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Консультация № 203164
20.09.2022, 21:05
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
Помогите решить задачу. Спасибо.
Частица движется так, что её радиус-вектор зависит от времени по закону
где – постоянные величины,
– единичные орты в декартовой системе координат.
Через сколько секунд ускорение частицы окажется перпендикулярной оси z, если с. А = 3 м, В = 4 м, рад/с.
а) 0,032 с; б) 0,132 с; в) 0,232 с; г) 0,432 с; д) 0,632 с.
Помогите решить задачу. Спасибо.
Частица движется так, что её радиус-вектор зависит от времени по закону
где – постоянные величины,
– единичные орты в декартовой системе координат.
Через сколько секунд ускорение частицы окажется перпендикулярной оси z, если с. А = 3 м, В = 4 м, рад/с.
а) 0,032 с; б) 0,132 с; в) 0,232 с; г) 0,432 с; д) 0,632 с.
Прикрепленные файлы:
Обсуждение
21.09.2022, 14:26
общий
Адресаты:
Здравствуйте! Сегодня мне некогда решать Вашу задачу, ограничусь подсказкой:
Условие "ускорение частицы окажется перпендикулярной оси z" означает равенство нулю вертикальной составляющей ускорения. Этот пункт очень упрощает решение, потому что составляющие по осям OX и OY можно игнорировать.
Вертикальную составляющую пути rz(t) = B·(t/[$964$])3 - A·(t/[$964$])5 дифференцируем 2жды по t-аргументу, приравниваем полученную вертикаль-составляющую ускорения к нулю. Решаем уравнение и получаем искомые секунды.
Посмотрите Решения задач, похожих на Вашу: rfpro.ru/question/201520 (Ссылка);
rfpro.ru/question/199533 ; rfpro.ru/question/197839 ; rfpro.ru/question/197143 ;
rfpro.ru/question/197840 ; rfpro.ru/question/197837 ; rfpro.ru/question/196430 ;
rfpro.ru/question/199679 ; rfpro.ru/question/199676 ; rfpro.ru/question/198337 .
Дальше сами справитесь?
Если Вы ещё нуждаетесь в помощи, то замените пожалуйста свой неприлично-длинный ник на скромный и уникальный для облегчения общения с Вами.
Условие "ускорение частицы окажется перпендикулярной оси z" означает равенство нулю вертикальной составляющей ускорения. Этот пункт очень упрощает решение, потому что составляющие по осям OX и OY можно игнорировать.
Вертикальную составляющую пути rz(t) = B·(t/[$964$])3 - A·(t/[$964$])5 дифференцируем 2жды по t-аргументу, приравниваем полученную вертикаль-составляющую ускорения к нулю. Решаем уравнение и получаем искомые секунды.
Посмотрите Решения задач, похожих на Вашу: rfpro.ru/question/201520 (Ссылка);
rfpro.ru/question/199533 ; rfpro.ru/question/197839 ; rfpro.ru/question/197143 ;
rfpro.ru/question/197840 ; rfpro.ru/question/197837 ; rfpro.ru/question/196430 ;
rfpro.ru/question/199679 ; rfpro.ru/question/199676 ; rfpro.ru/question/198337 .
Дальше сами справитесь?
Если Вы ещё нуждаетесь в помощи, то замените пожалуйста свой неприлично-длинный ник на скромный и уникальный для облегчения общения с Вами.
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