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Консультация № 118875
16.01.2008, 20:34
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Здравсвуйте эксперты. Очень прошу Вас помогите пожалуйста в решении задачи: Ареометр массой m представляет собой стеклянную колбу, заполненную дробью, соединенной с цилиндрической трубкой с поперечным сечением S. Он помещен в жидкость с плотностью p. Ареометр погружают в жидкость несколько глубже, чем нужно для его
равновесного положения, и затем отпускают. Найдите период свободных гармонических колебаний ареометра. Вязкостью жидкости пренебречь.
равновесного положения, и затем отпускают. Найдите период свободных гармонических колебаний ареометра. Вязкостью жидкости пренебречь.
Обсуждение
Неизвестный
21.01.2008, 04:16
общий
это ответ
Здравствуйте, Xbondx!
На плавающий ареометр действует сила тяжести Р, направленная вертикально вниз, и си-ла Архимеда FA, направленная вертикально вверх. В положении равновесия Р = FA, т.е.
Р = ρ*g*V‘‘, где ρ – плотность жидкости, g – ускорение силы тяжести, V‘‘ = V + S*h – часть объема ареометра, находящаяся в жидкости (V – объем колбы; S*h – объем части цилинд-рической трубки, погруженной в жидкость). Таким образом, в положении равновесия
Р = ρ*g*(V + S*h).
Если погрузить ареометр на глубину х, то результирующая выталкивающая сила
F = F‘‘A– P = ρ*g*(V+S*(h+x)) – P
Или F = ρ*g*(V+S*(h+x)) – ρ*g*(V+S*h) = ρ*g*S*x.
C другой стороны, F = kx, следовательно, k = ρ*g*S. Подставив выражение для k в форму-лу для периода колебаний Т = 2*π*√(m/k) получим
Т = 2*π*√((m/(ρ*g*S))
На плавающий ареометр действует сила тяжести Р, направленная вертикально вниз, и си-ла Архимеда FA, направленная вертикально вверх. В положении равновесия Р = FA, т.е.
Р = ρ*g*V‘‘, где ρ – плотность жидкости, g – ускорение силы тяжести, V‘‘ = V + S*h – часть объема ареометра, находящаяся в жидкости (V – объем колбы; S*h – объем части цилинд-рической трубки, погруженной в жидкость). Таким образом, в положении равновесия
Р = ρ*g*(V + S*h).
Если погрузить ареометр на глубину х, то результирующая выталкивающая сила
F = F‘‘A– P = ρ*g*(V+S*(h+x)) – P
Или F = ρ*g*(V+S*(h+x)) – ρ*g*(V+S*h) = ρ*g*S*x.
C другой стороны, F = kx, следовательно, k = ρ*g*S. Подставив выражение для k в форму-лу для периода колебаний Т = 2*π*√(m/k) получим
Т = 2*π*√((m/(ρ*g*S))
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