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Консультация № 149596
05.11.2008, 22:39
0.00 руб.
0
1
1
решите задачу:
Сплошной маховик массой 20 кг и радиусом 120 мм вращается, совершая 600 об/мин. С какой силой нужно прижать к нему тормозную колодку, чтобы он остановился за 3 с, если коэффициент трения между колодкой и маховиком равен 0,1?
Сплошной маховик массой 20 кг и радиусом 120 мм вращается, совершая 600 об/мин. С какой силой нужно прижать к нему тормозную колодку, чтобы он остановился за 3 с, если коэффициент трения между колодкой и маховиком равен 0,1?
Обсуждение
08.11.2008, 06:35
общий
это ответ
Здравствуйте, Маевская Мария Андреевна!
Окружная скорость V на поверхности маховика равна: V = π*R*n/30 (1), где R - радиус маховика, n - число оборотов в минуту. Чтобы остановить маховик за время t, необходимо тангенциальное ускорение aτ = V/t, с учётом (1) aτ = π*R*n/(30*t) (2). Приложенная к поверхности касательная сила F создаёт тормозной момент Mт = F*R (3), вызывающий угловое ускорение ε = M/J = F*R/J (4), где J - момент инерции маховика, а у точек на поверхности маховика - тангенциальное ускорение aτ = ε*R = F*R2/J (5). Момент инерции J сплошного маховика радиусом R и массой m равен: J = m*R2/2 (6) (см. здесь); подставляя это значение J в (5), после сокращений: aτ = 2*F/m (7). Приравняв (7) и (2), и решая относительно F, имеем: F = m*π*R*n/(60*t) (8). Поскольку F - сила трения, равная Fпр*k, где Fпр - сила прижатия тормозной колодки, k - коэффициент трения между колодкой и маховиком, окончательно: Fпр = m*π*R*n/(60*t*k) = 20*π*0.12*600/(60*3*0.1) = 251 Н.
Окружная скорость V на поверхности маховика равна: V = π*R*n/30 (1), где R - радиус маховика, n - число оборотов в минуту. Чтобы остановить маховик за время t, необходимо тангенциальное ускорение aτ = V/t, с учётом (1) aτ = π*R*n/(30*t) (2). Приложенная к поверхности касательная сила F создаёт тормозной момент Mт = F*R (3), вызывающий угловое ускорение ε = M/J = F*R/J (4), где J - момент инерции маховика, а у точек на поверхности маховика - тангенциальное ускорение aτ = ε*R = F*R2/J (5). Момент инерции J сплошного маховика радиусом R и массой m равен: J = m*R2/2 (6) (см. здесь); подставляя это значение J в (5), после сокращений: aτ = 2*F/m (7). Приравняв (7) и (2), и решая относительно F, имеем: F = m*π*R*n/(60*t) (8). Поскольку F - сила трения, равная Fпр*k, где Fпр - сила прижатия тормозной колодки, k - коэффициент трения между колодкой и маховиком, окончательно: Fпр = m*π*R*n/(60*t*k) = 20*π*0.12*600/(60*3*0.1) = 251 Н.
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