɪɲɧɟɦ, ɧɚɯɨɞɢɬɫɹ ɜɨɡɞɭɯ ɫɦ. ɪɢɫɭɧɨɤ). ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɨɫɭɞɚ ɪɚɜɧɚ 20 ɫɦ2, ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɞɧɚ ɫɨɫɭɞɚ ɞɨ ɩɨɪɲɧɹ ɪɚɜɧɨ 25 ɫɦ, ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ 100 ɤɉɚ, ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɜ ɫɨɫɭɞɟ ɪɚɜɧɨ ɚɬɦɨɫɮɟɪɧɨɦɭ. ɉɨɪɲɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɦɟɳɚɸɬ ɧɚ 5 ɫɦ ɜɥɟɜɨ, ɩɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɧɟ ɦɟɧɹɟɬɫɹ. Ʉɚɤɭɸ ɫɢɥɭ ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ, ɱɬɨɛɵ ɭɞɟɪɠɚɬɶ ɩɨɪɲɟɧɶ ɜ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ? 1) 41,7 ɇ 2) 50,0 ɇ 3) 208,3 ɇ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 ɉɨɥɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɋ1–ɋ6 ɧɟɨɛɯɨɞɢɦɨ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2. ɉɪɢ ɨɮɨɪɦɥɟɧɢɢ ɪɟɲɟɧɢɹ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2 ɡɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɡɚɞɚɧɢɹ ɋ1, ɋ2 ɢ ɬ. ɞ.), ɚ ɡɚɬɟɦ ɪɟɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɡɚɞɚɱɢ. Ɉɬɜɟɬɵ ɡɚɩɢɫɵɜɚɣɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ. C1 C2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ȼɟɧɟɪɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 243 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ ȼɟɧɟɪɵ ɫɨɫɬɚɜɥɹɟɬ 0,82 ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ ȼɟɧɟɪɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. C3 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 300 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ A24 Ⱦɜɟ ɬɨɧɤɢɟ ɜɟɪɬɢɤɚɥɶɧɵɟ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɩɥɚɫɬɢɧɵ ɪɚɫɩɨɥɨɠɟɧɵ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ, ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɪɚɜɧɨ 2 ɫɦ. ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ 1) 0 ȼ/ɦ 2) § 0,19 ȼ/ɦ 3) § 0,75 ȼ/ɦ A25 ɗɥɟɤɬɪɨɧ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɫ ɢɧɞɭɤɰɢɟɣ 6 ɦɤɌɥ. ɉɟɪɢɨɞ ɨɛɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɪɚɜɟɧ 1) | 6, 0 106 ɫ 3) | 1, 7 105 ɫ 4) § 0,38 ȼ/ɦ ɦɚɝɧɢɬɧɨɦ 2) | 6, 7 106 ɫ 4) | 5, 9 · 10–5 ɫ ɩɨɥɟ Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ ɨɪɝɚɧɚ ɞɥɢɧɵ ɛɨɥɶɲɢɟ, ɚ ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ɉɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ ɤɚɠɞɨɣ ɢɡ ɡɚɞɚɱ ɋ2–ɋ6 ɞɨɥɠɧɨ ɫɨɞɟɪɠɚɬɶ ɡɚɤɨɧɵ ɢ ɮɨɪɦɭɥɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɪɚɫɱɺɬɵ ɫ ɱɢɫɥɟɧɧɵɦ ɨɬɜɟɬɨɦ ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɢɫɭɧɨɤ, ɩɨɹɫɧɹɸɳɢɣ ɪɟɲɟɧɢɟ. 4) 312,5 ɇ ɫɟɱɟɧɢɹ ɤɚɠɞɨɣ ɢɡ ɩɥɚɫɬɢɧ ɪɚɜɧɚ 15 000 ɫɦ2. Ʌɟɜɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɡɚɪɹɞ q 5 ɩɄɥ, ɡɚɪɹɞ ɜɬɨɪɨɣ ɩɥɚɫɬɢɧɵ q. Ɇɨɞɭɥɶ ɧɚɩɪɹɠɺɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,5 ɫɦ ɨɬ ɥɟɜɨɣ ɩɥɚɫɬɢɧɵ ɪɚɜɟɧ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 2. C4 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,9 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 20 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 19 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? ɇɟ ɡɚɛɭɞɶɬɟ ɩɟɪɟɧɟɫɬɢ ɜɫɟ ɨɬɜɟɬɵ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1. © ɋɬɚɬȽɪɚɞ 2013 ɝ 16 © ɋɬɚɬȽɪɚɞ 2013 ɝ Физика. 11 класс. Вариант ФИ1601 17 С5 Определите фокусное расстояние тонкой линзы, если линейные размеры изображения тонкого карандаша, помещённого на расстоянии а = 60 см от линзы и расположенного перпендикулярно главной оптической оси, меньше размеров карандаша в n = 3 раза. С6 Согласно гипотезе де Бройля, все частицы обладают волновыми свойствами. Длина волны для частицы массой m, имеющей скорость v, составляет ߣ= -34 h mv , где h = 6,6 · 10 Дж · с – постоянная Планка. Для того, чтобы можно было применять модель идеального газа, среднее расстояние l между молекулами газа должно быть, в частности, гораздо больше ߣ. При какой температуре T для инертного газа гелия ߣ ≈ l , если концентрация его молекул 25 -3 равна n = 2,7 · 10 м ? -24 Масса молекулы гелия равна m = 6,6 · 10 г. © СтатГрад 2013 г. Физика. 11 класс. Вариант ФИ1602 2 Инструкция по выполнению работы Тренировочная работа № 4 по ФИЗИКЕ 30 апреля 2013 года 11 класс Вариант ФИ1602 Для выполнения экзаменационной работы по физике отводится 235 минут. Работа состоит из 3 частей, включающих в себя 35 заданий. Часть 1 содержит 21 задание (А1–А21). К каждому заданию даётся четыре варианта ответа, из которых только один правильный. Часть 2 содержит 4 задания (В1–В4), на которые надо дать краткий ответ в виде последовательности цифр Часть 3 содержит 10 задач: А22–А25 с выбором одного верного ответа и С1–С6, для которых требуется дать развёрнутые решения. При вычислениях разрешается использовать непрограммируемый калькулятор. Все бланки ЕГЭ заполняются яркими чёрными чернилами. Допускается использование гелевой, капиллярной или перьевой ручек. При выполнении заданий Вы можете пользоваться черновиком. Обращаем Ваше внимание на то, что записи в черновике не будут учитываться при оценивании работы. Советуем выполнять задания в том порядке, в котором они даны Для экономии времени пропускайте задание, которое не удаётся выполнить сразу, и переходите к следующему. Если после выполнения всей работы у Вас останется время, Вы сможете вернуться к пропущенным заданиям Баллы, полученные Вами за выполненные задания, суммируются. Постарайтесь выполнить как можно больше заданий и набрать наибольшее количество баллов. Район. Город (населённый пункт) Школа. Класс. Фамилия Имя Отчество. © СтатГрад 2013 г. Желаем успеха! © СтатГрад 2013 г. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 4 ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɫɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ȼɚɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬɵ. ɷɥɟɤɬɪɨɧɚ ɩɪɨɬɨɧɚ ɧɟɣɬɪɨɧɚ Ⱦɟɫɹɬɢɱɧɵɟ ɩɪɢɫɬɚɜɤɢ Ɇɚɫɫɵ ɱɚɫɬɢɰ 9,1 · 10–31 ɤɝ § 5,5·10–4 ɚ. ɟ. ɦ. 1,673 · 10–27 ɤɝ § 1,007 ɚ. ɟ. ɦ. 1,675 · 10–27 ɤɝ § 1,008 ɚ. ɟ. ɦ. ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɝɢɝɚ Ƚ 10 9 ɫɚɧɬɢ ɫ 10–2 ɦɟɝɚ Ɇ 10 6 ɦɢɥɥɢ ɦ 10–3 ɜɨɞɵ 1000 ɤɝɦ3 ɤɢɥɨ ɤ 10 3 ɦɢɤɪɨ ɦɤ 10–6 ɞɪɟɜɟɫɢɧɵ (ɫɨɫɧɚ) ɚɥɸɦɢɧɢɹ ɝɟɤɬɨ ɝ ɧɚɧɨ ɧ 400 ɤɝɦ3 2700 ɤɝɦ3 10 2 10–9 ɞɟɰɢ ɞ 10–1 ɩɢɤɨ ɩ 10–12 ɤɟɪɨɫɢɧɚ 800 ɤɝɦ3 ɠɟɥɟɡɚ 7800 ɤɝɦ3 ɪɬɭɬɢ 13 600 ɤɝɦ3 ɉɥɨɬɧɨɫɬɶ ɩɨɞɫɨɥɧɟɱɧɨɝɨ ɦɚɫɥɚ Ʉɨɧɫɬɚɧɬɵ ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɺɦɤɨɫɬɶ ɱɢɫɥɨ ʌ ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɧɚ Ɂɟɦɥɟ ʌ = 3,14 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ G = 6,7 · 10–11 ɇÂɦ2ɤɝ2 R = 8,31 Ⱦɠ/(ɦɨɥɶÂɄ) ɩɨɫɬɨɹɧɧɚɹ Ⱥɜɨɝɚɞɪɨ NȺ = 6·1023 ɦɨɥɶ–1 ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ ɫ = 3 · 108 ɦɫ 1 k= = 9 · 109 ɇÂɦ2Ʉɥ2 ʌ İ0 ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɜ ɡɚɤɨɧɟ Ʉɭɥɨɧɚ ɦɨɞɭɥɶ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ (ɷɥɟɦɟɧɬɚɪɧɵɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɡɚɪɹɞ) ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ g = 10 ɦɫ2 k = 1,38 · 10–23 ȾɠɄ ɜɨɞɵ 4,2 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɚɥɸɦɢɧɢɹ 900 Ⱦɠ/(ɤɝÂɄ) ɥɶɞɚ 2,1 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɦɟɞɢ 380 Ⱦɠ/(ɤɝÂɄ) ɠɟɥɟɡɚ ɫɜɢɧɰɚ 640 Ⱦɠ/(ɤɝÂɄ) 130 Ⱦɠ/(ɤɝÂɄ) ɱɭɝɭɧɚ 500 Ⱦɠ/(ɤɝÂɄ) ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɹ ɜɨɞɵ 2,3 · 10 6 Ⱦɠɤɝ ɩɥɚɜɥɟɧɢɹ ɫɜɢɧɰɚ ɩɥɚɜɥɟɧɢɹ ɥɶɞɚ e = 1,6 · 10–19 Ʉɥ 1 ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ ɷɤɜɢɜɚɥɟɧɬɧɚ 1 ɷɥɟɤɬɪɨɧɜɨɥɶɬ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2,5 · 10 4 Ⱦɠɤɝ 3,3 · 10 5 Ⱦɠɤɝ ɇɨɪɦɚɥɶɧɵɟ ɭɫɥɨɜɢɹ h = 6,6 · 10–34 ȾɠÂɫ ɞɚɜɥɟɧɢɟ: 105 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ: 0 °ɋ ɋɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɟɞɢɧɢɰɚɦɢ ɬɟɦɩɟɪɚɬɭɪɚ ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ 900 ɤɝɦ3 Ɇɨɥɹɪɧɚɹ ɦɚFɫɚ ɝɟɥɢɹ 0 Ʉ = – 273 °ɋ ɚɡɨɬɚ 28 · 10–3 ɤɝɦɨɥɶ 1 ɚ. ɟ. ɦ. = 1,66 · 10–27 ɤɝ 931,5 Ɇɷȼ ɚɪɝɨɧɚ 40 · 10–3 ɤɝɦɨɥɶ ɤɢɫɥɨɪɨɞɚ 32 · 10–3 ɤɝɦɨɥɶ ɜɨɞɨɪɨɞɚ 2 · 10–3 ɤɝɦɨɥɶ ɥɢɬɢɹ 1 ɷȼ = 1,6 · 10–19 Ⱦɠ 6 · 10–3 ɤɝɦɨɥɶ ɜɨɡɞɭɯɚ 29 · 10–3 ɤɝɦɨɥɶ ɧɟɨɧɚ 20 · 10–3 ɤɝɦɨɥɶ ɜɨɞɵ 18 · 10–3 ɤɝɦɨɥɶ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ 44 · 10–3 ɤɝɦɨɥɶ © ɋɬɚɬȽɪɚɞ 2013 ɝ 4 · 10–3 ɤɝɦɨɥɶ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 5 ɑɚɫɬɶ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 A4 ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɱɚɫɬɢ 1 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ (A1–A21) ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A1 ɉɨ ɩɥɨɫɤɨɫɬɢ XY ɞɜɢɠɭɬɫɹ ɱɟɬɵɪɟ ɬɨɱɟɱɧɵɯ ɬɟɥɚ – Ⱥ, Ȼ, ȼ ɢ Ƚ, ɬɪɚɟɤɬɨɪɢɢ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫɭɧɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬ ɨɞɧɨɝɨ ɢɡ ɷɬɢɯ ɬɟɥ ɨɬ ɜɪɟɦɟɧɢ ɢɦɟɸɬ ɜɢɞ: x 2t ɢ y 1 t. ɗɬɨ ɬɟɥɨ ɨɛɨɡɧɚɱɟɧɨ ɛɭɤɜɨɣ Ⱦɜɚ ɛɪɭɫɤɚ ɦɚɫɫɨɣ m ɢ 2m ɪɚɜɧɨɦɟɪɧɨ ɞɜɢɠɭɬɫɹ ɜɞɨɥɶ ɩɪɹɦɨɣ OX (ɫɦ. ɪɢɫɭɧɨɤ). ȼ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɛɪɭɫɤɨɦ 2, ɦɨɞɭɥɶ ɢɦɩɭɥɶɫɚ ɩɟɪɜɨɝɨ ɛɪɭɫɤɚ ɪɚɜɟɧ 1) m V A5 6 2) 2mV 3) 3mV 4) 4mV ɋɚɧɢ ɪɚɜɧɨɦɟɪɧɨ ɩɟɪɟɦɟɳɚɸɬ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɩɟɪɟɦɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɦɨɞɭɥɹ ɪɚɛɨɬɵ ɫɢɥɵ ɬɪɟɧɢɹ Aɬɪ ɨɬ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ S. Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ɧɚ ɩɪɨɣɞɟɧɧɨɦ ɩɭɬɢ ɪɚɜɧɨ 1) Ⱥ A2 A3 2) Ȼ 3) ȼ 4) Ƚ Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɪɚɜɧɨɦɟɪɧɨɝɨ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ r 1) ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɨɪɧɸ ɤɜɚɞɪɚɬɧɨɦɭ ɢɡ ɦɚɫɫɵ ɩɥɚɧɟɬɵ 2) ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɩɥɚɧɟɬɵ 3) ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɦɚɫɫɵ ɩɥɚɧɟɬɵ 4) ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɩɥɚɧɟɬɵ 1) 4 A6 4 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 4) 20 1 ɞɥɢɧɵ ɛɚɥɤɢ (ɫɦ. ɪɢɫɭɧɨɤ). 4 Ʉɚɤɭɸ ɫɢɥɭ F ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ ɤ ɤɨɧɰɭ A ɛɚɥɤɢ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ? 1) Mg A7 F ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɪɚɜɧɚ 0 . 3) 16 Ɉɞɧɨɪɨɞɧɚɹ ɫɩɥɨɲɧɚɹ ɛɚɥɤɚ ɦɚɫɫɨɣ M ɭɪɚɜɧɨɜɟɲɟɧɚ ɧɚ ɨɫɬɪɨɤɨɧɟɱɧɨɣ ɨɩɨɪɟ. Ɉɩɨɪɭ ɩɟɪɟɞɜɢɝɚɸɬ ɜɩɪɚɜɨ ɧɚ ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɱɟɬɵɪɟ ɩɚɪɵ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɬɨɱɟɱɧɵɯ ɬɟɥ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ ɧɚ ɪɚɡɧɵɯ ɪɚɫɫɬɨɹɧɢɹɯ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɷɬɢɯ ɬɟɥ. ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɬɟɥ ɨɞɢɧɚɤɨɜɵɯ ɦɚɫɫ M , ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ F0 , ɨɩɪɟɞɟɥɢɬɟ, ɞɥɹ ɤɚɤɨɣ ɩɚɪɵ ɬɟɥ ɫɢɥɚ 2) 8 2) Mg 2 3) Mg 3 4) Mg 4 Ⱦɢɦɚ ɢ Ʌɟɧɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɢɡɨɛɪɚɡɢɥɢ ɧɚ ɞɨɫɤɟ ɞɜɢɠɟɧɢɟ ɛɪɨɭɧɨɜɫɤɨɣ ɱɚɫɬɢɰɵ. Ɉɬɜɟɱɚɸɳɢɦ ɦɨɞɟɥɢ ɛɪɨɭɧɨɜɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɩɪɢɡɧɚɬɶ ɪɢɫɭɧɨɤ, ɫɞɟɥɚɧɧɵɣ Ⱥ) Ⱦɢɦɨɣ Ȼ) Ʌɟɧɨɣ 1) ɬɨɥɶɤɨ Ⱥ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) ɬɨɥɶɤɨ Ȼ 3) ɢ Ⱥ, ɢ Ȼ 4) ɧɢ Ⱥ, ɧɢ Ȼ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 A8 7 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɢɡ ɫɨɫɬɨɹɧɢɹ Ⱥ ɜ ɫɨɫɬɨɹɧɢɟ Ȼ. ȼ ɫɨɫɬɨɹɧɢɢ Ȼ ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɝɨ ɝɚɡɚ 1) ɜ 2 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 2) ɜ 2 ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 3) ɜ 4 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 4) ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ A9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 8 A11 Ɍɨɱɟɱɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ Q ɧɚɯɨɞɢɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x0 ɨɬ ɰɟɧɬɪɚ ɧɟɩɪɨɜɨɞɹɳɟɝɨ ɲɚɪɚ, ɪɚɜɧɨɦɟɪɧɨ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚɪɹɠɟɧɧɨɝɨ ɡɚɪɹɞɨɦ q (ɫɦ. ɪɢɫɭɧɨɤ). Ɂɚɪɹɞ Q ɧɚɱɢɧɚɸɬ ɩɟɪɟɦɟɳɚɬɶ ɜɞɨɥɶ ɪɚɞɢɭɫɚ ɲɚɪɚ, ɭɞɚɥɹɹ ɨɬ ɧɟɝɨ. ɇɚ ɤɚɤɨɦ ɢɡ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ ɝɪɚɮɢɤɨɜ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɫɢɥɵ F ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɞɚ Q ɫ ɲɚɪɨɦ ɨɬ ɪɚɫɫɬɨɹɧɢɹ x ɦɟɠɞɭ ɡɚɪɹɞɨɦ ɢ ɰɟɧɬɪɨɦ ɲɚɪɚ? ȼ ɬɚɛɥɢɰɟ ɭɤɚɡɚɧɚ ɩɥɨɬɧɨɫɬɶ ɝɚɡɨɜ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ. 1) 1 Ƚɚɡ ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɤɝɦ3 ɚɡɨɬ ɜɨɞɨɪɨɞ ɤɫɟɧɨɧ ɯɥɨɪ 1,25 0,09 5,9 3,2 2) 2 3) 3 4) 4 A12 ɂɞɟɚɥɶɧɵɣ ɚɦɩɟɪɦɟɬɪ ɢ ɬɪɢ ɪɟɡɢɫɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ R 11 Ɉɦ, 2R ɢ 3R ɜɤɥɸɱɟɧɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɰɟɩɶ, ɫɨɞɟɪɠɚɳɭɸ ɢɫɬɨɱɧɢɤ ɫ ɗȾɋ, ɪɚɜɧɨɣ 5 ȼ, ɢ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ r 4 Ɉɦ. ɉɨɤɚɡɚɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɪɚɜɧɵ 1) 50 Ⱥ ɉɪɢ ɷɬɨɦ ɧɚɢɛɨɥɶɲɭɸ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɭɸ ɫɤɨɪɨɫɬɶ ɢɦɟɸɬ ɦɨɥɟɤɭɥɵ 1) ɚɡɨɬɚ 2) ɜɨɞɨɪɨɞɚ 3) ɤɫɟɧɨɧɚ 4) ɯɥɨɪɚ A10 Ⱦɜɚ ɦɨɥɹ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɜɨɞɹɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T1 ɜ ɫɨɫɬɨɹɧɢɟ 2 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ 2) 2 Ⱥ 3) 0,5 Ⱥ 4) § 0,07 Ⱥ JG A13 ɗɥɟɤɬɪɨɧ, ɞɜɢɝɚɹɫɶ ɫɨ ɫɤɨɪɨɫɬɶɸ V , ɥɟɠɚɳɟɣ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ XY ɧɚ ɪɢɫɭɧɤɟ ɷɬɚ ɩɥɨɫɤɨɫɬɶ ɩɨɤɚɡɚɧɚ ɬɨɧɢɪɨɜɤɨɣ), ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɫɬɶ JG ɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɢɧɞɭɤɰɢɟɣ B , ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɞɨɥɶ ɨɫɢ X. ɉɪɚɜɢɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ, ɢɡɨɛɪɚɠɟɧɨ ɜɟɤɬɨɪɨɦ ɩɨɞ ɧɨɦɟɪɨɦ ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɤɬɪɨɧ, T2 (ɫɦ. ɪɢɫɭɧɨɤ). Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɫɨɨɛɳɟɧɨ ɝɚɡɭ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɝɢɫɬɨɝɪɚɦɦɟ, ɨɛɨɡɧɚɱɟɧɧɨɦɭ ɰɢɮɪɨɣ ɫɬɨɥɛɰɭ ɧɚ 1) 1 2) 2 3) 3 4) 4 A14 ɂɦɟɸɬɫɹ ɞɜɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ: ɩɟɪɜɚɹ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɩɨɤɨɹ, ɜɬɨɪɚɹ ɞɜɢɠɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 1) 2) 3) 4) ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɩɟɪɜɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɢ ɩɟɪɜɚɹ, ɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɧɟ ɢɡɥɭɱɚɟɬ ɧɢ ɩɟɪɜɚɹ, ɧɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 9 A15 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɨɩɬɢɱɟɫɤɚɹ ɨɫɶ OO c ɬɨɧɤɨɣ ɫɨɛɢɪɚɸɳɟɣ ɥɢɧɡɵ, ɥɭɱ ɫɜɟɬɚ 1, ɩɚɞɚɸɳɢɣ ɧɚ ɷɬɭ ɥɢɧɡɭ, ɢ ɥɭɱ ɫɜɟɬɚ 2, ɩɪɨɲɟɞɲɢɣ ɱɟɪɟɡ ɷɬɭ ɥɢɧɡɭ. ɇɚ ɪɢɫɭɧɤɟ ɪɚɡɦɟɪ ɨɞɧɨɣ ɤɥɟɬɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ 1 ɫɦ. Ɉɩɬɢɱɟɫɤɚɹ ɫɢɥɚ ɥɢɧɡɵ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɚ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 A19 Ⱦɨɥɹ ɚɬɨɦɨɜ ɪɚɞɢɨɚɤɬɢɜɧɨɝɨ ɢɡɨɬɨɩɚ, ɪɚɫɩɚɜɲɢɯɫɹ ɩɨ ɩɪɨɲɟɫɬɜɢɢ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ, ɪɚɜɧɨɝɨ ɩɨɥɨɜɢɧɟ ɩɟɪɢɨɞɚ ɩɨɥɭɪɚɫɩɚɞɚ, ɨɛɨɡɧɚɱɟɧɚ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ ɰɢɮɪɨɣ 1) 1 1) 5 ɞɩɬɪ 2) 10 ɞɩɬɪ 3) 25 ɞɩɬɪ 4) 50 ɞɩɬɪ A16 ɇɚ ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɭɸ ɫɬɟɤɥɹɧɧɭɸ ɩɥɚɫɬɢɧɤɭ ɢ ɫɬɟɤɥɹɧɧɭɸ ɩɪɢɡɦɭ ɩɚɞɚɟɬ ɥɭɱ ɛɟɥɨɝɨ ɫɜɟɬɚ (ɫɦ. ɪɢɫɭɧɨɤ). Ⱦɢɫɩɟɪɫɢɹ ɫɜɟɬɚ ɜ ɜɢɞɟ ɪɚɞɭɠɧɵɯ ɩɨɥɨɫ ɧɚ ɷɤɪɚɧɟ 1) 2) 3) 4) Ɍɟɦɩɟɪɚɬɭɪɚ ɫɭɯɨɝɨ ɬɟɪɦɨɦɟɬɪɚ, °ɋ 15 16 17 18 19 20 21 22 23 24 25 2) 2 3) 3 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 144 55 C s 3) 226 88 Ra Ɋɚɡɧɨɫɬɶ ɩɨɤɚɡɚɧɢɣ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, °ɋ 3 4 5 6 71 61 52 44 71 62 54 45 72 64 55 47 73 64 56 48 74 65 58 50 74 66 59 51 75 67 60 52 76 68 61 54 76 69 61 55 77 69 62 56 77 70 63 57 15 16 17 18 19 20 21 22 23 24 25 12,8 13,6 14,5 15,4 16,3 17,3 18,3 19,4 20,6 21,8 23,0 4) 4 35 4) 17 Cl 4) 4 ɉɥɨɬɧɨɫɬɶ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɜɨɞɵ ȡ, ɝɦ3 A18 Ɉɬɧɨɲɟɧɢɟ ɦɚɫɫɨɜɨɝɨ ɱɢɫɥɚ ɤ ɱɢɫɥɭ ɧɟɣɬɪɨɧɨɜ ɪɚɜɧɨ § 1,94 ɜ ɹɞɪɟ 30 1) 14 Si 3) 3 Ɍɟɦɩɟɪɚɬɭɪɚ, °ɋ ɦɟɬɚɥɥɢɱɟɫɤɭɸ ɩɥɚɫɬɢɧɤɭ. ɇɚ ɤɚɤɨɦ ɪɢɫɭɧɤɟ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ? 1) 1 2) 2 A20 ɉɨɤɚɡɚɧɢɹ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɧɟɤɨɬɨɪɨɦ ɩɨɦɟɳɟɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ 23 °ɋ ɢ 17 °ɋ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ ɬɚɛɥɢɰ, ɨɩɪɟɞɟɥɢɬɟ ɚɛɫɨɥɸɬɧɭɸ ɜɥɚɠɧɨɫɬɶ ɜɨɡɞɭɯɚ ɜ ɩɨɦɟɳɟɧɢɢ, ɝɞɟ ɭɫɬɚɧɨɜɥɟɧɵ ɞɚɧɧɵɟ ɬɟɪɦɨɦɟɬɪɵ. ȼ ɩɟɪɜɨɣ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ, ɜɵɪɚɠɟɧɧɚɹ ɜ %. ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ⱥ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ȼ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɢ ɜ ɫɥɭɱɚɟ Ȼ ɧɟ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɧɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɧɢ ɜ ɫɥɭɱɚɟ Ȼ A17 ɉɪɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦ ɢɡɭɱɟɧɢɢ ɮɨɬɨɷɮɮɟɤɬɚ ɩɨɥɭɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɡɚɩɢɪɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ Uɡ ɨɬ ɞɥɢɧɵ ɜɨɥɧɵ Ȝ ɫɜɟɬɚ, ɩɚɞɚɸɳɟɝɨ ɧɚ 10 1) 20,6 ɝɦ3 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 14,5 ɝɦ3 3) 11,3 ɝɦ3 4) 8,0 ɝɦ3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 11 A21 Ʉ ɢɫɬɨɱɧɢɤɭ ɬɨɤɚ ɩɨɞɤɥɸɱɟɧɵ ɪɟɨɫɬɚɬ, ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ (ɪɢɫɭɧɨɤ 1). ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɩɨɥɡɭɧɤɚ ɪɟɨɫɬɚɬɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɩɪɢɛɨɪɚɦɢ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ, ɢɡɨɛɪɚɠɺɧɧɵɟ ɧɚ ɪɢɫɭɧɤɚɯ 2 ɢ 3 (R – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɤɥɸɱɺɧɧɨɣ ɜ ɰɟɩɶ ɱɚɫɬɢ ɪɟɨɫɬɚɬɚ). Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 B2 ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ(-ɵɟ) ɭɬɜɟɪɠɞɟɧɢɟ(-ɹ), ɟɫɥɢ ɬɚɤɨɜɨɟ(-ɵɟ) ɢɦɟɟɬɫɹ(-ɸɬɫɹ). Ⱥ. ȼɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɨ 2 Ɉɦ. Ȼ. ɗȾɋ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɚ 15 ɦȼ. 4) ɧɢ Ⱥ, ɧɢ Ȼ 3) ɢ Ⱥ, ɢ Ȼ 2) ɬɨɥɶɤɨ Ȼ 1) ɬɨɥɶɤɨ Ⱥ Ɉɬɜɟɬɨɦ ɤ ɡɚɞɚɧɢɹɦ ɷɬɨɣ ɱɚɫɬɢ (ȼ1–ȼ4) ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɰɢɮɪ. ȼɩɢɲɢɬɟ ɨɬɜɟɬɵ ɫɧɚɱɚɥɚ ɜ ɬɟɤɫɬ ɪɚɛɨɬɵ, ɚ ɡɚɬɟɦ ɩɟɪɟɧɟɫɢɬɟ ɢɯ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ, ɛɟɡ ɡɚɩɹɬɵɯ, ɩɪɨɛɟɥɨɜ ɢ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɢɦɜɨɥɨɜ. Ʉɚɠɞɭɸ ɰɢɮɪɭ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɰɟɩɶ ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɗȾɋ ɫ ɧɟɤɨɬɨɪɵɦ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ, ɞɜɭɯ ɨɞɢɧɚɤɨɜɵɯ ɥɚɦɩɨɱɟɤ, ɤɥɸɱɚ, ɜɨɥɶɬɦɟɬɪɚ ɢ ɞɜɭɯ ɚɦɩɟɪɦɟɬɪɨɜ (ɫɦ. ɪɢɫɭɧɨɤ). ɂɡɦɟɪɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɵɦɢ. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɩɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɨɜ, ɟɫɥɢ ɪɚɡɨɦɤɧɭɬɶ ɤɥɸɱ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɉɈɄȺɁȺɇɂȿ ɉɊɂȻɈɊȺ Ⱥ) ɩɨɤɚɡɚɧɢɟ ɜɨɥɶɬɦɟɬɪɚ Ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ1 ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ2 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ ȼ Ɉɞɢɧ ɦɨɥɶ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 1. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɫɥɟɞɭɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ, ɟɫɥɢ ɡɚɦɟɧɢɬɶ ɢɫɯɨɞɧɵɣ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ ɧɚ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 2: ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɝɚɡɨɦ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ; ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ; ɄɉȾ ɰɢɤɥɚ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɑɚɫɬɶ 2 B1 12 ɎɂɁɂɑȿɋɄɂȿ ȼȿɅɂɑɂɇɕ Ⱥ) ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɧɚɝɪɟɜɚɬɟɥɹ Ȼ) ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ ȼ) ɄɉȾ ɰɢɤɥɚ Ɉɬɜɟɬ: B3 Ⱥ Ȼ ɂɏ ɂɁɆȿɇȿɇɂȿ ɝɚɡɨɦ ɨɬ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ ȼ ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɢɥɵ ɬɨɤɚ I ɜ ɤɚɬɭɲɤɟ ɢɧɞɭɤɬɢɜɧɨɫɬɶɸ 10 ɦȽɧ ɨɬ ɜɪɟɦɟɧɢ t. ȿȽɈ ɂɁɆȿɇȿɇɂȿ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɭɱɚɫɬɤɚɦɢ ɝɪɚɮɢɤɚ ɢ ɡɧɚɱɟɧɢɹɦɢ ɦɨɞɭɥɹ ɗȾɋ ɫɚɦɨɢɧɞɭɤɰɢɢ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 13 Ʉ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ ɩɟɪɜɨɝɨ ɫɬɨɥɛɰɚ ɩɨɞɛɟɪɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɨɡɢɰɢɸ ɜɬɨɪɨɝɨ ɫɬɨɥɛɰɚ ɢ ɡɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɩɨɞ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɛɭɤɜɚɦɢ. ɍɑȺɋɌɈɄ ȽɊȺɎɂɄȺ ɆɈȾɍɅɖ ɗȾɋ ɋȺɆɈɂɇȾɍɄɐɂɂ Ⱥ) ȺȻ Ȼ) Ȼȼ 1) 2) 3) 4) 5) Ɉɬɜɟɬ: B4 Ⱥ Ȼ 0ȼ 0,0075 ȼ 0,05 ɦȼ 0,0025 ȼ 0,2 ɦȼ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 14 ɑɚɫɬɶ 3 Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 3 ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɞɚɱɢ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɢɯ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ ɧɚ ɱɟɪɧɨɜɢɤɟ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ Ⱥ22–Ⱥ25 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A22 Ƚɪɭɡ ɧɚɱɢɧɚɟɬ ɫɜɨɛɨɞɧɨ ɩɚɞɚɬɶ ɫ ɧɟɤɨɬɨɪɨɣ ɜɵɫɨɬɵ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɨɥɟɬɟɜ 40 ɦ, ɝɪɭɡ ɩɪɢɨɛɪɺɥ ɫɤɨɪɨɫɬɶ 20 ɦɫ. ɇɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ ɨɬɧɨɲɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɝɪɭɡɚ ɤ ɪɚɛɨɬɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɪɚɜɧɨ 1) 1 ɇɚ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɫ ɩɟɪɢɨɞɨɦ d 0 ɧɨɪɦɚɥɶɧɨ ɩɚɞɚɟɬ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɣ ɩɭɱɨɤ ɫɜɟɬɚ, ɚ ɡɚ ɪɟɲɺɬɤɨɣ ɪɚɫɩɨɥɨɠɟɧ ɨɛɴɟɤɬɢɜ, ɜ ɮɨɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɧɚɛɥɸɞɚɸɬɫɹ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ ɫɦ. ɪɢɫɭɧɨɤ). Ɍɨɱɤɚɦɢ ɩɨɤɚɡɚɧɵ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ, ɚ ɰɢɮɪɚɦɢ ɨɛɨɡɧɚɱɟɧɵ ɢɯ ɧɨɦɟɪɚ. ɍɝɥɵ ɞɢɮɪɚɤɰɢɢ ɦɚɥɵ. ɗɬɭ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɩɨɨɱɟɪɺɞɧɨ ɡɚɦɟɧɹɸɬ ɞɪɭɝɢɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɦɢ ɪɟɲɺɬɤɚɦɢ – Ⱥ, Ȼ ɢ ȼ. ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɫɯɟɦɚɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɦɚɤɫɢɦɭɦɨɜ ɢ ɩɟɪɢɨɞɚɦɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɪɟɲɺɬɨɤ. 2) –1 3) 2 4) 4 A23 ɉɨɪɲɟɧɶ ɦɨɠɟɬ ɫɜɨɛɨɞɧɨ ɛɟɡ ɬɪɟɧɢɹ ɩɟɪɟɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɬɟɧɨɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɨɫɭɞɚ. ȼ ɨɛɴɺɦɟ, ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɧɨɦ ɫɨɫɭɞɚ ɢ ɩɨɪɲɧɟɦ, ɧɚɯɨɞɢɬɫɹ ɜɨɡɞɭɯ (ɫɦ. ɪɢɫɭɧɨɤ). ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɨɫɭɞɚ ɪɚɜɧɚ 25 ɫɦ2, ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɞɧɚ ɫɨɫɭɞɚ ɞɨ ɩɨɪɲɧɹ ɪɚɜɧɨ 20 ɫɦ, ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ 100 ɤɉɚ, ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɜ ɫɨɫɭɞɟ ɪɚɜɧɨ ɚɬɦɨɫɮɟɪɧɨɦɭ. ɉɨɪɲɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɦɟɳɚɸɬ ɧɚ 5 ɫɦ ɜɩɪɚɜɨ, ɩɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɧɟ ɦɟɧɹɟɬɫɹ. Ʉɚɤɭɸ ɫɢɥɭ ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ, ɱɬɨɛɵ ɭɞɟɪɠɚɬɶ ɩɨɪɲɟɧɶ ɜ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ? 1) 50 ɇ 2) 83,3 ɇ 3) 200 ɇ 4) 333,3 ɇ A24 Ⱦɜɟ ɬɨɧɤɢɟ ɜɟɪɬɢɤɚɥɶɧɵɟ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɩɥɚɫɬɢɧɵ ɪɚɫɩɨɥɨɠɟɧɵ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ, ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɪɚɜɧɨ 2 ɫɦ. ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɋɏȿɆȺ ȾɂɎɊȺɄɐɂɈɇɇɕɏ ɆȺɄɋɂɆɍɆɈȼ Ⱥ) Ⱥ Ȼ) Ȼ ɉȿɊɂɈȾ ȾɂɎɊȺɄɐɂɈɇɇɈɃ ɊȿɒȬɌɄɂ 1) 4d 0 2) d 0 4 3) 2d 0 4) 2 d 0 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ 3 5) 2 d 0 5 ɫɟɱɟɧɢɹ ɤɚɠɞɨɣ ɢɡ ɩɥɚɫɬɢɧ ɪɚɜɧɚ 15 000 ɫɦ2. Ʌɟɜɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɡɚɪɹɞ q = 5 ɩɄɥ, ɡɚɪɹɞ ɜɬɨɪɨɣ ɩɥɚɫɬɢɧɵ –q. Ɇɨɞɭɥɶ ɧɚɩɪɹɠɺɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,5 ɫɦ ɨɬ ɩɪɚɜɨɣ ɩɥɚɫɬɢɧɵ ɪɚɜɟɧ 1) 0 ȼ/ɦ 2) § 0,19 ȼ/ɦ 3) § 0,75 ȼ/ɦ 4) § 0,38 ȼ/ɦ A25 ɗɥɟɤɬɪɨɧ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɫ ɢɧɞɭɤɰɢɟɣ 6 ɦɤɌɥ. ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ 1) § 1,1 ɪɚɞɫ 3) | 9, 4 107 ɪɚɞɫ 2) 3,7 · 105 ɪɚɞɫ 4) | 1, 05 106 ɪɚɞɫ ɇɟ ɡɚɛɭɞɶɬɟ ɩɟɪɟɧɟɫɬɢ ɜɫɟ ɨɬɜɟɬɵ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1. © ɋɬɚɬȽɪɚɞ 2013 ɝ ɩɨɥɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 15 ɉɨɥɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɋ1–ɋ6 ɧɟɨɛɯɨɞɢɦɨ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2. ɉɪɢ ɨɮɨɪɦɥɟɧɢɢ ɪɟɲɟɧɢɹ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2 ɡɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɡɚɞɚɧɢɹ ɋ1, ɋ2 ɢ ɬ. ɞ.), ɚ ɡɚɬɟɦ ɪɟɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɡɚɞɚɱɢ. Ɉɬɜɟɬɵ ɡɚɩɢɫɵɜɚɣɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ. C1 Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɞɥɢɧɵ ɨɪɝɚɧɧɵɯ ɬɪɭɛ ɪɚɡɧɵɟ: ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ, ɚ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ – ɛɨɥɶɲɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ɉɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ ɤɚɠɞɨɣ ɢɡ ɡɚɞɚɱ ɋ2–ɋ6 ɞɨɥɠɧɨ ɫɨɞɟɪɠɚɬɶ ɡɚɤɨɧɵ ɢ ɮɨɪɦɭɥɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɪɚɫɱɺɬɵ ɫ ɱɢɫɥɟɧɧɵɦ ɨɬɜɟɬɨɦ ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɢɫɭɧɨɤ, ɩɨɹɫɧɹɸɳɢɣ ɪɟɲɟɧɢɟ. C2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ Ʌɭɧɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 1 28 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ Ʌɭɧɵ ɫɨɫɬɚɜɥɹɟɬ ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ 81 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C5 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 48 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 2 ɪɚɡɚ. C6 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ = ɪɚɜɧɚ n = 1,3 · 1025 ɦ–3? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 280 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 4. C4 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,95 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 12 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 11,9 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? © ɋɬɚɬȽɪɚɞ 2013 ɝ h , mv ɝɞɟ h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ l § 5Ȝ, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ Ʌɭɧɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. C3 16 © ɋɬɚɬȽɪɚɞ 2013 ɝ Физика. 11 класс. Вариант ФИ1603 2 Инструкция по выполнению работы Тренировочная работа № 4 по ФИЗИКЕ 30 апреля 2013 года 11 класс Вариант ФИ1603 Для выполнения экзаменационной работы по физике отводится 235 минут. Работа состоит из 3 частей, включающих в себя 35 заданий. Часть 1 содержит 21 задание (А1–А21). К каждому заданию даётся четыре варианта ответа, из которых только один правильный. Часть 2 содержит 4 задания (В1–В4), на которые надо дать краткий ответ в виде последовательности цифр Часть 3 содержит 10 задач: А22–А25 с выбором одного верного ответа и С1–С6, для которых требуется дать развёрнутые решения. При вычислениях разрешается использовать непрограммируемый калькулятор. Все бланки ЕГЭ заполняются яркими чёрными чернилами. Допускается использование гелевой, капиллярной или перьевой ручек. При выполнении заданий Вы можете пользоваться черновиком. Обращаем Ваше внимание на то, что записи в черновике не будут учитываться при оценивании работы. Советуем выполнять задания в том порядке, в котором они даны Для экономии времени пропускайте задание, которое не удаётся выполнить сразу, и переходите к следующему. Если после выполнения всей работы у Вас останется время, Вы сможете вернуться к пропущенным заданиям Баллы, полученные Вами за выполненные задания, суммируются. Постарайтесь выполнить как можно больше заданий и набрать наибольшее количество баллов. Район. Город (населённый пункт) Школа. Класс. Фамилия Имя Отчество. © СтатГрад 2013 г. Желаем успеха! © СтатГрад 2013 г. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 4 ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɫɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ȼɚɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬɵ. ɷɥɟɤɬɪɨɧɚ ɩɪɨɬɨɧɚ ɧɟɣɬɪɨɧɚ Ⱦɟɫɹɬɢɱɧɵɟ ɩɪɢɫɬɚɜɤɢ Ɇɚɫɫɵ ɱɚɫɬɢɰ 9,1 · 10–31 ɤɝ § 5,5·10–4 ɚ. ɟ. ɦ. 1,673 · 10–27 ɤɝ § 1,007 ɚ. ɟ. ɦ. 1,675 · 10–27 ɤɝ § 1,008 ɚ. ɟ. ɦ. ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɝɢɝɚ Ƚ 10 9 ɫɚɧɬɢ ɫ 10–2 ɦɟɝɚ Ɇ 10 6 ɦɢɥɥɢ ɦ 10–3 ɜɨɞɵ 1000 ɤɝɦ3 ɤɢɥɨ ɤ 10 3 ɦɢɤɪɨ ɦɤ 10–6 ɞɪɟɜɟɫɢɧɵ (ɫɨɫɧɚ) ɚɥɸɦɢɧɢɹ ɝɟɤɬɨ ɝ ɧɚɧɨ ɧ 400 ɤɝɦ3 2700 ɤɝɦ3 10 2 10–9 ɞɟɰɢ ɞ 10–1 ɩɢɤɨ ɩ 10–12 ɤɟɪɨɫɢɧɚ 800 ɤɝɦ3 ɠɟɥɟɡɚ 7800 ɤɝɦ3 ɪɬɭɬɢ 13 600 ɤɝɦ3 ɉɥɨɬɧɨɫɬɶ ɩɨɞɫɨɥɧɟɱɧɨɝɨ ɦɚɫɥɚ Ʉɨɧɫɬɚɧɬɵ ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɺɦɤɨɫɬɶ ɱɢɫɥɨ ʌ ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɧɚ Ɂɟɦɥɟ ʌ = 3,14 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ G = 6,7 · 10–11 ɇÂɦ2ɤɝ2 R = 8,31 Ⱦɠ/(ɦɨɥɶÂɄ) ɩɨɫɬɨɹɧɧɚɹ Ⱥɜɨɝɚɞɪɨ NȺ = 6·1023 ɦɨɥɶ–1 ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ ɫ = 3 · 108 ɦɫ 1 k= = 9 · 109 ɇÂɦ2Ʉɥ2 ʌ İ0 ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɜ ɡɚɤɨɧɟ Ʉɭɥɨɧɚ ɦɨɞɭɥɶ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ (ɷɥɟɦɟɧɬɚɪɧɵɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɡɚɪɹɞ) ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ g = 10 ɦɫ2 k = 1,38 · 10–23 ȾɠɄ ɜɨɞɵ 4,2 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɚɥɸɦɢɧɢɹ 900 Ⱦɠ/(ɤɝÂɄ) ɥɶɞɚ 2,1 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɦɟɞɢ 380 Ⱦɠ/(ɤɝÂɄ) ɠɟɥɟɡɚ ɫɜɢɧɰɚ 640 Ⱦɠ/(ɤɝÂɄ) 130 Ⱦɠ/(ɤɝÂɄ) ɱɭɝɭɧɚ 500 Ⱦɠ/(ɤɝÂɄ) ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɹ ɜɨɞɵ 2,3 · 10 6 Ⱦɠɤɝ ɩɥɚɜɥɟɧɢɹ ɫɜɢɧɰɚ ɩɥɚɜɥɟɧɢɹ ɥɶɞɚ e = 1,6 · 10–19 Ʉɥ 1 ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ ɷɤɜɢɜɚɥɟɧɬɧɚ 1 ɷɥɟɤɬɪɨɧɜɨɥɶɬ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2,5 · 10 4 Ⱦɠɤɝ 3,3 · 10 5 Ⱦɠɤɝ ɇɨɪɦɚɥɶɧɵɟ ɭɫɥɨɜɢɹ h = 6,6 · 10–34 ȾɠÂɫ ɞɚɜɥɟɧɢɟ: 105 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ: 0 °ɋ ɋɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɟɞɢɧɢɰɚɦɢ ɬɟɦɩɟɪɚɬɭɪɚ ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ 900 ɤɝɦ3 Ɇɨɥɹɪɧɚɹ ɦɚFɫɚ ɝɟɥɢɹ 0 Ʉ = – 273 °ɋ ɚɡɨɬɚ 28 · 10–3 ɤɝɦɨɥɶ 1 ɚ. ɟ. ɦ. = 1,66 · 10–27 ɤɝ 931,5 Ɇɷȼ ɚɪɝɨɧɚ 40 · 10–3 ɤɝɦɨɥɶ ɤɢɫɥɨɪɨɞɚ 32 · 10–3 ɤɝɦɨɥɶ ɜɨɞɨɪɨɞɚ 2 · 10–3 ɤɝɦɨɥɶ ɥɢɬɢɹ 1 ɷȼ = 1,6 · 10–19 Ⱦɠ 6 · 10–3 ɤɝɦɨɥɶ ɜɨɡɞɭɯɚ 29 · 10–3 ɤɝɦɨɥɶ ɧɟɨɧɚ 20 · 10–3 ɤɝɦɨɥɶ ɜɨɞɵ 18 · 10–3 ɤɝɦɨɥɶ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ 44 · 10–3 ɤɝɦɨɥɶ © ɋɬɚɬȽɪɚɞ 2013 ɝ 4 · 10–3 ɤɝɦɨɥɶ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 5 ɑɚɫɬɶ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 A4 ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɱɚɫɬɢ 1 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ (A1–A21) ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A1 ɉɨ ɩɥɨɫɤɨɫɬɢ XY ɞɜɢɠɭɬɫɹ ɱɟɬɵɪɟ ɬɨɱɟɱɧɵɯ ɬɟɥɚ – Ⱥ, Ȼ, ȼ ɢ Ƚ, ɬɪɚɟɤɬɨɪɢɢ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫɭɧɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬ ɨɞɧɨɝɨ ɢɡ ɷɬɢɯ ɬɟɥ ɨɬ ɜɪɟɦɟɧɢ ɢɦɟɸɬ ɜɢɞ x 1 t ɢ y 2t. ɗɬɨ ɬɟɥɨ ɨɛɨɡɧɚɱɟɧɨ ɛɭɤɜɨɣ 1) Ⱥ A2 3) ȼ 4) Ƚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɨɪɧɸ ɤɜɚɞɪɚɬɧɨɦɭ ɢɡ ɦɚɫɫɵ ɩɥɚɧɟɬɵ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɩɥɚɧɟɬɵ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɦɚɫɫɵ ɩɥɚɧɟɬɵ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɩɥɚɧɟɬɵ A6 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 2) 4 3) 6 4) 2mV 4) 8 Ɉɞɧɨɪɨɞɧɚɹ ɫɩɥɨɲɧɚɹ ɛɚɥɤɚ ɦɚɫɫɨɣ M ɭɪɚɜɧɨɜɟɲɟɧɚ ɧɚ ɨɫɬɪɨɤɨɧɟɱɧɨɣ ɨɩɨɪɟ. Ɉɩɨɪɭ ɩɟɪɟɞɜɢɝɚɸɬ ɜɩɪɚɜɨ ɧɚ 1 4 ɞɥɢɧɵ ɛɚɥɤɢ (ɫɦ. ɪɢɫɭɧɨɤ). Ʉɚɤɭɸ ɫɢɥɭ F ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ ɤ ɤɨɧɰɭ B ɛɚɥɤɢ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ? 1) Mg A7 1) 1 3) 3mV ɋɚɧɢ ɪɚɜɧɨɦɟɪɧɨ ɩɟɪɟɦɟɳɚɸɬ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɩɟɪɟɦɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɦɨɞɭɥɹ ɪɚɛɨɬɵ ɫɢɥɵ ɬɪɟɧɢɹ Aɬɪ ɨɬ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ S. 1) 2 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɱɟɬɵɪɟ ɩɚɪɵ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɬɨɱɟɱɧɵɯ ɬɟɥ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ ɧɚ ɪɚɡɧɵɯ ɪɚɫɫɬɨɹɧɢɹɯ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɷɬɢɯ ɬɟɥ. ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɬɟɥ ɨɞɢɧɚɤɨɜɵɯ ɦɚɫɫ M, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ F0, ɨɩɪɟɞɟɥɢɬɟ, ɞɥɹ ɤɚɤɨɣ ɩɚɪɵ ɬɟɥ ɫɢɥɚ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɪɚɜɧɚ 4F0. 2) 4mV Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ɧɚ ɩɪɨɣɞɟɧɧɨɦ ɩɭɬɢ ɪɚɜɧɨ Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɪɚɜɧɨɦɟɪɧɨɝɨ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ r 1) 2) 3) 4) A3 2) Ȼ Ⱦɜɚ ɛɪɭɫɤɚ ɦɚɫɫɨɣ m ɢ 2m ɪɚɜɧɨɦɟɪɧɨ ɞɜɢɠɭɬɫɹ ɜɞɨɥɶ ɩɪɹɦɨɣ OX (ɫɦ. ɪɢɫɭɧɨɤ). ȼ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɛɪɭɫɤɨɦ 1, ɦɨɞɭɥɶ ɢɦɩɭɥɶɫɚ ɜɬɨɪɨɝɨ ɛɪɭɫɤɚ ɪɚɜɟɧ 1) 6mV A5 6 2) M g 3) M g 2 3 4) Mg 4 Ⱦɢɦɚ ɢ Ʌɟɧɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɢɡɨɛɪɚɡɢɥɢ ɧɚ ɞɨɫɤɟ ɫɨɫɭɞ, ɜ ɤɨɬɨɪɨɦ ɧɚɯɨɞɢɬɫɹ ɢɞɟɚɥɶɧɵɣ ɝɚɡ. Ɉɬɜɟɱɚɸɳɢɦ ɦɨɞɟɥɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɦɨɠɧɨ ɩɪɢɡɧɚɬɶ ɪɢɫɭɧɨɤ, ɫɞɟɥɚɧɧɵɣ Ⱥ) Ⱦɢɦɨɣ Ȼ) Ʌɟɧɨɣ 3) ɢ Ⱥ, ɢ Ȼ 4) ɧɢ Ⱥ, ɧɢ Ȼ 1) ɬɨɥɶɤɨ Ⱥ 2) ɬɨɥɶɤɨ Ȼ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 A8 7 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɢɡ ɫɨɫɬɨɹɧɢɹ Ⱥ ɜ ɫɨɫɬɨɹɧɢɟ Ȼ. ȼ ɫɨɫɬɨɹɧɢɢ Ȼ ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɝɨ ɝɚɡɚ 1) 2) 3) 4) A9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 8 A11 Ɍɨɱɟɱɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ Q ɧɚɯɨɞɢɬɫɹ ɧɚ ɧɟɛɨɥɶɲɨɦ ɪɚɫɫɬɨɹɧɢɢ x0 ɨɬ ɩɪɨɬɹɠɺɧɧɨɣ ɧɟɩɪɨɜɨɞɹɳɟɣ ɡɚɪɹɠɟɧɧɨɣ ɩɥɚɫɬɢɧɵ, ɪɚɜɧɨɦɟɪɧɨ ɡɚɪɹɠɟɧɧɨɣ ɡɚɪɹɞɨɦ q (ɫɦ. ɪɢɫɭɧɨɤ). Ɂɚɪɹɞ Q ɧɚɱɢɧɚɸɬ ɩɟɪɟɦɟɳɚɬɶ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɩɥɚɫɬɢɧɟ, ɭɞɚɥɹɹ ɨɬ ɧɟɺ. ɇɚ ɤɚɤɨɦ ɢɡ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ ɝɪɚɮɢɤɨɜ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɫɢɥɵ F ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɞɚ Q ɫ ɩɥɚɫɬɢɧɨɣ ɨɬ ɪɚɫɫɬɨɹɧɢɹ x ɦɟɠɞɭ ɡɚɪɹɞɨɦ ɢ ɩɥɚɫɬɢɧɨɣ? ɜ 2 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɜ 2 ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɜ 4 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ ȼ ɬɚɛɥɢɰɟ ɭɤɚɡɚɧɚ ɩɥɨɬɧɨɫɬɶ ɝɚɡɨɜ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ. Ƚɚɡ ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɤɝɦ3 ɚɡɨɬ ɜɨɞɨɪɨɞ ɤɫɟɧɨɧ ɯɥɨɪ 1,25 0,09 5,9 3,2 1) 1 ɉɪɢ ɷɬɨɦ ɧɚɢɛɨɥɶɲɭɸ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɭɸ ɫɤɨɪɨɫɬɶ ɢɦɟɸɬ ɦɨɥɟɤɭɥɵ 1) ɚɡɨɬɚ 2) ɜɨɞɨɪɨɞɚ 3) ɤɫɟɧɨɧɚ 4) ɯɥɨɪɚ A10 Ⱦɜɚ ɦɨɥɹ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɜɨɞɹɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T1 ɜ ɫɨɫɬɨɹɧɢɟ 2 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T2 ɫɦ. ɪɢɫɭɧɨɤ). Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɫɨɨɛɳɟɧɨ ɝɚɡɭ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɬɨɥɛɰɭ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ, ɨɛɨɡɧɚɱɟɧɧɨɦɭ ɰɢɮɪɨɣ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 3) 3 4) 4 A12 ɂɞɟɚɥɶɧɵɣ ɚɦɩɟɪɦɟɬɪ ɢ ɬɪɢ ɪɟɡɢɫɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ R 2 Ɉɦ, 2R ɢ 3R ɜɤɥɸɱɟɧɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɰɟɩɶ, ɫɨɞɟɪɠɚɳɭɸ ɢɫɬɨɱɧɢɤ ɫ ɗȾɋ, ɪɚɜɧɨɣ 5 ȼ, ɢ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ r = 8 Ɉɦ. ɉɨɤɚɡɚɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɪɚɜɧɵ 1) 100 Ⱥ 2) 4 Ⱥ 3) § 0,56 Ⱥ 4) 0,25 Ⱥ JG A13 ɗɥɟɤɬɪɨɧ, ɞɜɢɝɚɹɫɶ ɫɨ ɫɤɨɪɨɫɬɶɸ V , ɧɚɩɪɚɜɥɟɧɧɨɣ JGɜɞɨɥɶ ɨɫɢ X, ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɫɬɶ ɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɢɧɞɭɤɰɢɟɣ B , ɥɟɠɚɳɟɣ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ XY (ɧɚ ɪɢɫɭɧɤɟ ɷɬɚ ɩɥɨɫɤɨɫɬɶ ɩɨɤɚɡɚɧɚ ɬɨɧɢɪɨɜɤɨɣ). ɉɪɚɜɢɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ, ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɤɬɪɨɧ, ɢɡɨɛɪɚɠɟɧɨ ɜɟɤɬɨɪɨɦ ɩɨɞ ɧɨɦɟɪɨɦ 1) 1 1) 1 2) 2 4) 4 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 9 A14 ɂɦɟɸɬɫɹ ɞɜɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ: ɩɟɪɜɚɹ ɞɜɢɠɟɬɫɹ ɫ ɭɫɤɨɪɟɧɢɟɦ, ɜɬɨɪɚɹ – ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ 1) 2) 3) 4) Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 10 A17 ɉɪɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦ ɢɡɭɱɟɧɢɢ ɮɨɬɨɷɮɮɟɤɬɚ ɩɨɥɭɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɡɚɩɢɪɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ Uɡ ɨɬ ɱɚɫɬɨɬɵ Ȟ ɫɜɟɬɚ, ɩɚɞɚɸɳɟɝɨ ɧɚ ɦɟɬɚɥɥɢɱɟɫɤɭɸ ɩɥɚɫɬɢɧɤɭ. ɇɚ ɤɚɤɨɦ ɪɢɫɭɧɤɟ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ? ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɩɟɪɜɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɢ ɩɟɪɜɚɹ, ɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɧɟ ɢɡɥɭɱɚɟɬ ɧɢ ɩɟɪɜɚɹ, ɧɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ A15 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɨɩɬɢɱɟɫɤɚɹ ɨɫɶ OO c ɬɨɧɤɨɣ ɫɨɛɢɪɚɸɳɟɣ ɥɢɧɡɵ, ɥɭɱ ɫɜɟɬɚ 1, ɩɚɞɚɸɳɢɣ ɧɚ ɷɬɭ ɥɢɧɡɭ, ɢ ɥɭɱ ɫɜɟɬɚ 2, ɩɪɨɲɟɞɲɢɣ ɱɟɪɟɡ ɷɬɭ ɥɢɧɡɭ. ɇɚ ɪɢɫɭɧɤɟ ɪɚɡɦɟɪ ɨɞɧɨɣ ɤɥɟɬɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ 1 ɫɦ. Ɏɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɥɢɧɡɵ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɨ 1) 1 1) 0,01 ɦ 2) 0,02 ɦ 3) 0,04 ɦ 4) 4 A18 Ɉɬɧɨɲɟɧɢɟ ɦɚɫɫɨɜɨɝɨ ɱɢɫɥɚ ɤ ɱɢɫɥɭ ɧɟɣɬɪɨɧɨɜ ɪɚɜɧɨ § 2,11 ɜ ɹɞɪɟ 1) 7Be 4 © ɋɬɚɬȽɪɚɞ 2013 ɝ 3) 3 4) 0,05 ɦ A16 ɇɚ ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɭɸ ɫɬɟɤɥɹɧɧɭɸ ɩɥɚɫɬɢɧɤɭ ɢ ɫɬɟɤɥɹɧɧɭɸ ɩɪɢɡɦɭ ɩɚɞɚɟɬ ɥɭɱ ɛɟɥɨɝɨ ɫɜɟɬɚ (ɫɦ. ɪɢɫɭɧɨɤ). Ⱦɢɫɩɟɪɫɢɹ ɫɜɟɬɚ ɜ ɜɢɞɟ ɪɚɞɭɠɧɵɯ ɩɨɥɨɫ ɧɚ ɷɤɪɚɧɟ 1) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ⱥ 2) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ȼ 3) ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɢ ɜ ɫɥɭɱɚɟ Ȼ 4) ɧɟ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɧɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɧɢ ɜ ɫɥɭɱɚɟ Ȼ 2) 2 2) 20Mg 12 3) 19 N e 10 4) 35C l 17 A19 Ⱦɨɥɹ ɚɬɨɦɨɜ ɪɚɞɢɨɚɤɬɢɜɧɨɝɨ ɢɡɨɬɨɩɚ, ɧɟ ɪɚɫɩɚɜɲɢɯɫɹ ɩɨ ɩɪɨɲɟɫɬɜɢɢ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ, ɪɚɜɧɨɝɨ ɩɨɥɨɜɢɧɟ ɩɟɪɢɨɞɚ ɩɨɥɭɪɚɫɩɚɞɚ, ɨɛɨɡɧɚɱɟɧɚ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ ɰɢɮɪɨɣ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 11 A20 ɉɨɤɚɡɚɧɢɹ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɧɟɤɨɬɨɪɨɦ ɩɨɦɟɳɟɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ 23 °ɋ ɢ 17 °ɋ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ ɬɚɛɥɢɰ, ɨɩɪɟɞɟɥɢɬɟ ɚɛɫɨɥɸɬɧɭɸ ɜɥɚɠɧɨɫɬɶ ɜɨɡɞɭɯɚ ɜ ɩɨɦɟɳɟɧɢɢ, ɝɞɟ ɭɫɬɚɧɨɜɥɟɧɵ ɞɚɧɧɵɟ ɬɟɪɦɨɦɟɬɪɵ. ȼ ɩɟɪɜɨɣ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ, ɜɵɪɚɠɟɧɧɚɹ ɜ %. Ɍɟɦɩɟɪɚɬɭɪɚ ɫɭɯɨɝɨ ɬɟɪɦɨɦɟɬɪɚ, °ɋ 15 16 17 18 19 20 21 22 23 24 25 Ɋɚɡɧɨɫɬɶ ɩɨɤɚɡɚɧɢɣ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, °ɋ 3 4 5 6 71 61 52 44 71 62 54 45 72 64 55 47 73 64 56 48 74 65 58 50 74 66 59 51 75 67 60 52 76 68 61 54 76 69 61 55 77 69 62 56 77 70 63 57 Ɍɟɦɩɟɪɚɬɭɪɚ, °ɋ ɉɥɨɬɧɨɫɬɶ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɜɨɞɵ ȡ, ɝɦ3 15 16 17 18 19 20 21 22 23 24 25 12,8 13,6 14,5 15,4 16,3 17,3 18,3 19,4 20,6 21,8 23,0 1) 20,6 ɝɦ3 2) 14,5 ɝɦ3 3) 11,3 ɝɦ3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 A21 Ʉ ɢɫɬɨɱɧɢɤɭ ɬɨɤɚ ɩɨɞɤɥɸɱɟɧɵ ɪɟɨɫɬɚɬ, ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ (ɪɢɫɭɧɨɤ 1). ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɩɨɥɡɭɧɤɚ ɪɟɨɫɬɚɬɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɩɪɢɛɨɪɚɦɢ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ, ɢɡɨɛɪɚɠɺɧɧɵɟ ɧɚ ɪɢɫɭɧɤɚɯ 2 ɢ 3 (R – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɤɥɸɱɺɧɧɨɣ ɜ ɰɟɩɶ ɱɚɫɬɢ ɪɟɨɫɬɚɬɚ). ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ(-ɵɟ) ɭɬɜɟɪɠɞɟɧɢɟ(-ɹ), ɟɫɥɢ ɬɚɤɨɜɨɟ(-ɵɟ) ɢɦɟɟɬɫɹ(-ɸɬɫɹ). Ⱥ. ȼɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɨ 2 Ɉɦ. Ȼ. ɗȾɋ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɚ 15 ɦȼ. 4) ɧɢ Ⱥ, ɧɢ Ȼ ɑɚɫɬɶ 2 Ɉɬɜɟɬɨɦ ɤ ɡɚɞɚɧɢɹɦ ɷɬɨɣ ɱɚɫɬɢ (ȼ1–ȼ4) ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɰɢɮɪ. ȼɩɢɲɢɬɟ ɨɬɜɟɬɵ ɫɧɚɱɚɥɚ ɜ ɬɟɤɫɬ ɪɚɛɨɬɵ, ɚ ɡɚɬɟɦ ɩɟɪɟɧɟɫɢɬɟ ɢɯ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ, ɛɟɡ ɡɚɩɹɬɵɯ, ɩɪɨɛɟɥɨɜ ɢ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɢɦɜɨɥɨɜ. Ʉɚɠɞɭɸ ɰɢɮɪɭ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɰɟɩɶ ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɗȾɋ ɫ ɧɟɤɨɬɨɪɵɦ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ, ɞɜɭɯ ɨɞɢɧɚɤɨɜɵɯ ɥɚɦɩɨɱɟɤ, ɤɥɸɱɚ, ɜɨɥɶɬɦɟɬɪɚ ɢ ɞɜɭɯ ɚɦɩɟɪɦɟɬɪɨɜ (ɫɦ. ɪɢɫɭɧɨɤ). ɂɡɦɟɪɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɵɦɢ. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɩɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɨɜ, ɟɫɥɢ ɡɚɦɤɧɭɬɶ ɤɥɸɱ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɉɈɄȺɁȺɇɂȿ ɉɊɂȻɈɊȺ Ⱥ) ɩɨɤɚɡɚɧɢɟ ɜɨɥɶɬɦɟɬɪɚ Ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ1 ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ2 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ 3) ɢ Ⱥ, ɢ Ȼ 2) ɬɨɥɶɤɨ Ȼ 1) ɬɨɥɶɤɨ Ⱥ B1 4) 8,0 ɝɦ3 12 © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ ȼ ȿȽɈ ɂɁɆȿɇȿɇɂȿ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 B2 13 ɂɏ ɂɁɆȿɇȿɇɂȿ ɎɂɁɂɑȿɋɄɂȿ ȼȿɅɂɑɂɇɕ Ⱥ) ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɧɚɝɪɟɜɚɬɟɥɹ Ȼ) ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ ȼ) ɄɉȾ ɰɢɤɥɚ Ɉɬɜɟɬ: Ⱥ Ȼ ɝɚɡɨɦ ɨɬ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ 14 Ʉ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ ɩɟɪɜɨɝɨ ɫɬɨɥɛɰɚ ɩɨɞɛɟɪɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɨɡɢɰɢɸ ɜɬɨɪɨɝɨ ɫɬɨɥɛɰɚ ɢ ɡɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɩɨɞ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɛɭɤɜɚɦɢ. ɍɑȺɋɌɈɄ ȽɊȺɎɂɄȺ ɆɈȾɍɅɖ ɗȾɋ ɋȺɆɈɂɇȾɍɄɐɂɂ 1) 0,625 ɦȼ Ⱥ) ȺȻ Ȼ) Ȼȼ 2) 0,027 ȼ 3) 0,4 ɦȼ 4) 0,1 ɦȼ 5) 0 ȼ Ⱥ Ȼ Ɉɬɜɟɬ: Ɉɞɢɧ ɦɨɥɶ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 1. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɫɥɟɞɭɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ, ɟɫɥɢ ɡɚɦɟɧɢɬɶ ɢɫɯɨɞɧɵɣ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ ɧɚ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 2: ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɝɚɡɨɦ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ; ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ; ɄɉȾ ɰɢɤɥɚ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. B3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 B4 ɇɚ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɫ ɩɟɪɢɨɞɨɦ d 0 ɧɨɪɦɚɥɶɧɨ ɩɚɞɚɟɬ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɣ ɩɭɱɨɤ ɫɜɟɬɚ, ɚ ɡɚ ɪɟɲɺɬɤɨɣ ɪɚɫɩɨɥɨɠɟɧ ɨɛɴɟɤɬɢɜ, ɜ ɮɨɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɧɚɛɥɸɞɚɸɬɫɹ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ ɫɦ. ɪɢɫɭɧɨɤ). Ɍɨɱɤɚɦɢ ɩɨɤɚɡɚɧɵ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ, ɚ ɰɢɮɪɚɦɢ ɨɛɨɡɧɚɱɟɧɵ ɢɯ ɧɨɦɟɪɚ. ɍɝɥɵ ɞɢɮɪɚɤɰɢɢ ɦɚɥɵ. ɗɬɭ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɩɨɨɱɟɪɺɞɧɨ ɡɚɦɟɧɹɸɬ ɞɪɭɝɢɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɦɢ ɪɟɲɺɬɤɚɦɢ – Ⱥ, Ȼ ɢ ȼ. ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɫɯɟɦɚɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɦɚɤɫɢɦɭɦɨɜ ɢ ɩɟɪɢɨɞɚɦɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɪɟɲɺɬɨɤ. ȼ ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɢɥɵ ɬɨɤɚ I ɜ ɤɚɬɭɲɤɟ ɢɧɞɭɤɬɢɜɧɨɫɬɶɸ 10 ɦȽɧ ɨɬ ɜɪɟɦɟɧɢ t. ɋɏȿɆȺ ȾɂɎɊȺɄɐɂɈɇɇɕɏ ɆȺɄɋɂɆɍɆɈȼ Ⱥ) Ⱥ Ȼ) Ȼ ɉȿɊɂɈȾ ȾɂɎɊȺɄɐɂɈɇɇɈɃ ɊȿɒȬɌɄɂ 1) 4d 0 2) d 0 4 3) 2d 0 4) 2 d 0 ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɭɱɚɫɬɤɚɦɢ ɝɪɚɮɢɤɚ ɢ ɡɧɚɱɟɧɢɹɦɢ ɦɨɞɭɥɹ ɗȾɋ ɫɚɦɨɢɧɞɭɤɰɢɢ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 3 5) 2 d 0 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 15 ɑɚɫɬɶ 3 Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 3 ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɞɚɱɢ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɢɯ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ ɧɚ ɱɟɪɧɨɜɢɤɟ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ Ⱥ22–Ⱥ25 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A22 Ƚɪɭɡ ɧɚɱɢɧɚɟɬ ɫɜɨɛɨɞɧɨ ɩɚɞɚɬɶ ɫ ɧɟɤɨɬɨɪɨɣ ɜɵɫɨɬɵ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɨɥɟɬɟɜ 40 ɦ, ɝɪɭɡ ɩɪɢɨɛɪɺɥ ɫɤɨɪɨɫɬɶ 20 ɦɫ. ɇɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ ɨɬɧɨɲɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɩɨɬɟɧɰɢɚɥɶɧɨɣ ɷɧɟɪɝɢɢ ɝɪɭɡɚ ɤ ɪɚɛɨɬɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɪɚɜɧɨ 1) 1 2) 2 3) –2 4) 4 A23 ɉɨɪɲɟɧɶ ɦɨɠɟɬ ɫɜɨɛɨɞɧɨ ɛɟɡ ɬɪɟɧɢɹ ɩɟɪɟɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɬɟɧɨɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɨɫɭɞɚ. ȼ ɨɛɴɺɦɟ, ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɧɨɦ ɫɨɫɭɞɚ ɢ ɩɨɪɲɧɟɦ, ɧɚɯɨɞɢɬɫɹ ɜɨɡɞɭɯ (ɫɦ. ɪɢɫɭɧɨɤ). ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ 2) 83,3 ɇ 3) 200 ɇ C1 ɉɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ ɤɚɠɞɨɣ ɢɡ ɡɚɞɚɱ ɋ2–ɋ6 ɞɨɥɠɧɨ ɫɨɞɟɪɠɚɬɶ ɡɚɤɨɧɵ ɢ ɮɨɪɦɭɥɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɪɚɫɱɺɬɵ ɫ ɱɢɫɥɟɧɧɵɦ ɨɬɜɟɬɨɦ ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɢɫɭɧɨɤ, ɩɨɹɫɧɹɸɳɢɣ ɪɟɲɟɧɢɟ. 2) § 0,19 ȼ/ɦ 3) § 0,75 ȼ/ɦ A25 ɗɥɟɤɬɪɨɧ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɫ ɢɧɞɭɤɰɢɟɣ 6 ɦɤɌɥ. ɉɟɪɢɨɞ ɨɛɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɪɚɜɟɧ 1) | 6, 0 106 ɫ 3) | 1, 7 105 ɫ ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ Ʌɭɧɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ C3 ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ 4) 333,3 ɇ 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 300 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 2. C4 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,95 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ 4) § 0,38 ȼ/ɦ U1 = 12 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɦɚɝɧɢɬɧɨɦ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 11,9 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ 2) | 6, 7 106 ɫ ɩɨɥɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? 4) | 5, 9 · 10–5 ɫ ɇɟ ɡɚɛɭɞɶɬɟ ɩɟɪɟɧɟɫɬɢ ɜɫɟ ɨɬɜɟɬɵ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1. © ɋɬɚɬȽɪɚɞ 2013 ɝ 1 81 ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ Ʌɭɧɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. A24 Ⱦɜɟ ɬɨɧɤɢɟ ɜɟɪɬɢɤɚɥɶɧɵɟ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɩɥɚɫɬɢɧɵ ɪɚɫɩɨɥɨɠɟɧɵ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ, ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɪɚɜɧɨ 2 ɫɦ. ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ 1) 0 ȼ/ɦ Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɞɥɢɧɵ ɨɪɝɚɧɧɵɯ ɬɪɭɛ ɪɚɡɧɵɟ: ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ, ɚ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ – ɛɨɥɶɲɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. 28 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ Ʌɭɧɵ ɫɨɫɬɚɜɥɹɟɬ ɫɟɱɟɧɢɹ ɤɚɠɞɨɣ ɢɡ ɩɥɚɫɬɢɧ ɪɚɜɧɚ 15 000 ɫɦ2. Ʌɟɜɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɡɚɪɹɞ q 5 ɩɄɥ, ɡɚɪɹɞ ɜɬɨɪɨɣ ɩɥɚɫɬɢɧɵ q. Ɇɨɞɭɥɶ ɧɚɩɪɹɠɺɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,5 ɫɦ ɨɬ ɥɟɜɨɣ ɩɥɚɫɬɢɧɵ ɪɚɜɟɧ 16 ɉɨɥɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɋ1–ɋ6 ɧɟɨɛɯɨɞɢɦɨ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2. ɉɪɢ ɨɮɨɪɦɥɟɧɢɢ ɪɟɲɟɧɢɹ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2 ɡɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɡɚɞɚɧɢɹ ɋ1, ɋ2 ɢ ɬ. ɞ.), ɚ ɡɚɬɟɦ ɪɟɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɡɚɞɚɱɢ. Ɉɬɜɟɬɵ ɡɚɩɢɫɵɜɚɣɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ. C2 ɫɟɱɟɧɢɹ ɫɨɫɭɞɚ ɪɚɜɧɚ 25 ɫɦ2, ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɞɧɚ ɫɨɫɭɞɚ ɞɨ ɩɨɪɲɧɹ ɪɚɜɧɨ 20 ɫɦ, ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ 100 ɤɉɚ, ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɜ ɫɨɫɭɞɟ ɪɚɜɧɨ ɚɬɦɨɫɮɟɪɧɨɦɭ. ɉɨɪɲɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɦɟɳɚɸɬ ɧɚ 5 ɫɦ ɜɩɪɚɜɨ, ɩɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɧɟ ɦɟɧɹɟɬɫɹ. Ʉɚɤɭɸ ɫɢɥɭ ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ, ɱɬɨɛɵ ɭɞɟɪɠɚɬɶ ɩɨɪɲɟɧɶ ɜ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ? 1) 50 ɇ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 © ɋɬɚɬȽɪɚɞ 2013 ɝ Физика. 11 класс. Вариант ФИ1603 17 С5 Определите фокусное расстояние тонкой линзы, если линейные размеры изображения тонкого карандаша, помещённого на расстоянии а = 60 см от линзы и расположенного перпендикулярно главной оптической оси, меньше размеров карандаша в n = 3 раза. С6 Согласно гипотезе де Бройля, все частицы обладают волновыми свойствами. Длина волны для частицы массой m, имеющей скорость v, составляет ߣ= -34 h mv , где h = 6,6 · 10 Дж · с – постоянная Планка. Для того, чтобы можно было применять модель идеального газа, среднее расстояние l между молекулами газа должно быть, в частности, гораздо больше ߣ. При какой температуре T для инертного газа гелия l ≈ 5ߣ если концентрация его молекул 25 –3 равна n = 1,3 · 10 м ? -24 Масса молекулы гелия равна m = 6,6 · 10 г. © СтатГрад 2013 г. Физика. 11 класс. Вариант ФИ1604 2 Инструкция по выполнению работы Тренировочная работа № 4 по ФИЗИКЕ 30 апреля 2013 года 11 класс Вариант ФИ1604 Для выполнения экзаменационной работы по физике отводится 235 минут. Работа состоит из 3 частей, включающих в себя 35 заданий. Часть 1 содержит 21 задание (А1–А21). К каждому заданию даётся четыре варианта ответа, из которых только один правильный. Часть 2 содержит 4 задания (В1–В4), на которые надо дать краткий ответ в виде последовательности цифр Часть 3 содержит 10 задач: А22–А25 с выбором одного верного ответа и С1–С6, для которых требуется дать развёрнутые решения. При вычислениях разрешается использовать непрограммируемый калькулятор. Все бланки ЕГЭ заполняются яркими чёрными чернилами. Допускается использование гелевой, капиллярной или перьевой ручек. При выполнении заданий Вы можете пользоваться черновиком. Обращаем Ваше внимание на то, что записи в черновике не будут учитываться при оценивании работы. Советуем выполнять задания в том порядке, в котором они даны Для экономии времени пропускайте задание, которое не удаётся выполнить сразу, и переходите к следующему. Если после выполнения всей работы у Вас останется время, Вы сможете вернуться к пропущенным заданиям Баллы, полученные Вами за выполненные задания, суммируются. Постарайтесь выполнить как можно больше заданий и набрать наибольшее количество баллов. Район. Город (населённый пункт) Школа. Класс. Фамилия Имя Отчество. © СтатГрад 2013 г. Желаем успеха! © СтатГрад 2013 г. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 4 ɇɢɠɟ ɩɪɢɜɟɞɟɧɵ ɫɩɪɚɜɨɱɧɵɟ ɞɚɧɧɵɟ, ɤɨɬɨɪɵɟ ɦɨɝɭɬ ɩɨɧɚɞɨɛɢɬɶɫɹ ȼɚɦ ɩɪɢ ɜɵɩɨɥɧɟɧɢɢ ɪɚɛɨɬɵ. ɷɥɟɤɬɪɨɧɚ ɩɪɨɬɨɧɚ ɧɟɣɬɪɨɧɚ Ⱦɟɫɹɬɢɱɧɵɟ ɩɪɢɫɬɚɜɤɢ Ɇɚɫɫɵ ɱɚɫɬɢɰ 9,1 · 10–31 ɤɝ § 5,5·10–4 ɚ. ɟ. ɦ. 1,673 · 10–27 ɤɝ § 1,007 ɚ. ɟ. ɦ. 1,675 · 10–27 ɤɝ § 1,008 ɚ. ɟ. ɦ. ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɇɚɢɦɟɧɨɜɚɧɢɟ Ɉɛɨɡɧɚɱɟɧɢɟ Ɇɧɨɠɢɬɟɥɶ ɝɢɝɚ Ƚ 10 9 ɫɚɧɬɢ ɫ 10–2 ɦɟɝɚ Ɇ 10 6 ɦɢɥɥɢ ɦ 10–3 ɜɨɞɵ 1000 ɤɝɦ3 ɤɢɥɨ ɤ 10 3 ɦɢɤɪɨ ɦɤ 10–6 ɞɪɟɜɟɫɢɧɵ (ɫɨɫɧɚ) ɚɥɸɦɢɧɢɹ ɝɟɤɬɨ ɝ ɧɚɧɨ ɧ 400 ɤɝɦ3 2700 ɤɝɦ3 10 2 10–9 ɞɟɰɢ ɞ 10–1 ɩɢɤɨ ɩ 10–12 ɤɟɪɨɫɢɧɚ 800 ɤɝɦ3 ɠɟɥɟɡɚ 7800 ɤɝɦ3 ɪɬɭɬɢ 13 600 ɤɝɦ3 ɉɥɨɬɧɨɫɬɶ ɩɨɞɫɨɥɧɟɱɧɨɝɨ ɦɚɫɥɚ Ʉɨɧɫɬɚɧɬɵ ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɺɦɤɨɫɬɶ ɱɢɫɥɨ ʌ ɭɫɤɨɪɟɧɢɟ ɫɜɨɛɨɞɧɨɝɨ ɩɚɞɟɧɢɹ ɧɚ Ɂɟɦɥɟ ʌ = 3,14 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ G = 6,7 · 10–11 ɇÂɦ2ɤɝ2 R = 8,31 Ⱦɠ/(ɦɨɥɶÂɄ) ɩɨɫɬɨɹɧɧɚɹ Ⱥɜɨɝɚɞɪɨ NȺ = 6·1023 ɦɨɥɶ–1 ɫɤɨɪɨɫɬɶ ɫɜɟɬɚ ɜ ɜɚɤɭɭɦɟ ɫ = 3 · 108 ɦɫ 1 k= = 9 · 109 ɇÂɦ2Ʉɥ2 ʌ İ0 ɤɨɷɮɮɢɰɢɟɧɬ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ ɜ ɡɚɤɨɧɟ Ʉɭɥɨɧɚ ɦɨɞɭɥɶ ɡɚɪɹɞɚ ɷɥɟɤɬɪɨɧɚ (ɷɥɟɦɟɧɬɚɪɧɵɣ ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɡɚɪɹɞ) ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ g = 10 ɦɫ2 k = 1,38 · 10–23 ȾɠɄ ɜɨɞɵ 4,2 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɚɥɸɦɢɧɢɹ 900 Ⱦɠ/(ɤɝÂɄ) ɥɶɞɚ 2,1 · 10 3 Ⱦɠ/(ɤɝÂɄ) ɦɟɞɢ 380 Ⱦɠ/(ɤɝÂɄ) ɠɟɥɟɡɚ ɫɜɢɧɰɚ 640 Ⱦɠ/(ɤɝÂɄ) 130 Ⱦɠ/(ɤɝÂɄ) ɱɭɝɭɧɚ 500 Ⱦɠ/(ɤɝÂɄ) ɍɞɟɥɶɧɚɹ ɬɟɩɥɨɬɚ ɩɚɪɨɨɛɪɚɡɨɜɚɧɢɹ ɜɨɞɵ 2,3 · 10 6 Ⱦɠɤɝ ɩɥɚɜɥɟɧɢɹ ɫɜɢɧɰɚ ɩɥɚɜɥɟɧɢɹ ɥɶɞɚ e = 1,6 · 10–19 Ʉɥ 1 ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ ɷɤɜɢɜɚɥɟɧɬɧɚ 1 ɷɥɟɤɬɪɨɧɜɨɥɶɬ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2,5 · 10 4 Ⱦɠɤɝ 3,3 · 10 5 Ⱦɠɤɝ ɇɨɪɦɚɥɶɧɵɟ ɭɫɥɨɜɢɹ h = 6,6 · 10–34 ȾɠÂɫ ɞɚɜɥɟɧɢɟ: 105 ɉɚ, ɬɟɦɩɟɪɚɬɭɪɚ: 0 °ɋ ɋɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞɭ ɪɚɡɥɢɱɧɵɦɢ ɟɞɢɧɢɰɚɦɢ ɬɟɦɩɟɪɚɬɭɪɚ ɚɬɨɦɧɚɹ ɟɞɢɧɢɰɚ ɦɚɫɫɵ 900 ɤɝɦ3 Ɇɨɥɹɪɧɚɹ ɦɚFɫɚ ɝɟɥɢɹ 0 Ʉ = – 273 °ɋ ɚɡɨɬɚ 28 · 10–3 ɤɝɦɨɥɶ 1 ɚ. ɟ. ɦ. = 1,66 · 10–27 ɤɝ 931,5 Ɇɷȼ ɚɪɝɨɧɚ 40 · 10–3 ɤɝɦɨɥɶ ɤɢɫɥɨɪɨɞɚ 32 · 10–3 ɤɝɦɨɥɶ ɜɨɞɨɪɨɞɚ 2 · 10–3 ɤɝɦɨɥɶ ɥɢɬɢɹ 1 ɷȼ = 1,6 · 10–19 Ⱦɠ 6 · 10–3 ɤɝɦɨɥɶ ɜɨɡɞɭɯɚ 29 · 10–3 ɤɝɦɨɥɶ ɧɟɨɧɚ 20 · 10–3 ɤɝɦɨɥɶ ɜɨɞɵ 18 · 10–3 ɤɝɦɨɥɶ ɭɝɥɟɤɢɫɥɨɝɨ ɝɚɡɚ 44 · 10–3 ɤɝɦɨɥɶ © ɋɬɚɬȽɪɚɞ 2013 ɝ 4 · 10–3 ɤɝɦɨɥɶ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 5 ɑɚɫɬɶ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 A4 ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ ɱɚɫɬɢ 1 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ (A1–A21) ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A1 ɉɨ ɩɥɨɫɤɨɫɬɢ XY ɞɜɢɠɭɬɫɹ ɱɟɬɵɪɟ ɬɨɱɟɱɧɵɯ ɬɟɥɚ – Ⱥ, Ȼ, ȼ ɢ Ƚ, ɬɪɚɟɤɬɨɪɢɢ ɤɨɬɨɪɵɯ ɢɡɨɛɪɚɠɟɧɵ ɧɚ ɪɢɫɭɧɤɟ. Ɂɚɜɢɫɢɦɨɫɬɢ ɤɨɨɪɞɢɧɚɬ ɨɞɧɨɝɨ ɢɡ ɷɬɢɯ ɬɟɥ ɨɬ ɜɪɟɦɟɧɢ ɢɦɟɸɬ ɜɢɞ: x 2t ɢ y 1 t. ɗɬɨ ɬɟɥɨ ɨɛɨɡɧɚɱɟɧɨ ɛɭɤɜɨɣ Ⱦɜɚ ɛɪɭɫɤɚ ɦɚɫɫɨɣ m ɢ 2m ɪɚɜɧɨɦɟɪɧɨ ɞɜɢɠɭɬɫɹ ɜɞɨɥɶ ɩɪɹɦɨɣ OX (ɫɦ. ɪɢɫɭɧɨɤ). ȼ ɫɢɫɬɟɦɟ ɨɬɫɱɺɬɚ, ɫɜɹɡɚɧɧɨɣ ɫ ɛɪɭɫɤɨɦ 2, ɦɨɞɭɥɶ ɢɦɩɭɥɶɫɚ ɩɟɪɜɨɝɨ ɛɪɭɫɤɚ ɪɚɜɟɧ 1) mV A5 6 2) 2mV 3) 3mV 4) 4mV ɋɚɧɢ ɪɚɜɧɨɦɟɪɧɨ ɩɟɪɟɦɟɳɚɸɬ ɩɨ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɫ ɩɟɪɟɦɟɧɧɵɦ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɬɪɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɦɨɞɭɥɹ ɪɚɛɨɬɵ ɫɢɥɵ ɬɪɟɧɢɹ Aɬɪ ɨɬ ɩɪɨɣɞɟɧɧɨɝɨ ɩɭɬɢ S. Ɉɬɧɨɲɟɧɢɟ ɦɚɤɫɢɦɚɥɶɧɨɝɨ ɤɨɷɮɮɢɰɢɟɧɬɚ ɬɪɟɧɢɹ ɤ ɦɢɧɢɦɚɥɶɧɨɦɭ ɧɚ ɩɪɨɣɞɟɧɧɨɦ ɩɭɬɢ ɪɚɜɧɨ 1) Ⱥ A2 3) ȼ 1) 4 4) Ƚ Ɇɨɞɭɥɶ ɫɤɨɪɨɫɬɢ ɪɚɜɧɨɦɟɪɧɨɝɨ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ r 1) 2) 3) 4) A3 2) Ȼ A6 1) Mg 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 2) Mg 2 A7 4 4) 20 1 4 ɞɥɢɧɵ ɛɚɥɤɢ (ɫɦ. ɪɢɫɭɧɨɤ). Ʉɚɤɭɸ ɫɢɥɭ F ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ ɤ ɤɨɧɰɭ A ɛɚɥɤɢ ɞɥɹ ɫɨɯɪɚɧɟɧɢɹ ɪɚɜɧɨɜɟɫɢɹ? ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɱɟɬɵɪɟ ɩɚɪɵ ɫɮɟɪɢɱɟɫɤɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɬɨɱɟɱɧɵɯ ɬɟɥ, ɪɚɫɩɨɥɨɠɟɧɧɵɯ ɨɬɧɨɫɢɬɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɚ ɧɚ ɪɚɡɧɵɯ ɪɚɫɫɬɨɹɧɢɹɯ ɦɟɠɞɭ ɰɟɧɬɪɚɦɢ ɷɬɢɯ ɬɟɥ. F ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɪɚɜɧɚ 0 . 3) 16 Ɉɞɧɨɪɨɞɧɚɹ ɫɩɥɨɲɧɚɹ ɛɚɥɤɚ ɦɚɫɫɨɣ M ɭɪɚɜɧɨɜɟɲɟɧɚ ɧɚ ɨɫɬɪɨɤɨɧɟɱɧɨɣ ɨɩɨɪɟ. Ɉɩɨɪɭ ɩɟɪɟɞɜɢɝɚɸɬ ɜɩɪɚɜɨ ɧɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɫɩɭɬɧɢɤɚ ɨɛɪɚɬɧɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɦɚɫɫɟ ɫɩɭɬɧɢɤɚ ɩɪɹɦɨ ɩɪɨɩɨɪɰɢɨɧɚɥɟɧ ɤɜɚɞɪɚɬɭ ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɋɱɢɬɚɹ, ɱɬɨ ɫɢɥɚ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɞɜɭɯ ɬɟɥ ɨɞɢɧɚɤɨɜɵɯ ɦɚɫɫ M, ɧɚɯɨɞɹɳɢɯɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ R ɞɪɭɝ ɨɬ ɞɪɭɝɚ, ɪɚɜɧɚ F0, ɨɩɪɟɞɟɥɢɬɟ, ɞɥɹ ɤɚɤɨɣ ɩɚɪɵ ɬɟɥ ɫɢɥɚ 2) 8 3) Mg 3 4) M g 4 Ⱦɢɦɚ ɢ Ʌɟɧɚ ɫɯɟɦɚɬɢɱɟɫɤɢ ɢɡɨɛɪɚɡɢɥɢ ɧɚ ɞɨɫɤɟ ɞɜɢɠɟɧɢɟ ɛɪɨɭɧɨɜɫɤɨɣ ɱɚɫɬɢɰɵ. Ɉɬɜɟɱɚɸɳɢɦ ɦɨɞɟɥɢ ɛɪɨɭɧɨɜɫɤɨɝɨ ɞɜɢɠɟɧɢɹ ɦɨɠɧɨ ɩɪɢɡɧɚɬɶ ɪɢɫɭɧɨɤ, ɫɞɟɥɚɧɧɵɣ Ⱥ) Ⱦɢɦɨɣ Ȼ) Ʌɟɧɨɣ 1) ɬɨɥɶɤɨ Ⱥ © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) ɬɨɥɶɤɨ Ȼ 3) ɢ Ⱥ, ɢ Ȼ 4) ɧɢ Ⱥ, ɧɢ Ȼ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 A8 7 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɺɧ ɩɪɨɰɟɫɫ ɩɟɪɟɯɨɞɚ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɢɡ ɫɨɫɬɨɹɧɢɹ Ⱥ ɜ ɫɨɫɬɨɹɧɢɟ Ȼ. ȼ ɫɨɫɬɨɹɧɢɢ Ȼ ɚɛɫɨɥɸɬɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɷɬɨɝɨ ɝɚɡɚ 1) ɜ 2 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 2) ɜ 2 ɪɚɡɚ ɦɟɧɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 3) ɜ 4 ɪɚɡɚ ɛɨɥɶɲɟ, ɱɟɦ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ 4) ɪɚɜɧɚ ɬɟɦɩɟɪɚɬɭɪɟ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ Ⱥ A9 ȼ ɬɚɛɥɢɰɟ ɭɤɚɡɚɧɚ ɩɥɨɬɧɨɫɬɶ ɝɚɡɨɜ ɩɪɢ ɧɨɪɦɚɥɶɧɨɦ ɚɬɦɨɫɮɟɪɧɨɦ ɞɚɜɥɟɧɢɢ. Ƚɚɡ ɉɥɨɬɧɨɫɬɶ ɝɚɡɚ, ɤɝɦ3 ɚɡɨɬ ɜɨɞɨɪɨɞ ɤɫɟɧɨɧ ɯɥɨɪ 1,25 0,09 5,9 3,2 2) ɜɨɞɨɪɨɞɚ 3) ɤɫɟɧɨɧɚ 8 A11 Ɍɨɱɟɱɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ Q ɧɚɯɨɞɢɬɫɹ ɧɚ ɪɚɫɫɬɨɹɧɢɢ x0 ɨɬ ɰɟɧɬɪɚ ɧɟɩɪɨɜɨɞɹɳɟɝɨ ɲɚɪɚ, ɪɚɜɧɨɦɟɪɧɨ ɩɨ ɩɨɜɟɪɯɧɨɫɬɢ ɡɚɪɹɠɟɧɧɨɝɨ ɡɚɪɹɞɨɦ q (ɫɦ. ɪɢɫɭɧɨɤ). Ɂɚɪɹɞ Q ɧɚɱɢɧɚɸɬ ɩɟɪɟɦɟɳɚɬɶ ɜɞɨɥɶ ɪɚɞɢɭɫɚ ɲɚɪɚ, ɭɞɚɥɹɹ ɨɬ ɧɟɝɨ. ɇɚ ɤɚɤɨɦ ɢɡ ɩɪɢɜɟɞɺɧɧɵɯ ɧɢɠɟ ɝɪɚɮɢɤɨɜ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɫɢɥɵ F ɤɭɥɨɧɨɜɫɤɨɝɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɡɚɪɹɞɚ Q ɫ ɲɚɪɨɦ ɨɬ ɪɚɫɫɬɨɹɧɢɹ x ɦɟɠɞɭ ɡɚɪɹɞɨɦ ɢ ɰɟɧɬɪɨɦ ɲɚɪɚ? 1) 1 2) 2 3) 3 4) 4 A12 ɂɞɟɚɥɶɧɵɣ ɚɦɩɟɪɦɟɬɪ ɢ ɬɪɢ ɪɟɡɢɫɬɨɪɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ R 11 Ɉɦ, 2R ɢ 3R ɜɤɥɸɱɟɧɵ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɰɟɩɶ, ɫɨɞɟɪɠɚɳɭɸ ɢɫɬɨɱɧɢɤ ɫ ɗȾɋ, ɪɚɜɧɨɣ 5 ȼ, ɢ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ r 4 Ɉɦ. ɉɨɤɚɡɚɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɪɚɜɧɵ 1) 50 Ⱥ ɉɪɢ ɷɬɨɦ ɧɚɢɦɟɧɶɲɭɸ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɭɸ ɫɤɨɪɨɫɬɶ ɢɦɟɸɬ ɦɨɥɟɤɭɥɵ 1) ɚɡɨɬɚ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 4) ɯɥɨɪɚ A10 Ⱦɜɚ ɦɨɥɹ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɜɨɞɹɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T1 ɜ ɫɨɫɬɨɹɧɢɟ 2 ɫ ɬɟɦɩɟɪɚɬɭɪɨɣ T2 (ɫɦ. ɪɢɫɭɧɨɤ). Ʉɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɤɨɬɨɪɨɟ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɫɨɨɛɳɟɧɨ ɝɚɡɭ, ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɬɨɥɛɰɭ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ, ɨɛɨɡɧɚɱɟɧɧɨɦɭ ɰɢɮɪɨɣ 2) 2 Ⱥ 3) 0,5 Ⱥ 4) § 0,07 Ⱥ JG A13 ɗɥɟɤɬɪɨɧ, ɞɜɢɝɚɹɫɶ ɫɨ ɫɤɨɪɨɫɬɶɸ V , ɥɟɠɚɳɟɣ ɜ ɝɨɪɢɡɨɧɬɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ XY ɧɚ ɪɢɫɭɧɤɟ ɷɬɚ ɩɥɨɫɤɨɫɬɶ ɩɨɤɚɡɚɧɚ ɬɨɧɢɪɨɜɤɨɣ), ɜɥɟɬɚɟɬ ɜ ɨɛɥɚɫɬɶ JG ɨɞɧɨɪɨɞɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ ɫ ɢɧɞɭɤɰɢɟɣ B , ɧɚɩɪɚɜɥɟɧɧɨɣ ɜɞɨɥɶ ɨɫɢ X. ɉɪɚɜɢɥɶɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɫɢɥɵ Ʌɨɪɟɧɰɚ, ɢɡɨɛɪɚɠɟɧɨ ɜɟɤɬɨɪɨɦ ɩɨɞ ɧɨɦɟɪɨɦ 1) 1 2) 2 3) 3 ɞɟɣɫɬɜɭɸɳɟɣ ɧɚ ɷɥɟɤɬɪɨɧ, 4) 4 A14 ɂɦɟɸɬɫɹ ɞɜɟ ɡɚɪɹɠɟɧɧɵɟ ɱɚɫɬɢɰɵ: ɩɟɪɜɚɹ ɧɚɯɨɞɢɬɫɹ ɜ ɫɨɫɬɨɹɧɢɢ ɩɨɤɨɹ, ɜɬɨɪɚɹ ɞɜɢɠɟɬɫɹ ɫ ɩɨɫɬɨɹɧɧɨɣ ɫɤɨɪɨɫɬɶɸ. ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɜɨɥɧɵ 1) 1 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 2 3) 3 4) 4 1) 2) 3) 4) ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɩɟɪɜɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɬɨɥɶɤɨ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɢɡɥɭɱɚɟɬ ɢ ɩɟɪɜɚɹ, ɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ ɧɟ ɢɡɥɭɱɚɟɬ ɧɢ ɩɟɪɜɚɹ, ɧɢ ɜɬɨɪɚɹ ɱɚɫɬɢɰɚ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 9 A15 ɇɚ ɪɢɫɭɧɤɟ ɢɡɨɛɪɚɠɟɧɵ ɨɩɬɢɱɟɫɤɚɹ ɨɫɶ OO c ɬɨɧɤɨɣ ɫɨɛɢɪɚɸɳɟɣ ɥɢɧɡɵ, ɥɭɱ ɫɜɟɬɚ 1, ɩɚɞɚɸɳɢɣ ɧɚ ɷɬɭ ɥɢɧɡɭ, ɢ ɥɭɱ ɫɜɟɬɚ 2, ɩɪɨɲɟɞɲɢɣ ɱɟɪɟɡ ɷɬɭ ɥɢɧɡɭ. ɇɚ ɪɢɫɭɧɤɟ ɪɚɡɦɟɪ ɨɞɧɨɣ ɤɥɟɬɨɱɤɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ 1 ɫɦ. Ɉɩɬɢɱɟɫɤɚɹ ɫɢɥɚ ɥɢɧɡɵ ɩɪɢɛɥɢɡɢɬɟɥɶɧɨ ɪɚɜɧɚ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 10 A19 Ⱦɨɥɹ ɚɬɨɦɨɜ ɪɚɞɢɨɚɤɬɢɜɧɨɝɨ ɢɡɨɬɨɩɚ, ɪɚɫɩɚɜɲɢɯɫɹ ɩɨ ɩɪɨɲɟɫɬɜɢɢ ɢɧɬɟɪɜɚɥɚ ɜɪɟɦɟɧɢ, ɪɚɜɧɨɝɨ ɩɨɥɨɜɢɧɟ ɩɟɪɢɨɞɚ ɩɨɥɭɪɚɫɩɚɞɚ, ɨɛɨɡɧɚɱɟɧɚ ɧɚ ɝɢɫɬɨɝɪɚɦɦɟ ɰɢɮɪɨɣ 1) 1 2) 2 3) 3 4) 4 A20 ɉɨɤɚɡɚɧɢɹ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, ɭɫɬɚɧɨɜɥɟɧɧɵɯ ɜ ɧɟɤɨɬɨɪɨɦ ɩɨɦɟɳɟɧɢɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɪɚɜɧɵ 20 °ɋ ɢ 15 °ɋ. ɂɫɩɨɥɶɡɭɹ ɞɚɧɧɵɟ ɬɚɛɥɢɰ, ɨɩɪɟɞɟɥɢɬɟ ɚɛɫɨɥɸɬɧɭɸ ɜɥɚɠɧɨɫɬɶ ɜɨɡɞɭɯɚ ɜ ɩɨɦɟɳɟɧɢɢ, ɝɞɟ ɭɫɬɚɧɨɜɥɟɧɵ ɞɚɧɧɵɟ ɬɟɪɦɨɦɟɬɪɵ. ȼ ɩɟɪɜɨɣ ɬɚɛɥɢɰɟ ɩɪɢɜɟɞɟɧɚ ɨɬɧɨɫɢɬɟɥɶɧɚɹ ɜɥɚɠɧɨɫɬɶ, ɜɵɪɚɠɟɧɧɚɹ ɜ %. 1) 5 ɞɩɬɪ 2) 10 ɞɩɬɪ 3) 25 ɞɩɬɪ 4) 50 ɞɩɬɪ A16 ɇɚ ɩɥɨɫɤɨɩɚɪɚɥɥɟɥɶɧɭɸ ɫɬɟɤɥɹɧɧɭɸ ɩɥɚɫɬɢɧɤɭ ɢ ɫɬɟɤɥɹɧɧɭɸ ɩɪɢɡɦɭ ɩɚɞɚɟɬ ɥɭɱ ɛɟɥɨɝɨ ɫɜɟɬɚ (ɫɦ. ɪɢɫɭɧɨɤ). Ⱦɢɫɩɟɪɫɢɹ ɫɜɟɬɚ ɜ ɜɢɞɟ ɪɚɞɭɠɧɵɯ ɩɨɥɨɫ ɧɚ ɷɤɪɚɧɟ 1) 2) 3) 4) Ɍɟɦɩɟɪɚɬɭɪɚ ɫɭɯɨɝɨ ɬɟɪɦɨɦɟɬɪɚ, °ɋ 15 16 17 18 19 20 21 22 23 24 25 ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ⱥ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɬɨɥɶɤɨ ɜ ɫɥɭɱɚɟ Ȼ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɢ ɜ ɫɥɭɱɚɟ Ȼ ɧɟ ɛɭɞɟɬ ɧɚɛɥɸɞɚɬɶɫɹ ɧɢ ɜ ɫɥɭɱɚɟ Ⱥ, ɧɢ ɜ ɫɥɭɱɚɟ Ȼ A17 ɉɪɢ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɦ ɢɡɭɱɟɧɢɢ ɮɨɬɨɷɮɮɟɤɬɚ ɩɨɥɭɱɟɧɚ ɡɚɜɢɫɢɦɨɫɬɶ ɡɚɩɢɪɚɸɳɟɝɨ ɧɚɩɪɹɠɟɧɢɹ Uɡ ɨɬ ɞɥɢɧɵ ɜɨɥɧɵ Ȝ ɫɜɟɬɚ, ɩɚɞɚɸɳɟɝɨ ɧɚ Ɍɟɦɩɟɪɚɬɭɪɚ, °ɋ ɉɥɨɬɧɨɫɬɶ ɧɚɫɵɳɟɧɧɵɯ ɩɚɪɨɜ ɜɨɞɵ ȡ, ɝɦ3 15 16 17 18 19 20 21 22 23 24 25 12,8 13,6 14,5 15,4 16,3 17,3 18,3 19,4 20,6 21,8 23,0 ɦɟɬɚɥɥɢɱɟɫɤɭɸ ɩɥɚɫɬɢɧɤɭ. ɇɚ ɤɚɤɨɦ ɪɢɫɭɧɤɟ ɩɪɚɜɢɥɶɧɨ ɢɡɨɛɪɚɠɟɧɚ ɷɬɚ ɡɚɜɢɫɢɦɨɫɬɶ? 1) 1 2) 2 3) 3 4) 4 A18 Ɉɬɧɨɲɟɧɢɟ ɦɚɫɫɨɜɨɝɨ ɱɢɫɥɚ ɤ ɱɢɫɥɭ ɧɟɣɬɪɨɧɨɜ ɪɚɜɧɨ § 1,94 ɜ ɹɞɪɟ 30 1) 14 Si © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 144 55 C s 3) 226 88 Ra 35 4) 17 Cl Ɋɚɡɧɨɫɬɶ ɩɨɤɚɡɚɧɢɣ ɫɭɯɨɝɨ ɢ ɜɥɚɠɧɨɝɨ ɬɟɪɦɨɦɟɬɪɨɜ, °ɋ 3 4 5 6 71 61 52 44 71 62 54 45 72 64 55 47 73 64 56 48 74 65 58 50 74 66 59 51 75 67 60 52 76 68 61 54 76 69 61 55 77 69 62 56 77 70 63 57 1) 7,6 ɝɦ3 © ɋɬɚɬȽɪɚɞ 2013 ɝ 2) 10,2 ɝɦ3 3) 12,8 ɝɦ3 4) 17,3 ɝɦ3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 11 A21 Ʉ ɢɫɬɨɱɧɢɤɭ ɬɨɤɚ ɩɨɞɤɥɸɱɟɧɵ ɪɟɨɫɬɚɬ, ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ (ɪɢɫɭɧɨɤ 1). ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɨɠɟɧɢɹ ɩɨɥɡɭɧɤɚ ɪɟɨɫɬɚɬɚ ɜ ɪɟɡɭɥɶɬɚɬɟ ɧɚɛɥɸɞɟɧɢɹ ɡɚ ɩɪɢɛɨɪɚɦɢ ɛɵɥɢ ɩɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ, ɢɡɨɛɪɚɠɺɧɧɵɟ ɧɚ ɪɢɫɭɧɤɚɯ 2 ɢ 3 (R – ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɤɥɸɱɺɧɧɨɣ ɜ ɰɟɩɶ ɱɚɫɬɢ ɪɟɨɫɬɚɬɚ). Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 B2 12 Ɉɞɢɧ ɦɨɥɶ ɨɞɧɨɚɬɨɦɧɨɝɨ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɫɨɜɟɪɲɚɟɬ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 1. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɫɥɟɞɭɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɜɟɥɢɱɢɧɵ, ɟɫɥɢ ɡɚɦɟɧɢɬɶ ɢɫɯɨɞɧɵɣ ɰɢɤɥɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ ɧɚ ɩɪɨɰɟɫɫ, ɢɡɨɛɪɚɠɺɧɧɵɣ ɧɚ ɪɢɫɭɧɤɟ 2: ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɝɚɡɨɦ ɨɬ ɧɚɝɪɟɜɚɬɟɥɹ; ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ; ɄɉȾ ɰɢɤɥɚ? ȼɵɛɟɪɢɬɟ ɜɟɪɧɨɟ(-ɵɟ) ɭɬɜɟɪɠɞɟɧɢɟ(-ɹ), ɟɫɥɢ ɬɚɤɨɜɨɟ(-ɵɟ) ɢɦɟɟɬɫɹ(-ɸɬɫɹ). Ⱥ. ȼɧɭɬɪɟɧɧɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɨ 2 Ɉɦ. Ȼ. ɗȾɋ ɢɫɬɨɱɧɢɤɚ ɬɨɤɚ ɪɚɜɧɚ 30 ɦȼ. 2) ɬɨɥɶɤɨ Ȼ 1) ɬɨɥɶɤɨ Ⱥ 3) ɢ Ⱥ, ɢ Ȼ Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. 4) ɧɢ Ⱥ, ɧɢ Ȼ ɑɚɫɬɶ 2 Ɉɬɜɟɬɨɦ ɤ ɡɚɞɚɧɢɹɦ ɷɬɨɣ ɱɚɫɬɢ (ȼ1–ȼ4) ɹɜɥɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɶ ɰɢɮɪ. ȼɩɢɲɢɬɟ ɨɬɜɟɬɵ ɫɧɚɱɚɥɚ ɜ ɬɟɤɫɬ ɪɚɛɨɬɵ, ɚ ɡɚɬɟɦ ɩɟɪɟɧɟɫɢɬɟ ɢɯ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1 ɫɩɪɚɜɚ ɨɬ ɧɨɦɟɪɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɝɨ ɡɚɞɚɧɢɹ, ɧɚɱɢɧɚɹ ɫ ɩɟɪɜɨɣ ɤɥɟɬɨɱɤɢ, ɛɟɡ ɡɚɩɹɬɵɯ, ɩɪɨɛɟɥɨɜ ɢ ɤɚɤɢɯ-ɥɢɛɨ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɫɢɦɜɨɥɨɜ. Ʉɚɠɞɭɸ ɰɢɮɪɭ ɩɢɲɢɬɟ ɜ ɨɬɞɟɥɶɧɨɣ ɤɥɟɬɨɱɤɟ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɜɟɞɺɧɧɵɦɢ ɜ ɛɥɚɧɤɟ ɨɛɪɚɡɰɚɦɢ. B1 ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɰɟɩɶ ɫɨɫɬɨɢɬ ɢɡ ɢɫɬɨɱɧɢɤɚ ɗȾɋ ɫ ɧɟɤɨɬɨɪɵɦ ɜɧɭɬɪɟɧɧɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ, ɞɜɭɯ ɨɞɢɧɚɤɨɜɵɯ ɥɚɦɩɨɱɟɤ, ɤɥɸɱɚ, ɜɨɥɶɬɦɟɬɪɚ ɢ ɞɜɭɯ ɚɦɩɟɪɦɟɬɪɨɜ (ɫɦ. ɪɢɫɭɧɨɤ). ɂɡɦɟɪɢɬɟɥɶɧɵɟ ɩɪɢɛɨɪɵ ɦɨɠɧɨ ɫɱɢɬɚɬɶ ɢɞɟɚɥɶɧɵɦɢ. Ʉɚɤ ɢɡɦɟɧɹɬɫɹ ɩɨɤɚɡɚɧɢɹ ɩɪɢɛɨɪɨɜ, ɟɫɥɢ ɪɚɡɨɦɤɧɭɬɶ ɤɥɸɱ? Ⱦɥɹ ɤɚɠɞɨɣ ɜɟɥɢɱɢɧɵ ɨɩɪɟɞɟɥɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɣ ɯɚɪɚɤɬɟɪ ɢɡɦɟɧɟɧɢɹ: 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ Ɂɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɞɥɹ ɤɚɠɞɨɣ ɮɢɡɢɱɟɫɤɨɣ ɜɟɥɢɱɢɧɵ. ɐɢɮɪɵ ɜ ɨɬɜɟɬɟ ɦɨɝɭɬ ɩɨɜɬɨɪɹɬɶɫɹ. ɉɈɄȺɁȺɇɂȿ ɉɊɂȻɈɊȺ Ⱥ) ɩɨɤɚɡɚɧɢɟ ɜɨɥɶɬɦɟɬɪɚ Ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ1 ȼ) ɩɨɤɚɡɚɧɢɟ ɚɦɩɟɪɦɟɬɪɚ Ⱥ2 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ ȼ ɎɂɁɂɑȿɋɄɂȿ ȼȿɅɂɑɂɇɕ Ⱥ) ɤɨɥɢɱɟɫɬɜɨ ɬɟɩɥɨɬɵ, ɩɨɥɭɱɟɧɧɨɟ ɧɚɝɪɟɜɚɬɟɥɹ Ȼ) ɪɚɛɨɬɚ ɝɚɡɚ ɡɚ ɨɞɢɧ ɰɢɤɥ ȼ) ɄɉȾ ɰɢɤɥɚ Ɉɬɜɟɬ: B3 Ⱥ Ȼ ɂɏ ɂɁɆȿɇȿɇɂȿ ɝɚɡɨɦ ɨɬ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ ȼ ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧ ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ ɫɢɥɵ ɬɨɤɚ I ɜ ɤɚɬɭɲɤɟ ɢɧɞɭɤɬɢɜɧɨɫɬɶɸ 10 ɦȽɧ ɨɬ ɜɪɟɦɟɧɢ t. ȿȽɈ ɂɁɆȿɇȿɇɂȿ 1) ɭɜɟɥɢɱɢɬɫɹ 2) ɭɦɟɧɶɲɢɬɫɹ 3) ɧɟ ɢɡɦɟɧɢɬɫɹ ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɭɱɚɫɬɤɚɦɢ ɝɪɚɮɢɤɚ ɢ ɡɧɚɱɟɧɢɹɦɢ ɦɨɞɭɥɹ ɗȾɋ ɫɚɦɨɢɧɞɭɤɰɢɢ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 13 Ʉ ɤɚɠɞɨɣ ɩɨɡɢɰɢɢ ɩɟɪɜɨɝɨ ɫɬɨɥɛɰɚ ɩɨɞɛɟɪɢɬɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɭɸ ɩɨɡɢɰɢɸ ɜɬɨɪɨɝɨ ɫɬɨɥɛɰɚ ɢ ɡɚɩɢɲɢɬɟ ɜ ɬɚɛɥɢɰɭ ɜɵɛɪɚɧɧɵɟ ɰɢɮɪɵ ɩɨɞ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɛɭɤɜɚɦɢ. ɍɑȺɋɌɈɄ ȽɊȺɎɂɄȺ ɆɈȾɍɅɖ ɗȾɋ ɋȺɆɈɂɇȾɍɄɐɂɂ Ⱥ) ȺȻ Ȼ) Ȼȼ Ɉɬɜɟɬ: B4 Ⱥ Ȼ 1) 2) 3) 4) 5) 0ȼ 0,0075 ȼ 0,05 ɦȼ 0,0025 ȼ 0,2 ɦȼ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 ɑɚɫɬɶ 3 Ɂɚɞɚɧɢɹ ɱɚɫɬɢ 3 ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣ ɡɚɞɚɱɢ. Ɋɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɜɟɫɬɢ ɢɯ ɩɪɟɞɜɚɪɢɬɟɥɶɧɨɟ ɪɟɲɟɧɢɟ ɧɚ ɱɟɪɧɨɜɢɤɟ. ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɡɚɞɚɧɢɣ Ⱥ22–Ⱥ25 ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 1 ɩɨɞ ɧɨɦɟɪɨɦ ɜɵɩɨɥɧɹɟɦɨɝɨ ȼɚɦɢ ɡɚɞɚɧɢɹ ɩɨɫɬɚɜɶɬɟ ɡɧɚɤ «×» ɜ ɤɥɟɬɨɱɤɟ, ɧɨɦɟɪ ɤɨɬɨɪɨɣ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɧɨɦɟɪɭ ɜɵɛɪɚɧɧɨɝɨ ȼɚɦɢ ɨɬɜɟɬɚ. A22 Ƚɪɭɡ ɧɚɱɢɧɚɟɬ ɫɜɨɛɨɞɧɨ ɩɚɞɚɬɶ ɫ ɧɟɤɨɬɨɪɨɣ ɜɵɫɨɬɵ ɛɟɡ ɧɚɱɚɥɶɧɨɣ ɫɤɨɪɨɫɬɢ. ɉɪɨɥɟɬɟɜ 40 ɦ, ɝɪɭɡ ɩɪɢɨɛɪɺɥ ɫɤɨɪɨɫɬɶ 20 ɦɫ. ɇɚ ɷɬɨɦ ɭɱɚɫɬɤɟ ɩɭɬɢ ɨɬɧɨɲɟɧɢɟ ɢɡɦɟɧɟɧɢɹ ɤɢɧɟɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɝɪɭɡɚ ɤ ɪɚɛɨɬɟ ɫɢɥɵ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜɨɡɞɭɯɚ ɪɚɜɧɨ 1) 1 ɇɚ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɫ ɩɟɪɢɨɞɨɦ d 0 ɧɨɪɦɚɥɶɧɨ ɩɚɞɚɟɬ ɦɨɧɨɯɪɨɦɚɬɢɱɟɫɤɢɣ ɩɭɱɨɤ ɫɜɟɬɚ, ɚ ɡɚ ɪɟɲɺɬɤɨɣ ɪɚɫɩɨɥɨɠɟɧ ɨɛɴɟɤɬɢɜ, ɜ ɮɨɤɚɥɶɧɨɣ ɩɥɨɫɤɨɫɬɢ ɤɨɬɨɪɨɝɨ ɧɚɛɥɸɞɚɸɬɫɹ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ ɫɦ. ɪɢɫɭɧɨɤ). Ɍɨɱɤɚɦɢ ɩɨɤɚɡɚɧɵ ɞɢɮɪɚɤɰɢɨɧɧɵɟ ɦɚɤɫɢɦɭɦɵ, ɚ ɰɢɮɪɚɦɢ ɨɛɨɡɧɚɱɟɧɵ ɢɯ ɧɨɦɟɪɚ. ɍɝɥɵ ɞɢɮɪɚɤɰɢɢ ɦɚɥɵ. ɗɬɭ ɞɢɮɪɚɤɰɢɨɧɧɭɸ ɪɟɲɺɬɤɭ ɩɨɨɱɟɪɺɞɧɨ ɡɚɦɟɧɹɸɬ ɞɪɭɝɢɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɦɢ ɪɟɲɺɬɤɚɦɢ – Ⱥ, Ȼ ɢ ȼ. ɍɫɬɚɧɨɜɢɬɟ ɫɨɨɬɜɟɬɫɬɜɢɟ ɦɟɠɞɭ ɫɯɟɦɚɦɢ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɦɚɤɫɢɦɭɦɨɜ ɢ ɩɟɪɢɨɞɚɦɢ ɢɫɩɨɥɶɡɭɟɦɵɯ ɞɢɮɪɚɤɰɢɨɧɧɵɯ ɪɟɲɺɬɨɤ. Ⱥ) Ⱥ Ȼ) Ȼ ɉȿɊɂɈȾ ȾɂɎɊȺɄɐɂɈɇɇɈɃ ɊȿɒȬɌɄɂ 1) 4d 0 2) d0 4 3) 2d 0 4) 2 d 0 3 Ɉɬɜɟɬ: © ɋɬɚɬȽɪɚɞ 2013 ɝ Ⱥ Ȼ 5) 2 d 0 5 2) –1 3) 2 4) 4 A23 ɉɨɪɲɟɧɶ ɦɨɠɟɬ ɫɜɨɛɨɞɧɨ ɛɟɡ ɬɪɟɧɢɹ ɩɟɪɟɦɟɳɚɬɶɫɹ ɜɞɨɥɶ ɫɬɟɧɨɤ ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɢɱɟɫɤɨɝɨ ɫɨɫɭɞɚ. ȼ ɨɛɴɺɦɟ, ɨɝɪɚɧɢɱɟɧɧɨɦ ɞɧɨɦ ɫɨɫɭɞɚ ɢ ɩɨɪɲɧɟɦ, ɧɚɯɨɞɢɬɫɹ ɜɨɡɞɭɯ ɫɦ. ɪɢɫɭɧɨɤ). ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɫɨɫɭɞɚ ɪɚɜɧɚ 20 ɫɦ2, ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɞɧɚ ɫɨɫɭɞɚ ɞɨ ɩɨɪɲɧɹ ɪɚɜɧɨ 25 ɫɦ, ɚɬɦɨɫɮɟɪɧɨɟ ɞɚɜɥɟɧɢɟ 100 ɤɉɚ, ɞɚɜɥɟɧɢɟ ɜɨɡɞɭɯɚ ɜ ɫɨɫɭɞɟ ɪɚɜɧɨ ɚɬɦɨɫɮɟɪɧɨɦɭ. ɉɨɪɲɟɧɶ ɦɟɞɥɟɧɧɨ ɩɟɪɟɦɟɳɚɸɬ ɧɚ 5 ɫɦ ɜɥɟɜɨ, ɩɪɢ ɷɬɨɦ ɬɟɦɩɟɪɚɬɭɪɚ ɜɨɡɞɭɯɚ ɧɟ ɦɟɧɹɟɬɫɹ. Ʉɚɤɭɸ ɫɢɥɭ ɬɪɟɛɭɟɬɫɹ ɩɪɢɥɨɠɢɬɶ, ɱɬɨɛɵ ɭɞɟɪɠɚɬɶ ɩɨɪɲɟɧɶ ɜ ɬɚɤɨɦ ɩɨɥɨɠɟɧɢɢ? 1) 41,7 ɇ ɋɏȿɆȺ ȾɂɎɊȺɄɐɂɈɇɇɕɏ ɆȺɄɋɂɆɍɆɈȼ 14 2) 50,0 ɇ 3) 208,3 ɇ 4) 312,5 ɇ A24 Ⱦɜɟ ɬɨɧɤɢɟ ɜɟɪɬɢɤɚɥɶɧɵɟ ɦɟɬɚɥɥɢɱɟɫɤɢɟ ɩɥɚɫɬɢɧɵ ɪɚɫɩɨɥɨɠɟɧɵ ɩɚɪɚɥɥɟɥɶɧɨ ɞɪɭɝ ɞɪɭɝɭ, ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɧɢɦɢ ɪɚɜɧɨ 2 ɫɦ. ɉɥɨɳɚɞɶ ɩɨɩɟɪɟɱɧɨɝɨ ɫɟɱɟɧɢɹ ɤɚɠɞɨɣ ɢɡ ɩɥɚɫɬɢɧ ɪɚɜɧɚ 15 000 ɫɦ2. Ʌɟɜɚɹ ɩɥɚɫɬɢɧɚ ɢɦɟɟɬ ɡɚɪɹɞ q = 5 ɩɄɥ, ɡɚɪɹɞ ɜɬɨɪɨɣ ɩɥɚɫɬɢɧɵ –q. Ɇɨɞɭɥɶ ɧɚɩɪɹɠɺɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɦɟɠɞɭ ɩɥɚɫɬɢɧɚɦɢ ɧɚ ɪɚɫɫɬɨɹɧɢɢ 0,5 ɫɦ ɨɬ ɩɪɚɜɨɣ ɩɥɚɫɬɢɧɵ ɪɚɜɟɧ 1) 0 ȼ/ɦ 2) § 0,19 ȼ/ɦ 3) § 0,75 ȼ/ɦ 4) § 0,38 ȼ/ɦ A25 ɗɥɟɤɬɪɨɧ ɞɜɢɠɟɬɫɹ ɩɨ ɨɤɪɭɠɧɨɫɬɢ ɜ ɨɞɧɨɪɨɞɧɨɦ ɦɚɝɧɢɬɧɨɦ ɫ ɢɧɞɭɤɰɢɟɣ 6 ɦɤɌɥ. ɍɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɷɥɟɤɬɪɨɧɚ ɪɚɜɧɚ 1) § 1,1 ɪɚɞɫ 3) | 9, 4 107 ɪɚɞɫ 2) 3,7 · 105 ɪɚɞɫ 4) | 1, 05 106 ɪɚɞɫ ɇɟ ɡɚɛɭɞɶɬɟ ɩɟɪɟɧɟɫɬɢ ɜɫɟ ɨɬɜɟɬɵ ɜ ɛɥɚɧɤ ɨɬɜɟɬɨɜ ʋ 1. © ɋɬɚɬȽɪɚɞ 2013 ɝ ɩɨɥɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 15 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 16 ɉɨɥɧɨɟ ɪɟɲɟɧɢɟ ɡɚɞɚɱ ɋ1–ɋ6 ɧɟɨɛɯɨɞɢɦɨ ɡɚɩɢɫɚɬɶ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2. ɉɪɢ ɨɮɨɪɦɥɟɧɢɢ ɪɟɲɟɧɢɹ ɜ ɛɥɚɧɤɟ ɨɬɜɟɬɨɜ ʋ 2 ɡɚɩɢɲɢɬɟ ɫɧɚɱɚɥɚ ɧɨɦɟɪ ɡɚɞɚɧɢɹ ɋ1, ɋ2 ɢ ɬ. ɞ.), ɚ ɡɚɬɟɦ ɪɟɲɟɧɢɟ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɡɚɞɚɱɢ. Ɉɬɜɟɬɵ ɡɚɩɢɫɵɜɚɣɬɟ ɱɺɬɤɨ ɢ ɪɚɡɛɨɪɱɢɜɨ. C5 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 48 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 2 ɪɚɡɚ. Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ ɨɪɝɚɧɚ ɞɥɢɧɵ ɛɨɥɶɲɢɟ, ɚ ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. C6 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. C1 ɉɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ ɤɚɠɞɨɣ ɢɡ ɡɚɞɚɱ ɋ2–ɋ6 ɞɨɥɠɧɨ ɫɨɞɟɪɠɚɬɶ ɡɚɤɨɧɵ ɢ ɮɨɪɦɭɥɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɢ ɞɨɫɬɚɬɨɱɧɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɚ ɬɚɤɠɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ, ɪɚɫɱɺɬɵ ɫ ɱɢɫɥɟɧɧɵɦ ɨɬɜɟɬɨɦ ɢ ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɪɢɫɭɧɨɤ, ɩɨɹɫɧɹɸɳɢɣ ɪɟɲɟɧɢɟ. C2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ȼɟɧɟɪɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 243 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ ȼɟɧɟɪɵ ɫɨɫɬɚɜɥɹɟɬ 0,82 ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ ȼɟɧɟɪɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. C3 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 280 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ ɝɞɟ h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ . ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ Ȝ § l, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɪɚɜɧɚ n = 2,7 · 1025 ɦ–3 ? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 4. C4 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,9 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 20 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 19 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? © ɋɬɚɬȽɪɚɞ 2013 ɝ h , mv © ɋɬɚɬȽɪɚɞ 2013 ɝ Физика. 11 класс. Вариант ФИ1601 Физика. 11 класс. Вариант ФИ1602 Ответы к заданиям с выбором ответа Ответы к заданиям с выбором ответа № задания А1 А2 А3 А4 А5 А6 А7 А8 А9 А10 А11 А12 А13 Ответ 3 4 3 4 4 1 1 1 3 4 3 4 3 № задания А14 А15 А16 А17 А18 А19 А20 А21 А22 А23 А24 А25 Ответ 1 1 2 2 3 2 2 3 2 2 4 1 № задания А1 А2 А3 А4 А5 А6 А7 А8 А9 А10 А11 А12 А13 Ответы к заданиям с кратким ответом № задания В1 В2 © СтатГрад 2013 г. Ответ 221 132 № задания В3 В4 Ответ 1 1 1 1 3 3 4 2 2 1 2 4 2 № задания А14 А15 А16 А17 А18 А19 А20 А21 А22 А23 А24 А25 Ответ 4 3 3 1 4 3 3 2 2 1 4 4 Ответы к заданиям с кратким ответом Ответ 54 43 № задания В1 В2 © СтатГрад 2013 г. Ответ 112 231 № задания В3 В4 Ответ 31 53 Физика. 11 класс. Вариант ФИ1603 Физика. 11 класс. Вариант ФИ1604 Ответы к заданиям с выбором ответа Ответы к заданиям с выбором ответа № задания А1 А2 А3 А4 А5 А6 А7 А8 А9 А10 А11 А12 А13 Ответ 3 1 3 4 4 1 1 1 2 4 3 4 3 № задания А14 А15 А16 А17 А18 А19 А20 А21 А22 А23 А24 А25 Ответ 1 1 2 2 3 2 3 2 2 1 4 1 № задания А1 А2 А3 А4 А5 А6 А7 А8 А9 А10 А11 А12 А13 Ответы к заданиям с кратким ответом № задания В1 В2 © СтатГрад 2013 г. Ответ 221 231 № задания В3 В4 Ответ 1 4 1 1 3 3 4 2 3 1 2 4 2 № задания А14 А15 А16 А17 А18 А19 А20 А21 А22 А23 А24 А25 Ответ 4 3 3 1 4 3 2 3 2 2 4 4 Ответы к заданиям с кратким ответом Ответ 54 53 № задания В1 В2 © СтатГрад 2013 г. Ответ 112 132 № задания В3 В4 Ответ 31 43 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 1 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ C1 Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ ɨɪɝɚɧɚ ɞɥɢɧɵ ɛɨɥɶɲɢɟ, ɚ ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ 1. Ƚɪɨɦɤɢɣ ɡɜɭɤ ɛɵɜɚɟɬ, ɤɨɝɞɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɨɪɝɚɧɧɨɣ ɬɪɭɛɵ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɭɱɧɨɫɬɶ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɭɱɧɨɫɬɢ ɤɨɥɟɛɚɧɢɹ ɜɨɡɞɭɯɚ ɩɪɨɢɫɯɨɞɹɬ ɫ ɦɚɤɫɢɦɚɥɶɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɚ ɚɦɩɥɢɬɭɞɚ ɨɩɪɟɞɟɥɹɟɬ ɝɪɨɦɤɨɫɬɶ ɡɜɭɤɚ. 2. ɉɨɫɤɨɥɶɤɭ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ, ɬɨ ɩɭɱɧɨɫɬɶ ɬɚɤɠɟ ɞɨɥɠɧɚ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɢ ɧɚ ɜɯɨɞɟ ɬɪɭɛɵ. 3. ɉɨɷɬɨɦɭ ɞɥɹ ɧɚɢɛɨɥɟɟ ɝɪɨɦɤɨɝɨ ɡɜɭɱɚɧɢɹ ɦɢɧɢɦɚɥɶɧɚɹ ɞɥɢɧɚ ɬɪɭɛɵ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ ɞɥɢɧɵ ɜɨɥɧɵ – ɩɪɢ ɷɬɨɦ ɩɨɫɟɪɟɞɢɧɟ ɬɪɭɛɵ ɧɚɯɨɞɢɬɫɹ ɭɡɟɥ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɚ ɧɚ ɟɺ ɤɨɧɰɚɯ – ɞɜɟ ɩɭɱɧɨɫɬɢ. 4. Ɂɜɭɤɢ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ Ȟ (ɛɚɫɵ) ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɛɨɥɶɲɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɚ ɜɵɫɨɤɨɣ c ɱɚɫɬɨɬɵ – ɦɚɥɟɧɶɤɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɩɨɫɤɨɥɶɤɭ ɞɥɢɧɚ ɜɨɥɧɵ Ȝ , ɚ ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ c Ȟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɟɝɨ ɱɚɫɬɨɬɵ. 5. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɡɦɟɪɵ ɬɪɭɛɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɞɥɢɧɟ ɜɨɥɧɵ ɡɜɭɤɚ: ɱɟɦ ɱɚɫɬɨɬɚ ɡɜɭɤɚ ɧɢɠɟ, ɬɟɦ ɞɥɢɧɚ ɬɪɭɛɵ ɛɨɥɶɲɟ, ɢ ɧɚɨɛɨɪɨɬ. Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩ. 1–5) ɢ ɢɫɱɟɪɩɵɜɚɸɳɢɟ ɜɟɪɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɫ ɭɤɚɡɚɧɢɟɦ ɧɚɛɥɸɞɚɟɦɵɯ ɹɜɥɟɧɢɣ ɢ ɡɚɤɨɧɨɜ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɫɬɚɧɨɜɥɟɧɢɟ ɫɬɨɹɱɟɣ 3 ɜɨɥɧɵ ɜ ɨɪɝɚɧɧɨɣ ɬɪɭɛɟ, ɫɜɹɡɶ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɜɨɡɞɭɯɚ ɫ ɝɪɨɦɤɨɫɬɶɸ ɡɜɭɤɚ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɵ ɞɥɹ ɫɜɹɡɢ ɞɥɢɧɵ ɜɨɥɧɵ ɢ ɱɚɫɬɨɬɵ ɡɜɭɤɚ). ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɢ ɞɚɧɨ ɩɪɚɜɢɥɶɧɨɟ ɨɛɴɹɫɧɟɧɢɟ, ɧɨ ɫɨɞɟɪɠɢɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɡɚɩɢɫɹɯ ɫɨɞɟɪɠɚɬɫɹ ɥɢɲɶ ɨɛɳɢɟ ɪɚɫɫɭɠɞɟɧɢɹ ɛɟɡ 2 ɩɪɢɜɹɡɤɢ ɤ ɤɨɧɤɪɟɬɧɨɣ ɫɢɬɭɚɰɢɢ ɡɚɞɚɱɢ. ɂɅɂ Ɋɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɨɬɜɟɬɭ, ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ, ɢɥɢ ɜ ɧɢɯ ɫɨɞɟɪɠɚɬɫɹ ɥɨɝɢɱɟɫɤɢɟ ɧɟɞɨɱɺɬɵ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɍɤɚɡɚɧɵ ɧɟ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɧɨ ɜ ɧɟɤɨɬɨɪɵɯ ɢɡ ɧɢɯ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ 1 ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɩɨɥɭɱɟɧɢɟ ɨɬɜɟɬɚ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ, ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɟɪɧɨɦɭ ɨɬɜɟɬɭ, ɫɨɞɟɪɠɚɬ ɨɲɢɛɤɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 C2 2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ȼɟɧɟɪɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 243 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ ȼɟɧɟɪɵ ɫɨɫɬɚɜɥɹɟɬ 0,82 ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ ȼɟɧɟɪɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɉɪɢ ɞɜɢɠɟɧɢɢ ɫɩɭɬɧɢɤɚ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ R ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɫɢɥɨɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ GmM ɫɩɭɬɧɢɤɚ ɤ ɩɥɚɧɟɬɟ: PȦ 2R , ɝɞɟ m ɢ M – ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɢ ɩɥɚɧɟɬɵ, G – R2 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɚ Ȧ – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ. Ⱦɥɹ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɩɭɬɧɢɤɚ Ȧ 2ʌ , ɝɞɟ T = 1 ɫɭɬɤɢ. T ɂɡ ɡɚɩɢɫɚɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɣ ɨɪɛɢɬɵ ɞɥɹ Ɂɟɦɥɢ § G M 3 2· 3 T , ɚ ɞɥɹ ȼɟɧɟɪɵ ¨ © 4ʌ 2 ¹̧ 1 ɪɚɜɟɧ R3 § G 0, 82MɁ ·3 (243T ) 2 ¨ 2 4ʌ © ¹̧ RɁ 0,82 2432 3 1 Rȼ ( ) 1 § 1 531 000 ɤɦ. Ɉɬɜɟɬ: Rȼ RɁ 0,82 2432 3 | 1 531 000 ɤɦ. © ɋɬɚɬȽɪɚɞ 2013 ɝ ( ) 1 42 000 0,82 2432 3 ɤɦ | ( ) 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – 2-ɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ ɞɥɹ ɤɪɭɝɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ, ɡɚɤɨɧ ɜɫɟɦɢɪɧɨɝɨ ɬɹɝɨɬɟɧɢɹ ɢ ɭɫɥɨɜɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɫɩɭɬɧɢɤɚ ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɥɚɧɟɬɵ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɜɫɟɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 C3 4 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 300 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 2. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɞɥɹ 1 ɦɨɥɹ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2: p0V0 RT0, n p0V2 RT0, ɝɞɟ V 0 ɢ V 2 – ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2 ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ V0 RT0 ɬɟɦɩɟɪɚɬɭɪɟ T0. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ 2 ɪɚɜɟɧ V2 . n n p0 ɉɪɨɰɟɫɫ 2–3 – ɢɡɨɛɚɪɢɱɟɫɤɢɣ ɩɪɢ ɞɚɜɥɟɧɢɢ n p0, ɬɚɤ ɱɬɨ ɪɚɛɨɬɚ ɝɚɡɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ A n p0 V3 V2 , ɩɪɢɱɺɦ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ Ʉɥɚɩɟɣɪɨɧɚ–Ɇɟɧɞɟɥɟɟɜɚ R kT0 n p0V3 R kT0, ɨɬɤɭɞɚ V3 . n p0 ( ) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɛɨɬɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ A § R kT0 RT0 · n p0¨ ¸ ¨ np n p0 ¸¹ 0 © Ɉɬɜɟɬ: A (k 1)RT0 © ɋɬɚɬȽɪɚɞ 2013 ɝ § · ¨k 1¸RT0 ¨ ¸ © ¹ 2490 Ⱦɠ. § · ¨2 1¸ 8, 3 300 ¨ ¸ © ¹ 2490 Ⱦɠ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɪɚɜɧɟɧɢɟ ɄɥɚɩɟɣɪɨɧɚɆɟɧɞɟɥɟɟɜɚ ɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɪɚɛɨɬɵ ɝɚɡɚ ɩɪɢ ɢɡɨɛɚɪɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 C4 6 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,9 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 20 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 19 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ȼɨɥɶɬɦɟɬɪ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨɤɚɡɵɜɚɟɬ ɩɨɫɬɨɹɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɢɫɬɨɱɧɢɤɚ, ɪɚɜɧɨɟ U1 = 20 ȼ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, ɫɭɦɦɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɦɩɟɪɦɟɬɪɟ ɢ ɩɨɤɚɡɚɧɢɣ ɜɨɥɶɬɦɟɬɪɚ: U1 = UȺ + U2 , ɨɬɤɭɞɚ UȺ = U1 – U2 = 1 ȼ, ɢ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɚɦɩɟɪɦɟɬɪɚ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ ɬɟɱɺɬ ɬɨɤ I2 = 1 Ⱥ, ɪɚɜɧɨ RA = U1 U2 = 1 Ɉɦ. I2 ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, U1 = I1 U 20 (RA + R), ɨɬɤɭɞɚ R = 1 RȺ= 1–1 § 21,2 Ɉɦ. I1 0, 9 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɬɨɤ I2 ɪɚɡɜɟɬɜɥɹɟɬɫɹ ɜ ɬɨɱɤɟ 2 ɧɚ ɞɜɚ ɬɨɤɚ – ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɢ ɱɟɪɟɡ ɪɟɡɢɫɬɨɪ, ɪɚɜɧɵɟ ɜ ɫɭɦɦɟ ɬɨɤɭ I2 ɩɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɨɷɬɨɦɭ ɬɨɤ ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɪɚɜɟɧ Iȼ = I2 – Rȼ = U2 § 0,105 A, ɬɚɤ ɱɬɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɪɚɜɧɨ R U2 § 181,5 Ɉɦ. Iȼ ɉɨɞɫɬɚɜɥɹɹ ɜɫɟ ɡɚɩɢɫɚɧɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨɥɭɱɚɟɦ Rȼ U2ª¬U1(I2 I1) U2I1º¼ 181, 45. RȺ U1(U1 U2)(I2 I1) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɩɪɢɦɟɪɧɨ ɜ 181,5 ɪɚɡ. U2ª¬U1(I2 I1) U2I1º¼ R 181, 45, ɬɨ ɟɫɬɶ ɩɪɢɦɟɪɧɨ ɜ 181,5 ɪɚɡɚ. Ɉɬɜɟɬ: ȼ U1(U1 U2)(I2 I1) RȺ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, ɢ ɫɜɹɡɶ ɫɢɥ ɬɨɤɚ ɜ ɪɚɡɜɟɬɜɥɺɧɧɨɣ ɰɟɩɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 7 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 C5 8 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 60 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 3 ɪɚɡɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɚɞɨ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɚ ɫɥɭɱɚɹ: ɤɨɝɞɚ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ ɢ ɤɨɝɞɚ ɨɧɚ ɪɚɫɫɟɢɜɚɸɳɚɹ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɟɞɦɟɬɚ ɦɨɠɟɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧɧɵɦ, ɬɨɥɶɤɨ ɟɫɥɢ ɨɧɨ 1 1 1 ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ (ɢ ɩɟɪɟɜɺɪɧɭɬɨɟ). ɉɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ ɡɚɩɢɫɵɜɚɟɦ: , a b F a ɚ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɢɡɨɛɪɚɠɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɪɟɞɦɟɬɨɦ ɢɦɟɟɦ: n, b n1 a 1 ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɥɢɧɡɵ ɞɨ ɢɡɨɛɪɚɠɟɧɢɹ. Ɉɬɫɸɞɚ b , ɢ a n F a 60 F ɫɦ = 15 ɫɦ. 4 n1 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɦɧɢɦɨɟ, ɩɪɹɦɨɟ, ɢ ɩɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ 1 1 1 , ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɦɧɢɦɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɟɞɦɟɬɚ ɞɨ ɪɚɫɫɟɢɜɚɸɳɟɣ a b F 1 1n a n, ɥɢɧɡɵ. ɉɪɢ ɷɬɨɦ ɩɨɩɪɟɠɧɟɦɭ ɢ ɩɨɥɭɱɚɟɦ: , F a b a 60 F ɫɦ 30 ɫɦ. 2 1n Ɉɬɜɟɬ: ɟɫɥɢ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ, ɬɨ F = 15 ɫɦ, ɚ ɟɫɥɢ ɪɚɫɫɟɢɜɚɸɳɚɹ, ɬɨ F = –30 ɫɦ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɬɨɧɤɨɣ ɥɢɧɡɵ ɢ ɮɨɪɦɭɥɚ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ, ɞɚɜɚɟɦɨɝɨ ɥɢɧɡɨɣ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 10 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. C6 Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ h , mv ɝɞɟ h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ Ȝ § l, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɪɚɜɧɚ n = 2,7 · 1025 ɦ–3 ? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɋɨɝɥɚɫɧɨ ɨɫɧɨɜɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɦɨɥɟɤɭɥɹɪɧɨ-ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ 3kT ɢ ɨɩɪɟɞɟɥɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ, ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ v , m ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ Ȝ= h = mv h . 3kTm ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɩɪɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ n ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, l=n 3 , 1 T h 2 23 n 3km Ɉɬɜɟɬ: T ɩɨɷɬɨɦɭ ɫɨɨɬɧɨɲɟɧɢɟ l§Ȝ 6, 62 1068 2 , 7 10 3 1,38 1023 6 , 6 1027 ( h2 23 n | 0, 14 Ʉ . 3km © ɋɬɚɬȽɪɚɞ 2013 ɝ ɜɵɩɨɥɧɹɟɬɫɹ 2 25 3 ) Ʉ | 0, 14 Ʉ . ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1601 11 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɦɨɥɟɤɭɥ ɝɚɡɚ, ɮɨɪɦɭɥɚ ɞɥɹ ɞɥɢɧɵ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɜ ɝɚɡɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ; ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 1 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɞɥɢɧɵ ɨɪɝɚɧɧɵɯ ɬɪɭɛ ɪɚɡɧɵɟ: ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ, ɚ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ – ɛɨɥɶɲɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ 1. Ƚɪɨɦɤɢɣ ɡɜɭɤ ɛɵɜɚɟɬ, ɤɨɝɞɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɨɪɝɚɧɧɨɣ ɬɪɭɛɵ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɭɱɧɨɫɬɶ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɭɱɧɨɫɬɢ ɤɨɥɟɛɚɧɢɹ ɜɨɡɞɭɯɚ ɩɪɨɢɫɯɨɞɹɬ ɫ ɦɚɤɫɢɦɚɥɶɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɚ ɚɦɩɥɢɬɭɞɚ ɨɩɪɟɞɟɥɹɟɬ ɝɪɨɦɤɨɫɬɶ ɡɜɭɤɚ. 2. ɉɨɫɤɨɥɶɤɭ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ, ɬɨ ɩɭɱɧɨɫɬɶ ɬɚɤɠɟ ɞɨɥɠɧɚ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɢ ɧɚ ɜɯɨɞɟ ɬɪɭɛɵ. 3. ɉɨɷɬɨɦɭ ɞɥɹ ɧɚɢɛɨɥɟɟ ɝɪɨɦɤɨɝɨ ɡɜɭɱɚɧɢɹ ɦɢɧɢɦɚɥɶɧɚɹ ɞɥɢɧɚ ɬɪɭɛɵ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ ɞɥɢɧɵ ɜɨɥɧɵ – ɩɪɢ ɷɬɨɦ ɩɨɫɟɪɟɞɢɧɟ ɬɪɭɛɵ ɧɚɯɨɞɢɬɫɹ ɭɡɟɥ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɚ ɧɚ ɟɟ ɤɨɧɰɚɯ – ɞɜɟ ɩɭɱɧɨɫɬɢ. 4. Ɂɜɭɤɢ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ Ȟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɦɚɥɟɧɶɤɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɚ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ c – ɛɨɥɶɲɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɩɨɫɤɨɥɶɤɭ ɞɥɢɧɚ ɜɨɥɧɵ Ȝ , ɚ ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ c ɧɟ ɡɚɜɢɫɢɬ Ȟ ɨɬ ɟɝɨ ɱɚɫɬɨɬɵ. 5. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɡɦɟɪɵ ɬɪɭɛɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɞɥɢɧɟ ɜɨɥɧɵ ɡɜɭɤɚ: ɱɟɦ ɱɚɫɬɨɬɚ ɡɜɭɤɚ ɜɵɲɟ, ɬɟɦ ɞɥɢɧɚ ɬɪɭɛɵ ɦɟɧɶɲɟ, ɢ ɧɚɨɛɨɪɨɬ. Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩ. 1–5) ɢ ɢɫɱɟɪɩɵɜɚɸɳɢɟ ɜɟɪɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɫ ɭɤɚɡɚɧɢɟɦ ɧɚɛɥɸɞɚɟɦɵɯ ɹɜɥɟɧɢɣ ɢ ɡɚɤɨɧɨɜ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɫɬɚɧɨɜɥɟɧɢɟ ɫɬɨɹɱɟɣ 3 ɜɨɥɧɵ ɜ ɨɪɝɚɧɧɨɣ ɬɪɭɛɟ, ɫɜɹɡɶ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɜɨɡɞɭɯɚ ɫ ɝɪɨɦɤɨɫɬɶɸ ɡɜɭɤɚ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɵ ɞɥɹ ɫɜɹɡɢ ɞɥɢɧɵ ɜɨɥɧɵ ɢ ɱɚɫɬɨɬɵ ɡɜɭɤɚ). ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɢ ɞɚɧɨ ɩɪɚɜɢɥɶɧɨɟ ɨɛɴɹɫɧɟɧɢɟ, ɧɨ ɫɨɞɟɪɠɢɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɡɚɩɢɫɹɯ ɫɨɞɟɪɠɚɬɫɹ ɥɢɲɶ ɨɛɳɢɟ ɪɚɫɫɭɠɞɟɧɢɹ ɛɟɡ 2 ɩɪɢɜɹɡɤɢ ɤ ɤɨɧɤɪɟɬɧɨɣ ɫɢɬɭɚɰɢɢ ɡɚɞɚɱɢ. C1 ɂɅɂ Ɋɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɨɬɜɟɬɭ, ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ, ɢɥɢ ɜ ɧɢɯ ɫɨɞɟɪɠɚɬɫɹ ɥɨɝɢɱɟɫɤɢɟ ɧɟɞɨɱɺɬɵ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɍɤɚɡɚɧɵ ɧɟ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɧɨ ɜ ɧɟɤɨɬɨɪɵɯ ɢɡ ɧɢɯ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɩɨɥɭɱɟɧɢɟ ɨɬɜɟɬɚ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ, ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɟɪɧɨɦɭ ɨɬɜɟɬɭ, ɫɨɞɟɪɠɚɬ ɨɲɢɛɤɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 1 0 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C2 2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ Ʌɭɧɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 1 28 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ Ʌɭɧɵ ɫɨɫɬɚɜɥɹɟɬ ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ 81 ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ Ʌɭɧɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɉɪɢ ɞɜɢɠɟɧɢɢ ɫɩɭɬɧɢɤɚ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ R ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɫɢɥɨɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ GmM ɫɩɭɬɧɢɤɚ ɤ ɩɥɚɧɟɬɟ: mȦ2R , ɝɞɟ m ɢ M – ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɢ ɩɥɚɧɟɬɵ, G – R2 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɚ Ȧ – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ. 2ʌ Ⱦɥɹ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɩɭɬɧɢɤɚ Ȧ , ɝɞɟ T = 1 ɫɭɬɤɢ. T ɂɡ ɡɚɩɢɫɚɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɣ ɨɪɛɢɬɵ ɞɥɹ Ɂɟɦɥɢ § GMɁ 2· 3 T , ɚ ɞɥɹ Ʌɭɧɵ ¨ © 4ʌ 2 ¹̧ 1 ɪɚɜɟɧ RɁ § G MɁ ·3 (28T ) 2 ¨ 2 © 4ʌ 81 ¹̧ 1 RɅ § 282 · 3 RɁ¨ © 81 ¹̧ 1 Ɉɬɜɟɬ: RɅ © ɋɬɚɬȽɪɚɞ 2013 ɝ § 282 · 3 RɁ¨ © 81 ¹̧ 1 § 282 · 3 42 000 ¨ ɤɦ | 89 500 ɤɦ. © 81 ¹̧ 1 § 282 · 3 42 000 ¨ ɤɦ | 89 500 ɤɦ. © 81 ¹̧ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – 2-ɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ ɞɥɹ ɤɪɭɝɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ, ɡɚɤɨɧ ɜɫɟɦɢɪɧɨɝɨ ɬɹɝɨɬɟɧɢɹ ɢ ɭɫɥɨɜɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɫɩɭɬɧɢɤɚ ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɥɚɧɟɬɵ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɜɫɟɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɩɨɥɧɨɦ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C3 4 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 280 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 4. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɞɥɹ 1 ɦɨɥɹ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2: p0V0 RT0, n p0V2 RT0, ɝɞɟ V 0 ɢ V 2 – ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2 ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ V0 RT0 ɬɟɦɩɟɪɚɬɭɪɟ T0. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ 2 ɪɚɜɟɧ V2 . n n p0 ɉɪɨɰɟɫɫ 2–3 – ɢɡɨɛɚɪɢɱɟɫɤɢɣ ɩɪɢ ɞɚɜɥɟɧɢɢ n p0, ɬɚɤ ɱɬɨ ɪɚɛɨɬɚ ɝɚɡɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ n p0V3 A A n p0 V3 V2 , ( R kT0, ɨɬɤɭɞɚ § R kT0 RT0 · n p0¨ ¸ ¨ np n p0 ¸¹ 0 © Ɉɬɜɟɬ: A (k 1)RT0 © ɋɬɚɬȽɪɚɞ 2013 ɝ ) ɩɪɢɱɺɦ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ Ʉɥɚɩɟɣɪɨɧɚ–Ɇɟɧɞɟɥɟɟɜɚ R kT0 V3 . Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɛɨɬɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ n p0 § · § · ¨k 1¸RT0 ¨4 1¸ 8, 3 280 6972 Ⱦɠ. ¨ ¨ ¸ ¸ © © ¹ ¹ 6972 Ⱦɠ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɪɚɛɨɬɵ ɝɚɡɚ ɩɪɢ ɢɡɨɛɚɪɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C4 6 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,95 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 12 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 11,9 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ȼɨɥɶɬɦɟɬɪ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨɤɚɡɵɜɚɟɬ ɩɨɫɬɨɹɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɢɫɬɨɱɧɢɤɚ, ɪɚɜɧɨɟ U1 = 20 ȼ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, ɫɭɦɦɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɦɩɟɪɦɟɬɪɟ ɢ ɩɨɤɚɡɚɧɢɣ ɜɨɥɶɬɦɟɬɪɚ: U1 = UȺ + U2 , ɨɬɤɭɞɚ UȺ = U1 – U2 = 0,1 ȼ, ɢ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɚɦɩɟɪɦɟɬɪɚ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ U U2 ɬɟɱɺɬ ɬɨɤ I2 = 1 Ⱥ, ɪɚɜɧɨ RA = 1 = 0,1 Ɉɦ. I2 ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, U1 = I1(RA + R), ɨɬɤɭɞɚ R = U1 12 – RA = – 0,1 § 12,5 Ɉɦ. I1 0, 95 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɬɨɤ I2 ɪɚɡɜɟɬɜɥɹɟɬɫɹ ɜ ɬɨɱɤɟ 2 ɧɚ ɞɜɚ ɬɨɤɚ – ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɢ ɱɟɪɟɡ ɪɟɡɢɫɬɨɪ, ɪɚɜɧɵɟ ɜ ɫɭɦɦɟ ɬɨɤɭ I2 ɩɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɨɷɬɨɦɭ ɬɨɤ ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɪɚɜɟɧ Iȼ = I2 – Rȼ = U2 § 0,0504 A, ɬɚɤ ɱɬɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɪɚɜɧɨ R U2 § 236,12 Ɉɦ. Iȼ ɉɨɞɫɬɚɜɥɹɹ ɜɫɟ ɡɚɩɢɫɚɧɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨɥɭɱɚɟɦ ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɱɢɫɥɟɧɧɵɯ U2ª¬U1(I2 I1) U2I1º¼ R | 2361, 2. ɡɧɚɱɟɧɢɣ: ȼ RȺ U1(U1 U2)(I2 I1) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɩɪɢɦɟɪɧɨ ɜ 2360 ɪɚɡ. R Ɉɬɜɟɬ: ȼ RȺ U2ª¬U1(I2 I1) U2I1º¼ © ɋɬɚɬȽɪɚɞ 2013 ɝ U1(U1 U2)(I2 I1) | 2360 ɪɚɡ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, ɢ ɫɜɹɡɶ ɫɢɥ ɬɨɤɚ ɜ ɪɚɡɜɟɬɜɥɺɧɧɨɣ ɰɟɩɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 7 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C5 8 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 48 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 2 ɪɚɡɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɚɞɨ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɚ ɫɥɭɱɚɹ: ɤɨɝɞɚ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ ɢ ɤɨɝɞɚ ɨɧɚ ɪɚɫɫɟɢɜɚɸɳɚɹ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɟɞɦɟɬɚ ɦɨɠɟɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧɧɵɦ, ɬɨɥɶɤɨ ɟɫɥɢ ɨɧɨ 1 1 1 ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ (ɢ ɩɟɪɟɜɺɪɧɭɬɨɟ). ɉɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ ɡɚɩɢɫɵɜɚɟɦ: , a b F a ɚ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɢɡɨɛɪɚɠɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɪɟɞɦɟɬɨɦ ɢɦɟɟɦ: n, b a 1 n1 ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɥɢɧɡɵ ɞɨ ɢɡɨɛɪɚɠɟɧɢɹ. Ɉɬɫɸɞɚ b , ɢ n F a a 48 F ɫɦ = 16 ɫɦ. n1 3 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɦɧɢɦɨɟ, ɩɪɹɦɨɟ, ɢ ɩɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ 1 1 1 , ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɦɧɢɦɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɟɞɦɟɬɚ ɞɨ ɪɚɫɫɟɢɜɚɸɳɟɣ a b F a 1 1n n, ɥɢɧɡɵ. ɉɪɢ ɷɬɨɦ ɩɨɩɪɟɠɧɟɦɭ ɢ ɩɨɥɭɱɚɟɦ: , b F a a 48 F ɫɦ 48 ɫɦ. 1 1n Ɉɬɜɟɬ: ɟɫɥɢ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ, ɬɨ F = 16 ɫɦ, ɚ ɟɫɥɢ ɪɚɫɫɟɢɜɚɸɳɚɹ, ɬɨ F = –48 ɫɦ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɬɨɧɤɨɣ ɥɢɧɡɵ ɢ ɮɨɪɦɭɥɚ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ, ɞɚɜɚɟɦɨɝɨ ɥɢɧɡɨɣ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 C6 10 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. h Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ = , mv ɝɞɟ h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ l § 5Ȝ, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɪɚɜɧɚ n = 1,3 · 1025 ɦ–3? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɋɨɝɥɚɫɧɨ ɨɫɧɨɜɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɦɨɥɟɤɭɥɹɪɧɨ-ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ 3kT ɢ ɨɩɪɟɞɟɥɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ, ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ v , m ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ h h Ȝ= = . 3kTm mv ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɩɪɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ n ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, l= T n 3, 1 25 h2 23 n 3km Ɉɬɜɟɬ: T ɩɨɷɬɨɦɭ ɫɨɨɬɧɨɲɟɧɢɟ l § 5Ȝ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ 2 25 6, 62 1068 25 3 1 , 3 10 K | 2, 15Ʉ. 3 1,38 1023 6 , 6 1027 25 h2 23 n | 2, 15 Ʉ . 3km © ɋɬɚɬȽɪɚɞ 2013 ɝ ( ) ɬɟɦɩɟɪɚɬɭɪɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1602 11 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɦɨɥɟɤɭɥ ɝɚɡɚ, ɮɨɪɦɭɥɚ ɞɥɹ ɞɥɢɧɵ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɜ ɝɚɡɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ; ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɞɥɢɧɵ ɨɪɝɚɧɧɵɯ ɬɪɭɛ ɪɚɡɧɵɟ: ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ, ɚ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ – ɛɨɥɶɲɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ 1. Ƚɪɨɦɤɢɣ ɡɜɭɤ ɛɵɜɚɟɬ, ɤɨɝɞɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɨɪɝɚɧɧɨɣ ɬɪɭɛɵ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɭɱɧɨɫɬɶ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɭɱɧɨɫɬɢ ɤɨɥɟɛɚɧɢɹ ɜɨɡɞɭɯɚ ɩɪɨɢɫɯɨɞɹɬ ɫ ɦɚɤɫɢɦɚɥɶɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɚ ɚɦɩɥɢɬɭɞɚ ɨɩɪɟɞɟɥɹɟɬ ɝɪɨɦɤɨɫɬɶ ɡɜɭɤɚ. 2. ɉɨɫɤɨɥɶɤɭ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ, ɬɨ ɩɭɱɧɨɫɬɶ ɬɚɤɠɟ ɞɨɥɠɧɚ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɢ ɧɚ ɜɯɨɞɟ ɬɪɭɛɵ. 3. ɉɨɷɬɨɦɭ ɞɥɹ ɧɚɢɛɨɥɟɟ ɝɪɨɦɤɨɝɨ ɡɜɭɱɚɧɢɹ ɦɢɧɢɦɚɥɶɧɚɹ ɞɥɢɧɚ ɬɪɭɛɵ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ ɞɥɢɧɵ ɜɨɥɧɵ – ɩɪɢ ɷɬɨɦ ɩɨɫɟɪɟɞɢɧɟ ɬɪɭɛɵ ɧɚɯɨɞɢɬɫɹ ɭɡɟɥ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɚ ɧɚ ɟɟ ɤɨɧɰɚɯ – ɞɜɟ ɩɭɱɧɨɫɬɢ. 4. Ɂɜɭɤɢ ɜɵɫɨɤɨɣ ɱɚɫɬɨɬɵ Ȟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɦɚɥɟɧɶɤɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɚ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ c – ɛɨɥɶɲɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɩɨɫɤɨɥɶɤɭ ɞɥɢɧɚ ɜɨɥɧɵ Ȝ , ɚ ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ c ɧɟ ɡɚɜɢɫɢɬ Ȟ ɨɬ ɟɝɨ ɱɚɫɬɨɬɵ. 5. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɡɦɟɪɵ ɬɪɭɛɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɞɥɢɧɟ ɜɨɥɧɵ ɡɜɭɤɚ: ɱɟɦ ɱɚɫɬɨɬɚ ɡɜɭɤɚ ɜɵɲɟ, ɬɟɦ ɞɥɢɧɚ ɬɪɭɛɵ ɦɟɧɶɲɟ, ɢ ɧɚɨɛɨɪɨɬ. C1 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩ. 1–5) ɢ ɢɫɱɟɪɩɵɜɚɸɳɢɟ ɜɟɪɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɫ ɭɤɚɡɚɧɢɟɦ ɧɚɛɥɸɞɚɟɦɵɯ ɹɜɥɟɧɢɣ ɢ ɡɚɤɨɧɨɜ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɫɬɚɧɨɜɥɟɧɢɟ ɫɬɨɹɱɟɣ 3 ɜɨɥɧɵ ɜ ɨɪɝɚɧɧɨɣ ɬɪɭɛɟ, ɫɜɹɡɶ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɜɨɡɞɭɯɚ ɫ ɝɪɨɦɤɨɫɬɶɸ ɡɜɭɤɚ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɵ ɞɥɹ ɫɜɹɡɢ ɞɥɢɧɵ ɜɨɥɧɵ ɢ ɱɚɫɬɨɬɵ ɡɜɭɤɚ). ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɢ ɞɚɧɨ ɩɪɚɜɢɥɶɧɨɟ ɨɛɴɹɫɧɟɧɢɟ, ɧɨ ɫɨɞɟɪɠɢɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɡɚɩɢɫɹɯ ɫɨɞɟɪɠɚɬɫɹ ɥɢɲɶ ɨɛɳɢɟ ɪɚɫɫɭɠɞɟɧɢɹ ɛɟɡ 2 ɩɪɢɜɹɡɤɢ ɤ ɤɨɧɤɪɟɬɧɨɣ ɫɢɬɭɚɰɢɢ ɡɚɞɚɱɢ. ɂɅɂ Ɋɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɨɬɜɟɬɭ, ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ, ɢɥɢ ɜ ɧɢɯ ɫɨɞɟɪɠɚɬɫɹ ɥɨɝɢɱɟɫɤɢɟ ɧɟɞɨɱɺɬɵ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɍɤɚɡɚɧɵ ɧɟ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɧɨ ɜ ɧɟɤɨɬɨɪɵɯ ɢɡ ɧɢɯ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ 1 ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɩɨɥɭɱɟɧɢɟ ɨɬɜɟɬɚ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ, ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɟɪɧɨɦɭ ɨɬɜɟɬɭ, ɫɨɞɟɪɠɚɬ ɨɲɢɛɤɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ C2 2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ Ʌɭɧɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 1 28 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ Ʌɭɧɵ ɫɨɫɬɚɜɥɹɟɬ ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ 81 ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ Ʌɭɧɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɉɪɢ ɞɜɢɠɟɧɢɢ ɫɩɭɬɧɢɤɚ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ R ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɫɢɥɨɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ GmM ɫɩɭɬɧɢɤɚ ɤ ɩɥɚɧɟɬɟ: mȦ2R , ɝɞɟ m ɢ M – ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɢ ɩɥɚɧɟɬɵ, G – R2 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɚ Ȧ – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ. Ⱦɥɹ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɩɭɬɧɢɤɚ Ȧ 2ʌ , ɝɞɟ T = 1 ɫɭɬɤɢ. T ɂɡ ɡɚɩɢɫɚɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɣ ɨɪɛɢɬɵ ɞɥɹ Ɂɟɦɥɢ § GMɁ 2· 3 T , ɚ ɞɥɹ Ʌɭɧɵ ¨ © 4ʌ 2 ¹̧ 1 ɪɚɜɟɧ RɁ § G MɁ ·3 (28T ) 2 ¨ 2 © 4ʌ 81 ¹̧ 1 RɅ § 282 · 3 RɁ¨ © 81 ¹̧ 1 Ɉɬɜɟɬ: RɅ © ɋɬɚɬȽɪɚɞ 2013 ɝ § 282 · 3 RɁ¨ © 81 ¹̧ 1 § 282 · 3 42 000 ¨ ɤɦ | 89 500 ɤɦ. © 81 ¹̧ 1 § 282 · 3 42 000 ¨ ɤɦ | 89 500 ɤɦ. © 81 ¹̧ 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – 2-ɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ ɞɥɹ ɤɪɭɝɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ, ɡɚɤɨɧ ɜɫɟɦɢɪɧɨɝɨ ɬɹɝɨɬɟɧɢɹ ɢ ɭɫɥɨɜɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɫɩɭɬɧɢɤɚ ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɥɚɧɟɬɵ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɜɫɟɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɩɨɥɧɨɦ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 C3 4 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 300 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 2. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɞɥɹ 1 ɦɨɥɹ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2: p0V0 RT0, n p0V2 RT0, ɝɞɟ V 0 ɢ V 2 – ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2 ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ V0 RT0 ɬɟɦɩɟɪɚɬɭɪɟ T0. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ 2 ɪɚɜɟɧ V2 . n n p0 ɉɪɨɰɟɫɫ 2–3 – ɢɡɨɛɚɪɢɱɟɫɤɢɣ ɩɪɢ ɞɚɜɥɟɧɢɢ n p0, ɬɚɤ ɱɬɨ ɪɚɛɨɬɚ ɝɚɡɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ A n p0 V3 V2 , ɩɪɢɱɺɦ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ Ʉɥɚɩɟɣɪɨɧɚ–Ɇɟɧɞɟɥɟɟɜɚ ( n p0V3 ) R kT0, ɨɬɤɭɞɚ V3 R kT0 . n p0 Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɛɨɬɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ A § R kT0 RT0 · n p0¨ ¸ ¨ np n p0 ¸¹ 0 © Ɉɬɜɟɬ: A (k 1)RT0 © ɋɬɚɬȽɪɚɞ 2013 ɝ § · ¨k 1¸RT0 ¨ ¸ © ¹ 2490 Ⱦɠ. § · ¨2 1¸ 8, 3 300 ¨ ¸ © ¹ 2490 Ⱦɠ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɪɚɜɧɟɧɢɟ ɄɥɚɩɟɣɪɨɧɚɆɟɧɞɟɥɟɟɜɚ ɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɪɚɛɨɬɵ ɝɚɡɚ ɩɪɢ ɢɡɨɛɚɪɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 C4 6 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,95 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 12 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 11,9 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ȼɨɥɶɬɦɟɬɪ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨɤɚɡɵɜɚɟɬ ɩɨɫɬɨɹɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɢɫɬɨɱɧɢɤɚ, ɪɚɜɧɨɟ U1 = 20 ȼ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, ɫɭɦɦɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɦɩɟɪɦɟɬɪɟ ɢ ɩɨɤɚɡɚɧɢɣ ɜɨɥɶɬɦɟɬɪɚ: U1 = UȺ + U2 , ɨɬɤɭɞɚ UȺ = U1 – U2 = 0,1 ȼ, ɢ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɚɦɩɟɪɦɟɬɪɚ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ U U2 ɬɟɱɺɬ ɬɨɤ I2 = 1 Ⱥ, ɪɚɜɧɨ RA = 1 = 0,1 Ɉɦ. I2 ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, U1 = I1(RA + R), ɨɬɤɭɞɚ R = U1 12 – RA = – 0,1 § 12,5 Ɉɦ. I1 0, 95 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɬɨɤ I2 ɪɚɡɜɟɬɜɥɹɟɬɫɹ ɜ ɬɨɱɤɟ 2 ɧɚ ɞɜɚ ɬɨɤɚ – ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɢ ɱɟɪɟɡ ɪɟɡɢɫɬɨɪ, ɪɚɜɧɵɟ ɜ ɫɭɦɦɟ ɬɨɤɭ I2 ɩɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɨɷɬɨɦɭ ɬɨɤ ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɪɚɜɟɧ Iȼ = I2 – Rȼ = U2 § 0,0504 A, ɬɚɤ ɱɬɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɪɚɜɧɨ R U2 § 236,12 Ɉɦ. Iȼ ɉɨɞɫɬɚɜɥɹɹ ɜɫɟ ɡɚɩɢɫɚɧɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨɥɭɱɚɟɦ ɩɨɫɥɟ ɩɨɞɫɬɚɧɨɜɤɢ ɱɢɫɥɟɧɧɵɯ U2ª¬U1(I2 I1) U2I1º¼ R | 2361, 2. ɡɧɚɱɟɧɢɣ: ȼ RȺ U1(U1 U2)(I2 I1) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɩɪɢɦɟɪɧɨ ɜ 2360 ɪɚɡ. R Ɉɬɜɟɬ: ȼ RȺ U2ª¬U1(I2 I1) U2I1º¼ © ɋɬɚɬȽɪɚɞ 2013 ɝ U1(U1 U2)(I2 I1) | 2360 ɪɚɡ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, ɢ ɫɜɹɡɶ ɫɢɥ ɬɨɤɚ ɜ ɪɚɡɜɟɬɜɥɺɧɧɨɣ ɰɟɩɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 7 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 C5 8 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 60 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 3 ɪɚɡɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɚɞɨ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɚ ɫɥɭɱɚɹ: ɤɨɝɞɚ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ ɢ ɤɨɝɞɚ ɨɧɚ ɪɚɫɫɟɢɜɚɸɳɚɹ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɟɞɦɟɬɚ ɦɨɠɟɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧɧɵɦ, ɬɨɥɶɤɨ ɟɫɥɢ ɨɧɨ 1 1 1 ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ (ɢ ɩɟɪɟɜɺɪɧɭɬɨɟ). ɉɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ ɡɚɩɢɫɵɜɚɟɦ: , a b F a ɚ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɢɡɨɛɪɚɠɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɪɟɞɦɟɬɨɦ ɢɦɟɟɦ: n, b n1 a 1 ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɥɢɧɡɵ ɞɨ ɢɡɨɛɪɚɠɟɧɢɹ. Ɉɬɫɸɞɚ b , ɢ a n F a 60 F ɫɦ = 15 ɫɦ. 4 n1 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɦɧɢɦɨɟ, ɩɪɹɦɨɟ, ɢ ɩɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ 1 1 1 , ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɦɧɢɦɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɟɞɦɟɬɚ ɞɨ ɪɚɫɫɟɢɜɚɸɳɟɣ a b F a 1 1n ɉɪɢ ɷɬɨɦ ɩɨɩɪɟɠɧɟɦɭ n, ɢ ɩɨɥɭɱɚɟɦ: , ɥɢɧɡɵ. b F a a 60 F ɫɦ 30 ɫɦ. 2 1n Ɉɬɜɟɬ: ɟɫɥɢ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ, ɬɨ F = 15 ɫɦ, ɚ ɟɫɥɢ ɪɚɫɫɟɢɜɚɸɳɚɹ, ɬɨ F = –30 ɫɦ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɬɨɧɤɨɣ ɥɢɧɡɵ ɢ ɮɨɪɦɭɥɚ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ, ɞɚɜɚɟɦɨɝɨ ɥɢɧɡɨɣ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 C6 10 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ = h , mv ɝɞɟ h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ l § 5Ȝ, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɪɚɜɧɚ n = 1,3 · 1025 ɦ–3? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɋɨɝɥɚɫɧɨ ɨɫɧɨɜɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɦɨɥɟɤɭɥɹɪɧɨ-ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ 3kT ɢ ɨɩɪɟɞɟɥɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ, ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ v , m ɝɞɟ k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ Ȝ= h = mv h . 3kTm ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɩɪɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ n ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, l= T n 3, 1 25 h2 23 n 3km Ɉɬɜɟɬ: T ɩɨɷɬɨɦɭ ɫɨɨɬɧɨɲɟɧɢɟ l § 5Ȝ ɜɵɩɨɥɧɹɟɬɫɹ ɩɪɢ 2 25 6, 62 1068 25 3 1, 3 10 K | 2, 15Ʉ. 3 1, 38 1023 6, 6 1027 25 h2 23 n | 2, 15 Ʉ . 3km © ɋɬɚɬȽɪɚɞ 2013 ɝ ( ) ɬɟɦɩɟɪɚɬɭɪɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1603 11 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɦɨɥɟɤɭɥ ɝɚɡɚ, ɮɨɪɦɭɥɚ ɞɥɹ ɞɥɢɧɵ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɜ ɝɚɡɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ; ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 1 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɢɜɚɧɢɹ ɡɚɞɚɧɢɣ ɫ ɪɚɡɜɺɪɧɭɬɵɦ ɨɬɜɟɬɨɦ Ɉɛɴɹɫɧɢɬɟ, ɨɫɧɨɜɵɜɚɹɫɶ ɧɚ ɢɡɜɟɫɬɧɵɯ ɮɢɡɢɱɟɫɤɢɯ ɡɚɤɨɧɚɯ ɢ ɡɚɤɨɧɨɦɟɪɧɨɫɬɹɯ, ɩɨɱɟɦɭ ɭ ɛɚɫɨɜɵɯ ɬɪɭɛ ɨɪɝɚɧɚ ɞɥɢɧɵ ɛɨɥɶɲɢɟ, ɚ ɭ ɬɪɭɛ ɫ ɜɵɫɨɤɢɦɢ ɬɨɧɚɦɢ – ɦɚɥɟɧɶɤɢɟ. Ɉɪɝɚɧɧɚɹ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ ɢ ɡɜɭɱɢɬ ɩɪɢ ɩɪɨɞɭɜɚɧɢɢ ɱɟɪɟɡ ɧɟɺ ɩɨɬɨɤɚ ɜɨɡɞɭɯɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ 1. Ƚɪɨɦɤɢɣ ɡɜɭɤ ɛɵɜɚɟɬ, ɤɨɝɞɚ ɧɚ ɜɵɯɨɞɟ ɢɡ ɨɪɝɚɧɧɨɣ ɬɪɭɛɵ ɭɫɬɚɧɚɜɥɢɜɚɟɬɫɹ ɩɭɱɧɨɫɬɶ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɬɚɤ ɤɚɤ ɜɛɥɢɡɢ ɩɭɱɧɨɫɬɢ ɤɨɥɟɛɚɧɢɹ ɜɨɡɞɭɯɚ ɩɪɨɢɫɯɨɞɹɬ ɫ ɦɚɤɫɢɦɚɥɶɧɨɣ ɚɦɩɥɢɬɭɞɨɣ, ɚ ɚɦɩɥɢɬɭɞɚ ɨɩɪɟɞɟɥɹɟɬ ɝɪɨɦɤɨɫɬɶ ɡɜɭɤɚ. 2. ɉɨɫɤɨɥɶɤɭ ɬɪɭɛɚ ɨɬɤɪɵɬɚ ɫ ɨɛɨɢɯ ɤɨɧɰɨɜ, ɬɨ ɩɭɱɧɨɫɬɶ ɬɚɤɠɟ ɞɨɥɠɧɚ ɭɫɬɚɧɚɜɥɢɜɚɬɶɫɹ ɢ ɧɚ ɜɯɨɞɟ ɬɪɭɛɵ. 3. ɉɨɷɬɨɦɭ ɞɥɹ ɧɚɢɛɨɥɟɟ ɝɪɨɦɤɨɝɨ ɡɜɭɱɚɧɢɹ ɦɢɧɢɦɚɥɶɧɚɹ ɞɥɢɧɚ ɬɪɭɛɵ ɞɨɥɠɧɚ ɛɵɬɶ ɪɚɜɧɚ ɩɨɥɨɜɢɧɟ ɞɥɢɧɵ ɜɨɥɧɵ – ɩɪɢ ɷɬɨɦ ɩɨɫɟɪɟɞɢɧɟ ɬɪɭɛɵ ɧɚɯɨɞɢɬɫɹ ɭɡɟɥ ɫɬɨɹɱɟɣ ɜɨɥɧɵ, ɚ ɧɚ ɟɺ ɤɨɧɰɚɯ – ɞɜɟ ɩɭɱɧɨɫɬɢ. 4. Ɂɜɭɤɢ ɧɢɡɤɨɣ ɱɚɫɬɨɬɵ Ȟ (ɛɚɫɵ) ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɛɨɥɶɲɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɚ ɜɵɫɨɤɨɣ ɫ ɱɚɫɬɨɬɵ – ɦɚɥɟɧɶɤɢɦ ɞɥɢɧɚɦ ɜɨɥɧ, ɩɨɫɤɨɥɶɤɭ ɞɥɢɧɚ ɜɨɥɧɵ Ȝ , ɚ ɫɤɨɪɨɫɬɶ ɡɜɭɤɚ c Ȟ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɟɝɨ ɱɚɫɬɨɬɵ. 5. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɡɦɟɪɵ ɬɪɭɛɵ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɵ ɞɥɢɧɟ ɜɨɥɧɵ ɡɜɭɤɚ: ɱɟɦ ɱɚɫɬɨɬɚ ɡɜɭɤɚ ɧɢɠɟ, ɬɟɦ ɞɥɢɧɚ ɬɪɭɛɵ ɛɨɥɶɲɟ, ɢ ɧɚɨɛɨɪɨɬ. C1 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɩɪɚɜɢɥɶɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ ɩ. 1–5) ɢ ɢɫɱɟɪɩɵɜɚɸɳɢɟ ɜɟɪɧɵɟ ɪɚɫɫɭɠɞɟɧɢɹ ɫ ɭɤɚɡɚɧɢɟɦ ɧɚɛɥɸɞɚɟɦɵɯ ɹɜɥɟɧɢɣ ɢ ɡɚɤɨɧɨɜ (ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɫɬɚɧɨɜɥɟɧɢɟ ɫɬɨɹɱɟɣ 3 ɜɨɥɧɵ ɜ ɨɪɝɚɧɧɨɣ ɬɪɭɛɟ, ɫɜɹɡɶ ɚɦɩɥɢɬɭɞɵ ɤɨɥɟɛɚɧɢɣ ɜɨɡɞɭɯɚ ɫ ɝɪɨɦɤɨɫɬɶɸ ɡɜɭɤɚ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɵ ɞɥɹ ɫɜɹɡɢ ɞɥɢɧɵ ɜɨɥɧɵ ɢ ɱɚɫɬɨɬɵ ɡɜɭɤɚ). ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɢ ɞɚɧɨ ɩɪɚɜɢɥɶɧɨɟ ɨɛɴɹɫɧɟɧɢɟ, ɧɨ ɫɨɞɟɪɠɢɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɵɯ ɡɚɩɢɫɹɯ ɫɨɞɟɪɠɚɬɫɹ ɥɢɲɶ ɨɛɳɢɟ ɪɚɫɫɭɠɞɟɧɢɹ ɛɟɡ 2 ɩɪɢɜɹɡɤɢ ɤ ɤɨɧɤɪɟɬɧɨɣ ɫɢɬɭɚɰɢɢ ɡɚɞɚɱɢ. ɂɅɂ Ɋɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɨɬɜɟɬɭ, ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ, ɢɥɢ ɜ ɧɢɯ ɫɨɞɟɪɠɚɬɫɹ ɥɨɝɢɱɟɫɤɢɟ ɧɟɞɨɱɺɬɵ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɍɤɚɡɚɧɵ ɧɟ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɹɜɥɟɧɢɹ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɧɨ ɜ ɧɟɤɨɬɨɪɵɯ ɢɡ ɧɢɯ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɞɚɠɟ ɟɫɥɢ ɞɚɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ. ɂɅɂ 1 ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɩɨɥɭɱɟɧɢɟ ɨɬɜɟɬɚ ɧɚ ɜɨɩɪɨɫ ɡɚɞɚɧɢɹ, ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɍɤɚɡɚɧɵ ɜɫɟ ɧɟɨɛɯɨɞɢɦɵɟ ɞɥɹ ɨɛɴɹɫɧɟɧɢɹ ɹɜɥɟɧɢɹ ɢ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɧɨ ɢɦɟɸɳɢɟɫɹ ɪɚɫɫɭɠɞɟɧɢɹ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɜɟɪɧɨɦɭ ɨɬɜɟɬɭ, ɫɨɞɟɪɠɚɬ ɨɲɢɛɤɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 C2 2 ɂɡɜɟɫɬɧɨ, ɱɬɨ ɨɞɢɧ ɨɛɨɪɨɬ ɜɨɤɪɭɝ ɫɜɨɟɣ ɨɫɢ ȼɟɧɟɪɚ ɫɨɜɟɪɲɚɟɬ ɩɪɢɦɟɪɧɨ ɡɚ 243 ɡɟɦɧɵɯ ɫɭɬɨɤ, ɚ ɦɚɫɫɚ ȼɟɧɟɪɵ ɫɨɫɬɚɜɥɹɟɬ 0,82 ɨɬ ɦɚɫɫɵ Ɂɟɦɥɢ. ɇɚ ɨɪɛɢɬɭ ɤɚɤɨɝɨ ɪɚɞɢɭɫɚ ɧɚɞɨ ɜɵɜɟɫɬɢ ɫɩɭɬɧɢɤ ȼɟɧɟɪɵ, ɱɬɨɛɵ ɨɧ ɜɫɺ ɜɪɟɦɹ «ɜɢɫɟɥ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ? ɂɡɜɟɫɬɧɨ, ɱɬɨ ɫɩɭɬɧɢɤɢ Ɂɟɦɥɢ, ©ɜɢɫɹɳɢɟ» ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ, ɥɟɬɚɸɬ ɩɨ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ RɁ § 42 000 ɤɦ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɉɪɢ ɞɜɢɠɟɧɢɢ ɫɩɭɬɧɢɤɚ ɩɨ ɤɪɭɝɨɜɨɣ ɨɪɛɢɬɟ ɪɚɞɢɭɫɨɦ R ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ ɰɟɧɬɪɨɫɬɪɟɦɢɬɟɥɶɧɨɟ ɭɫɤɨɪɟɧɢɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ ɫɢɥɨɣ ɝɪɚɜɢɬɚɰɢɨɧɧɨɝɨ ɩɪɢɬɹɠɟɧɢɹ GmM ɫɩɭɬɧɢɤɚ ɤ ɩɥɚɧɟɬɟ: PȦ 2R , ɝɞɟ m ɢ M – ɦɚɫɫɵ ɫɩɭɬɧɢɤɚ ɢ ɩɥɚɧɟɬɵ, G – R2 ɝɪɚɜɢɬɚɰɢɨɧɧɚɹ ɩɨɫɬɨɹɧɧɚɹ, ɚ Ȧ – ɭɝɥɨɜɚɹ ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ. Ⱦɥɹ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɝɨ ɫɩɭɬɧɢɤɚ Ȧ 2ʌ , ɝɞɟ T = 1 ɫɭɬɤɢ. T ɂɡ ɡɚɩɢɫɚɧɧɵɯ ɫɨɨɬɧɨɲɟɧɢɣ ɫɥɟɞɭɟɬ, ɱɬɨ ɪɚɞɢɭɫ ɝɟɨɫɬɚɰɢɨɧɚɪɧɨɣ ɨɪɛɢɬɵ ɞɥɹ Ɂɟɦɥɢ § GM3 2· 3 T , ɚ ɞɥɹ ȼɟɧɟɪɵ ¨ © 4ʌ 2 ¹̧ 1 ɪɚɜɟɧ R3 § G 0, 82MɁ ·3 (243T ) 2 ¨ 2 4ʌ © ¹̧ RɁ 0, 82 2432 3 1 Rȼ ( ) 1 § 1 531 000 ɤɦ. Ɉɬɜɟɬ: Rȼ RɁ 0, 82 2432 © ɋɬɚɬȽɪɚɞ 2013 ɝ ( 1/3 ) | 1 531 000 ɤɦ. 42 000 0, 82 2432 3 ɤɦ | ( ) 1 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – 2-ɣ ɡɚɤɨɧ ɇɶɸɬɨɧɚ ɞɥɹ ɤɪɭɝɨɜɨɝɨ ɞɜɢɠɟɧɢɹ ɫɩɭɬɧɢɤɚ ɜɨɤɪɭɝ ɩɥɚɧɟɬɵ, ɡɚɤɨɧ ɜɫɟɦɢɪɧɨɝɨ ɬɹɝɨɬɟɧɢɹ ɢ ɭɫɥɨɜɢɟ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɯɨɠɞɟɧɢɹ ɫɩɭɬɧɢɤɚ ɧɚɞ ɨɞɧɨɣ ɢ ɬɨɣ ɠɟ ɬɨɱɤɨɣ ɩɥɚɧɟɬɵ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɜɫɟɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 3 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 C3 4 1 ɦɨɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ ɩɟɪɟɯɨɞɢɬ ɢɡ ɫɨɫɬɨɹɧɢɹ 1 ɜ ɫɨɫɬɨɹɧɢɟ 2, ɚ ɩɨɬɨɦ – ɜ ɫɨɫɬɨɹɧɢɟ 3 ɬɚɤ, ɤɚɤ ɷɬɨ ɩɨɤɚɡɚɧɨ ɧɚ (p, T) ɞɢɚɝɪɚɦɦɟ. ɇɚɱɚɥɶɧɚɹ ɬɟɦɩɟɪɚɬɭɪɚ ɝɚɡɚ ɪɚɜɧɚ T0 = 280 K. Ɉɩɪɟɞɟɥɢɬɟ ɪɚɛɨɬɭ ɝɚɡɚ ɩɪɢ ɩɟɪɟɯɨɞɟ ɢɡ ɫɨɫɬɨɹɧɢɹ 2 ɜ ɫɨɫɬɨɹɧɢɟ 3, ɟɫɥɢ k = 4. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ɂɚɩɢɲɟɦ ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɞɥɹ 1 ɦɨɥɹ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2: p0V0 RT0, n p0V2 RT0, ɝɞɟ V 0 ɢ V 2 – ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɹɯ 1 ɢ 2 ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ V0 RT0 ɬɟɦɩɟɪɚɬɭɪɟ T0. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɨɛɴɺɦ ɝɚɡɚ ɜ ɫɨɫɬɨɹɧɢɢ 2 ɪɚɜɟɧ V2 . n n p0 ɉɪɨɰɟɫɫ 2–3 – ɢɡɨɛɚɪɢɱɟɫɤɢɣ ɩɪɢ ɞɚɜɥɟɧɢɢ n p0, ɬɚɤ ɱɬɨ ɪɚɛɨɬɚ ɝɚɡɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ A n p0 V3 V2 , ɩɪɢɱɺɦ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɸ Ʉɥɚɩɟɣɪɨɧɚ–Ɇɟɧɞɟɥɟɟɜɚ R kT0 n p0V3 R kT0, ɨɬɤɭɞɚ V3 . Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɛɨɬɚ ɧɚ ɭɱɚɫɬɤɟ 2–3 ɪɚɜɧɚ n p0 · § · § R kT0 RT0 · § A n p0¨ k 1¸RT0 ¨4 1¸ 8, 3 280 6972 Ⱦɠ. ¨ ¸ ¨ np ¨ ¸ ¸ n p0 ¸¹ ¨© 0 © © ¹ ¹ ( Ɉɬɜɟɬ: A (k 1)RT0 © ɋɬɚɬȽɪɚɞ 2013 ɝ ) 6972 Ⱦɠ. Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɭɪɚɜɧɟɧɢɟ Ʉɥɚɩɟɣɪɨɧɚ±Ɇɟɧɞɟɥɟɟɜɚ ɢ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɪɚɛɨɬɵ ɝɚɡɚ ɩɪɢ ɢɡɨɛɚɪɢɱɟɫɤɨɦ ɩɪɨɰɟɫɫɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 5 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 6 ɒɤɨɥɶɧɢɤ ɫɨɛɪɚɥ ɫɯɟɦɭ, ɢɡɨɛɪɚɠɺɧɧɭɸ ɧɚ ɩɟɪɜɨɦ ɪɢɫɭɧɤɟ. ɉɨɫɥɟ ɟɺ ɩɨɞɤɥɸɱɟɧɢɹ ɤ ɢɞɟɚɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɨɤɚɡɚɥɨɫɶ, ɱɬɨ ɚɦɩɟɪɦɟɬɪ ɩɨɤɚɡɵɜɚɟɬ ɬɨɤ I1 = 0,9 Ⱥ, ɚ ɜɨɥɶɬɦɟɬɪ – ɧɚɩɪɹɠɟɧɢɟ U1 = 20 ȼ. Ʉɨɝɞɚ ɲɤɨɥɶɧɢɤ ɩɟɪɟɤɥɸɱɢɥ ɨɞɢɧ ɢɡ ɩɪɨɜɨɞɧɢɤɨɜ ɜɨɥɶɬɦɟɬɪɚ ɨɬ ɬɨɱɤɢ 1 ɤ ɬɨɱɤɟ 2 (ɫɦ. ɜɬɨɪɨɣ ɪɢɫɭɧɨɤ), ɜɨɥɶɬɦɟɬɪ ɫɬɚɥ ɩɨɤɚɡɵɜɚɬɶ ɧɚɩɪɹɠɟɧɢɟ U2 = 19 ȼ, ɚ ɚɦɩɟɪɦɟɬɪ – ɬɨɤ I2 = 1 Ⱥ. ȼɨ ɫɤɨɥɶɤɨ ɪɚɡ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ? C4 ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ȼɨɥɶɬɦɟɬɪ ɜ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨɤɚɡɵɜɚɟɬ ɩɨɫɬɨɹɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɢɫɬɨɱɧɢɤɚ, ɪɚɜɧɨɟ U1 = 20 ȼ. ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɷɬɨ ɧɚɩɪɹɠɟɧɢɟ ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, ɫɭɦɦɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɦɩɟɪɦɟɬɪɟ ɢ ɩɨɤɚɡɚɧɢɣ ɜɨɥɶɬɦɟɬɪɚ: U1 = UȺ + U2 , ɨɬɤɭɞɚ UȺ = U1 – U2 = 1 ȼ, ɢ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɚɦɩɟɪɦɟɬɪɚ, ɱɟɪɟɡ ɤɨɬɨɪɵɣ ɬɟɱɺɬ ɬɨɤ I2 = 1 Ⱥ, ɪɚɜɧɨ RA = U1 U2 = 1 Ɉɦ. I2 ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɩɨ ɡɚɤɨɧɭ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, U1 = I1 U 20 (RA + R), ɨɬɤɭɞɚ R = 1 RȺ= 1–1 § 21,2 Ɉɦ. I1 0, 9 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɬɨɤ I2 ɪɚɡɜɟɬɜɥɹɟɬɫɹ ɜ ɬɨɱɤɟ 2 ɧɚ ɞɜɚ ɬɨɤɚ – ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɢ ɱɟɪɟɡ ɪɟɡɢɫɬɨɪ, ɪɚɜɧɵɟ ɜ ɫɭɦɦɟ ɬɨɤɭ I2 ɩɨ ɡɚɤɨɧɭ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ. ɉɨɷɬɨɦɭ ɬɨɤ ɱɟɪɟɡ ɜɨɥɶɬɦɟɬɪ ɪɚɜɟɧ Iȼ = I2 – Rȼ = U2 § 0,105 A, ɬɚɤ ɱɬɨ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɪɚɜɧɨ R U2 § 181,5 Ɉɦ. Iȼ ɉɨɞɫɬɚɜɥɹɹ ɜɫɟ ɡɚɩɢɫɚɧɧɵɟ ɜɵɪɚɠɟɧɢɹ, ɩɨɥɭɱɚɟɦ Rȼ U2ª¬U1(I2 I1) U2I1º¼ 181, 45. RȺ U1(U1 U2)(I2 I1) Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜɨɥɶɬɦɟɬɪɚ ɛɨɥɶɲɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɚɦɩɟɪɦɟɬɪɚ ɩɪɢɦɟɪɧɨ ɜ 181,5 ɪɚɡ. U2ª¬U1(I2 I1) U2I1º¼ R 181, 45, ɬɨ ɟɫɬɶ ɩɪɢɦɟɪɧɨ ɜ 181,5 ɪɚɡɚ. Ɉɬɜɟɬ: ȼ U1(U1 U2)(I2 I1) RȺ © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɭɱɚɫɬɤɚ ɰɟɩɢ, ɫɨɞɟɪɠɚɳɟɝɨ ɪɟɡɢɫɬɨɪɵ, ɢ ɫɜɹɡɶ ɫɢɥ ɬɨɤɚ ɜ ɪɚɡɜɟɬɜɥɺɧɧɨɣ ɰɟɩɢ ɤɚɤ ɫɥɟɞɫɬɜɢɟ ɡɚɤɨɧɚ ɫɨɯɪɚɧɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɡɚɪɹɞɚ ɞɥɹ ɰɟɩɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 7 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 C5 8 Ɉɩɪɟɞɟɥɢɬɟ ɮɨɤɭɫɧɨɟ ɪɚɫɫɬɨɹɧɢɟ ɬɨɧɤɨɣ ɥɢɧɡɵ, ɟɫɥɢ ɥɢɧɟɣɧɵɟ ɪɚɡɦɟɪɵ ɢɡɨɛɪɚɠɟɧɢɹ ɬɨɧɤɨɝɨ ɤɚɪɚɧɞɚɲɚ, ɩɨɦɟɳɺɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ a = 48 ɫɦ ɨɬ ɥɢɧɡɵ ɢ ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨ ɝɥɚɜɧɨɣ ɨɩɬɢɱɟɫɤɨɣ ɨɫɢ, ɦɟɧɶɲɟ ɪɚɡɦɟɪɨɜ ɤɚɪɚɧɞɚɲɚ ɜ n = 2 ɪɚɡɚ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɚɞɨ ɪɚɫɫɦɨɬɪɟɬɶ ɞɜɚ ɫɥɭɱɚɹ: ɤɨɝɞɚ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ ɢ ɤɨɝɞɚ ɨɧɚ ɪɚɫɫɟɢɜɚɸɳɚɹ. ȼ ɩɟɪɜɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɟɞɦɟɬɚ ɦɨɠɟɬ ɛɵɬɶ ɭɦɟɧɶɲɟɧɧɵɦ, ɬɨɥɶɤɨ ɟɫɥɢ ɨɧɨ 1 1 1 ɞɟɣɫɬɜɢɬɟɥɶɧɨɟ (ɢ ɩɟɪɟɜɺɪɧɭɬɨɟ). ɉɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ ɡɚɩɢɫɵɜɚɟɦ: , a b F a ɚ ɞɥɹ ɭɦɟɧɶɲɟɧɢɹ ɪɚɡɦɟɪɨɜ ɢɡɨɛɪɚɠɟɧɢɹ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɩɪɟɞɦɟɬɨɦ ɢɦɟɟɦ: n, b a 1 n1 ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɥɢɧɡɵ ɞɨ ɢɡɨɛɪɚɠɟɧɢɹ. Ɉɬɫɸɞɚ b , ɢ n F a a 48 F ɫɦ = 16 ɫɦ. n1 3 ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɢɡɨɛɪɚɠɟɧɢɟ ɦɧɢɦɨɟ, ɩɪɹɦɨɟ, ɢ ɩɨ ɮɨɪɦɭɥɟ ɬɨɧɤɨɣ ɥɢɧɡɵ 1 1 1 , ɝɞɟ b – ɪɚɫɫɬɨɹɧɢɟ ɨɬ ɦɧɢɦɨɝɨ ɢɡɨɛɪɚɠɟɧɢɹ ɩɪɟɞɦɟɬɚ ɞɨ ɪɚɫɫɟɢɜɚɸɳɟɣ a b F a 1 1n ɥɢɧɡɵ. ɉɪɢ ɷɬɨɦ ɩɨɩɪɟɠɧɟɦɭ n, ɢ ɩɨɥɭɱɚɟɦ: , b F a a 48 F ɫɦ 48 ɫɦ. 1n 1 Ɉɬɜɟɬ: ɟɫɥɢ ɥɢɧɡɚ ɫɨɛɢɪɚɸɳɚɹ, ɬɨ F = 16 ɫɦ, ɚ ɟɫɥɢ ɪɚɫɫɟɢɜɚɸɳɚɹ, ɬɨ F = –48 ɫɦ. © ɋɬɚɬȽɪɚɞ 2013 ɝ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɬɨɧɤɨɣ ɥɢɧɡɵ ɢ ɮɨɪɦɭɥɚ ɞɥɹ ɭɜɟɥɢɱɟɧɢɹ, ɞɚɜɚɟɦɨɝɨ ɥɢɧɡɨɣ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɟɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ 9 Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 10 ɋɨɝɥɚɫɧɨ ɝɢɩɨɬɟɡɟ ɞɟ Ȼɪɨɣɥɹ, ɜɫɟ ɱɚɫɬɢɰɵ ɨɛɥɚɞɚɸɬ ɜɨɥɧɨɜɵɦɢ ɫɜɨɣɫɬɜɚɦɢ. h , Ⱦɥɢɧɚ ɜɨɥɧɵ ɞɥɹ ɱɚɫɬɢɰɵ ɦɚɫɫɨɣ m, ɢɦɟɸɳɟɣ ɫɤɨɪɨɫɬɶ v, ɫɨɫɬɚɜɥɹɟɬ Ȝ C6 mv h = 6,6 ǜ 10–34 Ⱦɠ · ɫ – ɩɨɫɬɨɹɧɧɚɹ ɉɥɚɧɤɚ. Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɦɨɠɧɨ ɛɵɥɨ ɝɞɟ ɩɪɢɦɟɧɹɬɶ ɦɨɞɟɥɶ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ, ɫɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ l ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɞɨɥɠɧɨ ɛɵɬɶ, ɜ ɱɚɫɬɧɨɫɬɢ, ɝɨɪɚɡɞɨ ɛɨɥɶɲɟ Ȝ. ɉɪɢ ɤɚɤɨɣ ɬɟɦɩɟɪɚɬɭɪɟ T ɞɥɹ ɢɧɟɪɬɧɨɝɨ ɝɚɡɚ ɝɟɥɢɹ Ȝ § l, ɟɫɥɢ ɤɨɧɰɟɧɬɪɚɰɢɹ ɟɝɨ ɦɨɥɟɤɭɥ ɪɚɜɧɚ n = 2,7 · 1025 ɦ–3 ? Ɇɚɫɫɚ ɦɨɥɟɤɭɥɵ ɝɟɥɢɹ ɪɚɜɧɚ m = 6,6 · 10–24 ɝ. ȼɨɡɦɨɠɧɨɟ ɪɟɲɟɧɢɟ ɋɨɝɥɚɫɧɨ ɨɫɧɨɜɧɨɦɭ ɭɪɚɜɧɟɧɢɸ ɦɨɥɟɤɭɥɹɪɧɨ-ɤɢɧɟɬɢɱɟɫɤɨɣ ɬɟɨɪɢɢ ɢɞɟɚɥɶɧɨɝɨ ɝɚɡɚ 3kT ɢ ɨɩɪɟɞɟɥɟɧɢɸ ɬɟɦɩɟɪɚɬɭɪɵ, ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɚɹ ɫɤɨɪɨɫɬɶ ɦɨɥɟɤɭɥ ɝɚɡɚ v , m ɝɞɟ Ȝ= k – ɩɨɫɬɨɹɧɧɚɹ Ȼɨɥɶɰɦɚɧɚ, ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɞɥɢɧɚ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ h = mv h . 3kTm ɋɪɟɞɧɟɟ ɪɚɫɫɬɨɹɧɢɟ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɝɚɡɚ ɩɪɢ ɢɯ ɤɨɧɰɟɧɬɪɚɰɢɢ n ɪɚɜɧɨ, ɨɱɟɜɢɞɧɨ, l = n 3 , 1 2 T h 23 n 3km Ɉɬɜɟɬ: T ɩɨɷɬɨɦɭ ɫɨɨɬɧɨɲɟɧɢɟ 68 l§Ȝ 6, 6 10 2, 7 10 3 1, 38 1023 6, 6 1027 2 h2 23 n | 0, 14 Ʉ . 3km © ɋɬɚɬȽɪɚɞ 2013 ɝ ( ɜɵɩɨɥɧɹɟɬɫɹ 2 25 3 ) Ʉ | 0, 14 Ʉ . ɩɪɢ ɬɟɦɩɟɪɚɬɭɪɟ Ɏɢɡɢɤɚ 11 ɤɥɚɫɫ ȼɚɪɢɚɧɬ Ɏɂ1604 11 Ʉɪɢɬɟɪɢɢ ɨɰɟɧɤɢ ɜɵɩɨɥɧɟɧɢɹ ɡɚɞɚɧɢɹ Ȼɚɥɥɵ ɉɪɢɜɟɞɟɧɨ ɩɨɥɧɨɟ ɪɟɲɟɧɢɟ, ɜɤɥɸɱɚɸɳɟɟ ɫɥɟɞɭɸɳɢɟ ɷɥɟɦɟɧɬɵ: I) ɡɚɩɢɫɚɧɵ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɜɵɛɪɚɧɧɵɦ ɫɩɨɫɨɛɨɦ ɜ ɞɚɧɧɨɦ ɫɥɭɱɚɟ – ɮɨɪɦɭɥɚ ɞɥɹ ɫɪɟɞɧɟɤɜɚɞɪɚɬɢɱɧɨɣ ɫɤɨɪɨɫɬɢ ɦɨɥɟɤɭɥ ɝɚɡɚ, ɮɨɪɦɭɥɚ ɞɥɹ ɞɥɢɧɵ ɜɨɥɧɵ ɞɟ Ȼɪɨɣɥɹ, ɚ ɬɚɤɠɟ ɮɨɪɦɭɥɚ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɫɪɟɞɧɟɝɨ ɪɚɫɫɬɨɹɧɢɹ ɦɟɠɞɭ ɦɨɥɟɤɭɥɚɦɢ ɜ ɝɚɡɟ); II) ɨɩɢɫɚɧɵ ɜɫɟ ɜɜɨɞɢɦɵɟ ɜ ɪɟɲɟɧɢɟ ɛɭɤɜɟɧɧɵɟ ɨɛɨɡɧɚɱɟɧɢɹ ɮɢɡɢɱɟɫɤɢɯ ɜɟɥɢɱɢɧ (ɡɚ ɢɫɤɥɸɱɟɧɢɟɦ, ɜɨɡɦɨɠɧɨ, ɨɛɨɡɧɚɱɟɧɢɣ ɤɨɧɫɬɚɧɬ, ɭɤɚɡɚɧɧɵɯ 3 ɜ ɜɚɪɢɚɧɬɟ ɄɂɆ, ɢ ɨɛɨɡɧɚɱɟɧɢɣ, ɢɫɩɨɥɶɡɭɟɦɵɯ ɜ ɭɫɥɨɜɢɢ ɡɚɞɚɱɢ); III) ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ (ɞɨɩɭɫɤɚɟɬɫɹ ɜɟɪɛɚɥɶɧɨɟ ɭɤɚɡɚɧɢɟ ɧɚ ɢɯ ɩɪɨɜɟɞɟɧɢɟ) ɢ ɪɚɫɱɺɬɵ, ɩɪɢɜɨɞɹɳɢɟ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɱɢɫɥɨɜɨɦɭ ɨɬɜɟɬɭ (ɞɨɩɭɫɤɚɟɬɫɹ ɪɟɲɟɧɢɟ «ɩɨ ɱɚɫɬɹɦ» ɫ ɩɪɨɦɟɠɭɬɨɱɧɵɦɢ ɜɵɱɢɫɥɟɧɢɹɦɢ); IV) ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ; ɉɪɚɜɢɥɶɧɨ ɡɚɩɢɫɚɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɨɥɨɠɟɧɢɹ ɬɟɨɪɢɢ ɢ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɢ, ɩɪɨɜɟɞɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɢ ɩɪɟɞɫɬɚɜɥɟɧ ɩɪɚɜɢɥɶɧɵɣ ɨɬɜɟɬ ɫ ɭɤɚɡɚɧɢɟɦ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɢɫɤɨɦɨɣ ɜɟɥɢɱɢɧɵ. ɇɨ ɢɦɟɟɬɫɹ ɨɞɢɧ ɢɡ ɫɥɟɞɭɸɳɢɯ ɧɟɞɨɫɬɚɬɤɨɜ. Ɂɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɥɢ ɨɛɨɢɦ ɩɭɧɤɬɚɦ: II ɢ III – ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɟ ɜ ɩɨɥɧɨɦ ɨɛɴɺɦɟ ɢɥɢ ɨɬɫɭɬɫɬɜɭɸɬ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɩɪɚɜɢɥɶɧɨɦ ɪɟɲɟɧɢɢ ɥɢɲɧɢɟ ɡɚɩɢɫɢ, ɧɟ ɜɯɨɞɹɳɢɟ ɜ ɪɟɲɟɧɢɟ 2 ɜɨɡɦɨɠɧɨ, ɧɟɜɟɪɧɵɟ), ɧɟ ɨɬɞɟɥɟɧɵ ɨɬ ɪɟɲɟɧɢɹ (ɧɟ ɡɚɱɺɪɤɧɭɬɵ, ɧɟ ɡɚɤɥɸɱɟɧɵ ɜ ɫɤɨɛɤɢ, ɪɚɦɤɭ ɢ ɬ. ɩ.). ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɜ ɧɟɨɛɯɨɞɢɦɵɯ ɦɚɬɟɦɚɬɢɱɟɫɤɢɯ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹɯ ɢɥɢ ɜɵɱɢɫɥɟɧɢɹɯ ɞɨɩɭɳɟɧɵ ɨɲɢɛɤɢ, ɢ (ɢɥɢ) ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ/ɜɵɱɢɫɥɟɧɢɹ ɧɟ ɞɨɜɟɞɟɧɵ ɞɨ ɤɨɧɰɚ. ɂɅɂ ɉɪɢ ɉɈɅɇɈɆ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɩɭɧɤɬ IV, ɢɥɢ ɜ ɧɺɦ ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɡɚɩɢɫɢ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɨɞɧɨɦɭ ɢɡ ɫɥɟɞɭɸɳɢɯ ɫɥɭɱɚɟɜ. ɉɪɟɞɫɬɚɜɥɟɧɵ ɬɨɥɶɤɨ ɩɨɥɨɠɟɧɢɹ ɢ ɮɨɪɦɭɥɵ, ɜɵɪɚɠɚɸɳɢɟ ɮɢɡɢɱɟɫɤɢɟ ɡɚɤɨɧɵ, ɩɪɢɦɟɧɟɧɢɟ ɤɨɬɨɪɵɯ ɧɟɨɛɯɨɞɢɦɨ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ, ɛɟɡ ɤɚɤɢɯɥɢɛɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɣ ɫ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ, ɧɚɩɪɚɜɥɟɧɧɵɯ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ, ɢ ɨɬɜɟɬɚ. ɂɅɂ ȼ ɪɟɲɟɧɢɢ ɨɬɫɭɬɫɬɜɭɟɬ ɈȾɇȺ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɚɹ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɟ, ɥɟɠɚɳɟɟ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɧɨ 1 ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ɂɅɂ ȼ ɈȾɇɈɃ ɢɡ ɢɫɯɨɞɧɵɯ ɮɨɪɦɭɥ, ɧɟɨɛɯɨɞɢɦɵɯ ɞɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ (ɢɥɢ ɭɬɜɟɪɠɞɟɧɢɢ, ɥɟɠɚɳɟɦ ɜ ɨɫɧɨɜɟ ɪɟɲɟɧɢɹ), ɞɨɩɭɳɟɧɚ ɨɲɢɛɤɚ, ɧɨ ɩɪɢɫɭɬɫɬɜɭɸɬ ɥɨɝɢɱɟɫɤɢ ɜɟɪɧɵɟ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɫ ɢɦɟɸɳɢɦɢɫɹ ɮɨɪɦɭɥɚɦɢ, ɧɚɩɪɚɜɥɟɧɧɵɟ ɧɚ ɪɟɲɟɧɢɟ ɡɚɞɚɱɢ. ȼɫɟ ɫɥɭɱɚɢ ɪɟɲɟɧɢɹ, ɤɨɬɨɪɵɟ ɧɟ ɫɨɨɬɜɟɬɫɬɜɭɸɬ ɜɵɲɟɭɤɚɡɚɧɧɵɦ ɤɪɢɬɟɪɢɹɦ 0 ɜɵɫɬɚɜɥɟɧɢɹ ɨɰɟɧɨɤ ɜ 1, 2, 3 ɛɚɥɥɚ. © ɋɬɚɬȽɪɚɞ 2013 ɝ
