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Консультация № 197132
19.11.2019, 14:35
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1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Динамика тела:
Самолет описывает петлю Нестерова с радиусом r=180м. Какова должна быть наименьшая скорость самолета, чтобы летчик не оторвался от сиденья в верхней части петли?
Динамика тела:
Самолет описывает петлю Нестерова с радиусом r=180м. Какова должна быть наименьшая скорость самолета, чтобы летчик не оторвался от сиденья в верхней части петли?
Обсуждение
21.11.2019, 17:19
общий
это ответ
Здравствуйте, stailes!
Дано : радиус r=180м
Вычислить скорость V .
Решение : Если бы не было силы земного тяготения, то в случае прямолинейного и равномерного движения лётчик ощущал бы невесомость.
Однако, траектория самолёта в фигуре "петля Нестерова" с радиусом петли r=180 м создаёт силу, величиной как у центростремительной силы
Fц = m·V2/r , но направленную не к центру петли, а в противоположную сторону, то есть ОТ центра вращения (раньше эту силу называли центробежной).
В верхней части петли эта сила направлена вертикально вверх и должна уравновешиваться силой земного притяжения
Fп = m·g , чтобы лётчик при минимальной скорости V самолёта не оторвался от сиденья.
Здесь m - масса лётчика, g=9,81 м/с2 - ускорение земного притяжения.
Решая уравнение m·V2/r = m·g
получаем значение скорости V = [$8730$](g·r) = [$8730$](9,81·180) = 42 м/с
Ответ: наименьшая скорость самолета равна 42 м/с.
Дано : радиус r=180м
Вычислить скорость V .
Решение : Если бы не было силы земного тяготения, то в случае прямолинейного и равномерного движения лётчик ощущал бы невесомость.
Однако, траектория самолёта в фигуре "петля Нестерова" с радиусом петли r=180 м создаёт силу, величиной как у центростремительной силы
Fц = m·V2/r , но направленную не к центру петли, а в противоположную сторону, то есть ОТ центра вращения (раньше эту силу называли центробежной).
В верхней части петли эта сила направлена вертикально вверх и должна уравновешиваться силой земного притяжения
Fп = m·g , чтобы лётчик при минимальной скорости V самолёта не оторвался от сиденья.
Здесь m - масса лётчика, g=9,81 м/с2 - ускорение земного притяжения.
Решая уравнение m·V2/r = m·g
получаем значение скорости V = [$8730$](g·r) = [$8730$](9,81·180) = 42 м/с
Ответ: наименьшая скорость самолета равна 42 м/с.
5
Добрый день. Не сразу заметил ваш ответ т.к мы уже разобрались с данным вопросом. Спасибо за решение, по крайней мере мы смогли проверить правильность нашего решения.)
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