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Консультация № 202776
11.05.2022, 08:32
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Диск вращается с угловым ускорением, зависимость от времени которого задается графиком. Найти максимальную угловую скорость диска в интервале времени от 0 до 4 с, если 3 с–2. (данные во вложении)
а) 3 с–1; б) 5 с–1; в) 7 с–1; г) 9 с–1; д) 11 с–1;
Диск вращается с угловым ускорением, зависимость от времени которого задается графиком. Найти максимальную угловую скорость диска в интервале времени от 0 до 4 с, если 3 с–2. (данные во вложении)
а) 3 с–1; б) 5 с–1; в) 7 с–1; г) 9 с–1; д) 11 с–1;
Прикрепленные файлы:
Обсуждение
11.05.2022, 09:25
общий
11.05.2022, 15:30
это ответ
Здравствуйте Sema !
Дано: График раскрутки, максимальное угловое ускорение [$949$]max = 3 c-2 . Длительность разгона T = 4 с.
Вычислить максимальную угловую скорость в интервале времени от 0 до T .
Решение : По определению Угловое ускорение - это производная угловой скорости по времени :
[$949$] = [$969$]'t = d[$949$] / dt .
Поэтому чтобы получить угловую скорость, надо проинтегрировать данное нам Угловое ускорение:
[$969$]max = 0T[$8747$][$949$](t)·dt
В нашей задаче функция [$949$](t) задана графиком, и её зависимость - кусочно-линейная. Это позволяет обойтись без применения интегралов, а просто вычислить площадь трапеции, которую я выделил голубой заливкой на увеличенной копии Вашего графика. График прилагаю ниже.
Если заметить, что треугольники OHA и BCD равны, то площать трапеции равна площади прямоугольника OHBD ,
то есть искомая максимальная угловая скорость [$969$]max = OH·OD = [$949$]max·3 = 3·3 = 9 рад/с .
Значит, правильный Ответ : г) 9 с-1.
Дано: График раскрутки, максимальное угловое ускорение [$949$]max = 3 c-2 . Длительность разгона T = 4 с.
Вычислить максимальную угловую скорость в интервале времени от 0 до T .
Решение : По определению Угловое ускорение - это производная угловой скорости по времени :
[$949$] = [$969$]'t = d[$949$] / dt .
Поэтому чтобы получить угловую скорость, надо проинтегрировать данное нам Угловое ускорение:
[$969$]max = 0T[$8747$][$949$](t)·dt
В нашей задаче функция [$949$](t) задана графиком, и её зависимость - кусочно-линейная. Это позволяет обойтись без применения интегралов, а просто вычислить площадь трапеции, которую я выделил голубой заливкой на увеличенной копии Вашего графика. График прилагаю ниже.
то есть искомая максимальная угловая скорость [$969$]max = OH·OD = [$949$]max·3 = 3·3 = 9 рад/с .
Значит, правильный Ответ : г) 9 с-1.
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