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Консультация № 201981
25.12.2021, 13:29
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Какую силу необходимо приложить к нижнему бруску (рис. 39), чтобы выдернуть его из-под верхнего? Коэффициенты трения для верхнего и нижнего брусков - q1 и q2, а их массы m1 и m2.
Какую силу необходимо приложить к нижнему бруску (рис. 39), чтобы выдернуть его из-под верхнего? Коэффициенты трения для верхнего и нижнего брусков - q1 и q2, а их массы m1 и m2.
Прикрепленные файлы:
Обсуждение
28.12.2021, 11:21
общий
Задачка интересная, и Ответ по ссылке Андрея Владимировича - правильный для той задачи. Но изза разгильдяйства верстальщика там мозги сломаешь в попытках вникнуть в причинно-следственную связь. Мне пришлось решить ту задачу, чтоб понять её изящное Решение. Я публикую свой перевод ниже, может он кому пригодится?
Решение: Запишем 2й закон Ньютона в проекции на горизонтальное направлени для каждого из брусков:
m2·a2 = Fтр2[$8195$] ,[$8195$] m1·a1 = F - Fтр1 - Fтр2
Здесь Fтр1 - сила трения, возникающая м-ду горизонтальной поверхностью и нижним бруском,
Fтр2 - сила трения, возникающая м-ду брусками. a1 и a2 - ускорения нижнего и верхнего бруска соответственно.
Найдём величины сил трения: Fтр2 = µ·m2·g[$8195$] ,[$8195$] Fтр1 = µ·(m1 + m2)·g
Отсюда получаем, что a2 = Fтр2 / m2 = µ·g
m1·a1 = F - µ·(m1 + m2)·g - µ·m2·g = F - µ·g·(m1 + 2·m2)
a1 = [F - µ·(m1 + 2·m2)·g] / m1
Тк по условию, нижний груз нужно выдернуть из-под верхнего, то a1 > a2 .
Подставляя в это неравенство выражения для ускорений, находим, что
[F - µ·(m1 + 2·m2)·g] / m1 > µ·g
F - µ·(m1 + 2·m2)·g > µ·g·m1
F > µ·(m1 + 2·m2)·g > µ·(m1 + 2·m2)·g + µ·g·m1 = µ·g·(m1 + 2·m2 + m1) = 2·µ·g·(m1 + m2)
Ответ : F > 2·µ·(m1 + m2)·g
Решение: Запишем 2й закон Ньютона в проекции на горизонтальное направлени для каждого из брусков:
m2·a2 = Fтр2[$8195$] ,[$8195$] m1·a1 = F - Fтр1 - Fтр2
Здесь Fтр1 - сила трения, возникающая м-ду горизонтальной поверхностью и нижним бруском,
Fтр2 - сила трения, возникающая м-ду брусками. a1 и a2 - ускорения нижнего и верхнего бруска соответственно.
Найдём величины сил трения: Fтр2 = µ·m2·g[$8195$] ,[$8195$] Fтр1 = µ·(m1 + m2)·g
Отсюда получаем, что a2 = Fтр2 / m2 = µ·g
m1·a1 = F - µ·(m1 + m2)·g - µ·m2·g = F - µ·g·(m1 + 2·m2)
a1 = [F - µ·(m1 + 2·m2)·g] / m1
Тк по условию, нижний груз нужно выдернуть из-под верхнего, то a1 > a2 .
Подставляя в это неравенство выражения для ускорений, находим, что
[F - µ·(m1 + 2·m2)·g] / m1 > µ·g
F - µ·(m1 + 2·m2)·g > µ·g·m1
F > µ·(m1 + 2·m2)·g > µ·(m1 + 2·m2)·g + µ·g·m1 = µ·g·(m1 + 2·m2 + m1) = 2·µ·g·(m1 + m2)
Ответ : F > 2·µ·(m1 + m2)·g
28.12.2021, 16:31
общий
Адресаты:
Владимир Николаевич, я думаю имеет смысл ваше решение оформить ответом...
Об авторе:
С уважением
shvetski
С уважением
shvetski
28.12.2021, 18:19
общий
Адресаты:
Моё решение соответствует другой задаче (по выше-ссылке Андрея Владимировича). Я поделился опытом с товарищами по партии.
Если кто-то хочет доработать его для текущей задачи, пусть доработает и пишет Ответ.
А мне жалко убивать время на Михаила, он у меня в Чёрном списке, см rfpro.ru/question/201819#323094 .
Если кто-то хочет доработать его для текущей задачи, пусть доработает и пишет Ответ.
А мне жалко убивать время на Михаила, он у меня в Чёрном списке, см rfpro.ru/question/201819#323094 .
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