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Консультация № 176153
20.01.2010, 00:46
0.00 руб.
0
1
1
Дверь высотой 210 см и шириной 91 см имеет массу 27 кг. Дверь поддерживается петлями, расположенными на расстоянии 30 см - одна от верхней, другая от нижней кромки дверей. На каждую петлю приходится половина веса двери. Считая, что центр тяжести находится в геометрическом центре двери, рассчитать горизонтальную и вертикальную силы, действующие со стороны петель на двери.
Обсуждение
20.01.2010, 13:32
общий
это ответ
Здравствуйте, Кузьмина Ирина Владимировна.
На основании теоремы о трех силах из рассмотрения подобных треугольников OAB и силового, сторонами которого являются сила тяжести P = mg и реакции нижней и верхней петель R[sub]A[/sub] и R[sub]B[/sub], получаем
P/|AB| = RA/|OA| = RB/|OB|.
В силу симметрии |OA| = |OB|. Кроме того,
|AB| = 210 – 2 • 30 = 150 (см) = 1,5 м,
|OA| = √((45,5)2 + (75)2) ≈ 87,7 (см) = 0,877 м.
Поэтому 27 • 9,81/1,5 = RA/0,877, RA ≈ 155 Н. Реакция RB равна по величине реакции RA и направлена так, как показано на рисунке.
С уважением.
На основании теоремы о трех силах из рассмотрения подобных треугольников OAB и силового, сторонами которого являются сила тяжести P = mg и реакции нижней и верхней петель R[sub]A[/sub] и R[sub]B[/sub], получаем
P/|AB| = RA/|OA| = RB/|OB|.
В силу симметрии |OA| = |OB|. Кроме того,
|AB| = 210 – 2 • 30 = 150 (см) = 1,5 м,
|OA| = √((45,5)2 + (75)2) ≈ 87,7 (см) = 0,877 м.
Поэтому 27 • 9,81/1,5 = RA/0,877, RA ≈ 155 Н. Реакция RB равна по величине реакции RA и направлена так, как показано на рисунке.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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