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Консультация № 201245
30.06.2021, 11:55
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Здравствуйте! У меня возникли сложности с таким вопросом:Три кубика с массами 3m, 2m и m связаны двумя лёгкими нерастяжимыми нитями. Приложив к самому тяжёлому кубику вертикальную силу, связку кубиков поднимают вверх так, что обе нити остаются вертикальны (см. рисунок). Во сколько раз сила натяжения верхней нити больше, чем сила натяжения нижней? Силами сопротивления воздуха пренебрегите. Ответ округлите до десятых. 
Обсуждение
30.06.2021, 15:58
общий
это ответ
Даны 3 кубика с массами 3·m, 2·m и m .
Вычислить отношение сил натяжения верхней и нижней нитей.
Решение простое: Для начала предположим, будто сила F равна весу всех кубиков. Кубики просто висят (покоятся).
Тогда сила натяжения нижней нити равна весу нижнего кубика : Fн = m·g , где g = 9,8 м/с2 - ускорение замного тяготения.
А сила натяжения верхней нити равна весу 2х нижних кубиков : Fв = (m + 2·m)·g = 3·m·g
Ответ : искомое отношение сил натяжения равно Fв / Fн = 3·m·g / (m·g) = 3
Если связку кубиков поднимают вверх с постоянной скоростью, то силы Fн и Fв остаются прежними, их отношение тоже.
Если связку кубиков поднимают вверх с ускорением "a", то силы Fн и Fв увеличатся в (a+g) / g раз, но их отношение НЕ изменится, поскольку нити НЕрастяжимые, и поэтому ускорение всех кубиков одинаково.
Вычислить отношение сил натяжения верхней и нижней нитей.
Решение простое: Для начала предположим, будто сила F равна весу всех кубиков. Кубики просто висят (покоятся).
Тогда сила натяжения нижней нити равна весу нижнего кубика : Fн = m·g , где g = 9,8 м/с2 - ускорение замного тяготения.
А сила натяжения верхней нити равна весу 2х нижних кубиков : Fв = (m + 2·m)·g = 3·m·g
Ответ : искомое отношение сил натяжения равно Fв / Fн = 3·m·g / (m·g) = 3
Если связку кубиков поднимают вверх с постоянной скоростью, то силы Fн и Fв остаются прежними, их отношение тоже.
Если связку кубиков поднимают вверх с ускорением "a", то силы Fн и Fв увеличатся в (a+g) / g раз, но их отношение НЕ изменится, поскольку нити НЕрастяжимые, и поэтому ускорение всех кубиков одинаково.
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