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Консультация № 130902
06.04.2008, 23:07
0.00 руб.
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Здравствуйте, уважаемые эксперты, помогите пожалуйста с задачей
винт аэросаней вращется с частотой 360 минут в минус первой степени. скорость поступательного движения аэросаней равна 54 км/ч. с какой скоростью движется один из концов винта, если радиус винта равен 1 м?
винт аэросаней вращется с частотой 360 минут в минус первой степени. скорость поступательного движения аэросаней равна 54 км/ч. с какой скоростью движется один из концов винта, если радиус винта равен 1 м?
Обсуждение
07.04.2008, 03:37
общий
это ответ
Здравствуйте, Николай Фаворисович Басманов!
Прежде всего переводим числа, заданные в условии, в единицы СИ; поскольку почти всегда приходится это делать, полезно запомнить готовые формулы: окружная скорость V<sub>окр</sub> вращающегося тела (в данном случае винта), если задан радиус R в метрах и частота (она же скорость) вращения n в мин<sup>-1</sup>("оборотах в минуту"): V<sub>окр</sub> = (π*R*n)/30 (1), или, в нашем случае: V<sub>окр</sub> = (3.14*1*360)/30 = 37.7 м/с. Формула для перевода км/ч в м/с: V<sub>(м/с)</sub> = V<sub>(км/ч)</sub>/3.6, или, в нашем случае: V<sub>пост(м/с)</sub> = 54/3.6 = 15 м/с. Поскольку скорости V<sub>окр</sub> и V<sub>пост</sub> взаимно перпендикулярны, результирующая скорость одного из концов винта V<sub>окр</sub> = √(V<sub>окр</sub><sup>2</sup> + V<sub>пост</sub><sup>2</sup>) = √(37.7<sup>2</sup> + 15<sup>2</sup>) = 40.6 м/с.
Прежде всего переводим числа, заданные в условии, в единицы СИ; поскольку почти всегда приходится это делать, полезно запомнить готовые формулы: окружная скорость V<sub>окр</sub> вращающегося тела (в данном случае винта), если задан радиус R в метрах и частота (она же скорость) вращения n в мин<sup>-1</sup>("оборотах в минуту"): V<sub>окр</sub> = (π*R*n)/30 (1), или, в нашем случае: V<sub>окр</sub> = (3.14*1*360)/30 = 37.7 м/с. Формула для перевода км/ч в м/с: V<sub>(м/с)</sub> = V<sub>(км/ч)</sub>/3.6, или, в нашем случае: V<sub>пост(м/с)</sub> = 54/3.6 = 15 м/с. Поскольку скорости V<sub>окр</sub> и V<sub>пост</sub> взаимно перпендикулярны, результирующая скорость одного из концов винта V<sub>окр</sub> = √(V<sub>окр</sub><sup>2</sup> + V<sub>пост</sub><sup>2</sup>) = √(37.7<sup>2</sup> + 15<sup>2</sup>) = 40.6 м/с.
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