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Консультация № 109295
13.11.2007, 22:23
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Уважаемые эксперты, убедительно прошу помочь в решении простейшей задачки для 7 класса!
Дверь высотой 2 метра и шириной 1 метр подвешена на 2 петлях, находящихся на расстянии от каждого из краев двери. Масса двери 36 кг. С какой силой дверь тянет верхнюю петлю в гризонтальном направлении?
Заранее спасибо каждому...
Дверь высотой 2 метра и шириной 1 метр подвешена на 2 петлях, находящихся на расстянии от каждого из краев двери. Масса двери 36 кг. С какой силой дверь тянет верхнюю петлю в гризонтальном направлении?
Заранее спасибо каждому...
Обсуждение
14.11.2007, 03:01
общий
это ответ
Здравствуйте, Serega1988!
"находящихся на расстоянии от каждого из краев двери" - забыли указать, каком именно. Допустим, 0.25 метра - тогда расстояние между петлями L = 2 - 2*0.25 = 1.5 метра - это всё, чего нам не хватало. Составляем уравнение моментов сил относительно нижней петли (условно считая петлю точкой) - тогда реакция нижней петли в этом уравнении фигурировать не будет, поскольку "плечо" этой реакции равно нулю. Вес двери G приложен к её центру тяжести, т.е. к середине; ширина двери 1 метр, значит её центр тяжести находится на расстоянии b = 0.5 метра от края; это и есть "плечо" силы тяжести относительно нижней петли. Что касается реакции верхней петли, нас интересует лишь её горизонтальная составляющая -F (противоположная по направлению искомой силе F, которую эта реакция должна уравновешивать), "плечо" которой равно L. Итак: G*b - F*L = 0, откуда F = G*b/L = m*g*b/L = 36*g*0.5/1.5 = 12*g ньютонов.
"находящихся на расстоянии от каждого из краев двери" - забыли указать, каком именно. Допустим, 0.25 метра - тогда расстояние между петлями L = 2 - 2*0.25 = 1.5 метра - это всё, чего нам не хватало. Составляем уравнение моментов сил относительно нижней петли (условно считая петлю точкой) - тогда реакция нижней петли в этом уравнении фигурировать не будет, поскольку "плечо" этой реакции равно нулю. Вес двери G приложен к её центру тяжести, т.е. к середине; ширина двери 1 метр, значит её центр тяжести находится на расстоянии b = 0.5 метра от края; это и есть "плечо" силы тяжести относительно нижней петли. Что касается реакции верхней петли, нас интересует лишь её горизонтальная составляющая -F (противоположная по направлению искомой силе F, которую эта реакция должна уравновешивать), "плечо" которой равно L. Итак: G*b - F*L = 0, откуда F = G*b/L = m*g*b/L = 36*g*0.5/1.5 = 12*g ньютонов.
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