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Консультация № 201884
12.12.2021, 19:58
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Здравствуйте! У меня прошу помощь с таким вопросом:
Лёгкая катушка, с намотанным на шкивы нитями и подвешенными на них грузиками, изображена на рисунке. Радиус большого шкива 5 см, радиус малого шкива 1 см. Система находится в равновесии. Масса грузика, подвешенного к оси катушки, M=40 г. Найдите массу m второго грузика. Ответ приведите в г.
Рисунок прикрепила. Заранее благодарю за помощь!
Лёгкая катушка, с намотанным на шкивы нитями и подвешенными на них грузиками, изображена на рисунке. Радиус большого шкива 5 см, радиус малого шкива 1 см. Система находится в равновесии. Масса грузика, подвешенного к оси катушки, M=40 г. Найдите массу m второго грузика. Ответ приведите в г.
Рисунок прикрепила. Заранее благодарю за помощь!
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Обсуждение
13.12.2021, 06:37
общий
это ответ
Условие: Радиус большого шкива R = 5 см, радиус малого шкива r = 1 см. Масса грузика, подвешенного к оси катушки, M=40 г.
Вычислить массу m второго грузика.
Решение: Поскольку в Условии задано "Система находится в равновесии", значит, движений и ускорений нет. И наша катушка со шкивами работает, как обыкновенные рычажные весы с коромыслом AC и точкой подвеса "B". Поясняющий рисунок прилагаю ниже.
Мудрый старец Архимед научил нас простой формуле равенства крутящих сил-моментов:
F1·AB = F2·BC , где F1 = m·g - вес грузика массой m , F2 = M·g - вес грузика массой M ,
g = 9,807 м/с2 - ускорение земного тяготения, BC = r - правый рычаг весов, AB = R - r - левый рычаг.
Вводим известные нам данные в Архимед-формулу: m·g·(R - r) = M·g·r
и вычисляем искомую массу: m = M·r / (R - r) = 40·1 / (5 - 1) = 40 / 4 = 10 г .
Ответ : масса малого (левого) грузика равна 10 граммов.
Проверка по Архимеду: 10·g·(5-1) = 40·g·1 [$8658$] 40·g = 40·g - верное тождество! Проверка успешна! =Удачи!
Вычислить массу m второго грузика.
Решение: Поскольку в Условии задано "Система находится в равновесии", значит, движений и ускорений нет. И наша катушка со шкивами работает, как обыкновенные рычажные весы с коромыслом AC и точкой подвеса "B". Поясняющий рисунок прилагаю ниже.
F1·AB = F2·BC , где F1 = m·g - вес грузика массой m , F2 = M·g - вес грузика массой M ,
g = 9,807 м/с2 - ускорение земного тяготения, BC = r - правый рычаг весов, AB = R - r - левый рычаг.
Вводим известные нам данные в Архимед-формулу: m·g·(R - r) = M·g·r
и вычисляем искомую массу: m = M·r / (R - r) = 40·1 / (5 - 1) = 40 / 4 = 10 г .
Ответ : масса малого (левого) грузика равна 10 граммов.
Проверка по Архимеду: 10·g·(5-1) = 40·g·1 [$8658$] 40·g = 40·g - верное тождество! Проверка успешна! =Удачи!
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