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Консультация № 202226
26.02.2022, 10:12
0.00 руб.
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1
Здравствуйте! У меня возникли сложности с таким вопросом:
Шар массой m1 , летящий со скоростью 1 v , сталкивается с неподвижным шаром
массой m2 . После удара шары разлетаются под углом ? друг к другу. Удар
абсолютно упругий, столкновение происходит в горизонтальной плоскости.
Найти скорости шаров 1 u и 2 u после удара.
m1=100г; m2=300г; v1=15м/с; a=120градусов
Шар массой m1 , летящий со скоростью 1 v , сталкивается с неподвижным шаром
массой m2 . После удара шары разлетаются под углом ? друг к другу. Удар
абсолютно упругий, столкновение происходит в горизонтальной плоскости.
Найти скорости шаров 1 u и 2 u после удара.
m1=100г; m2=300г; v1=15м/с; a=120градусов
Обсуждение
03.03.2022, 18:28
общий
Ответ N1 НЕправильный. Второй шар никак не может отлететь быстрее, чем налетел первый шар, потому что второй шар втрое массивнее первого!
Дано: m1 = 0,1 кг, m2 = 0,3 кг, V1 = 15 м/с , [$945$] = 120° = 2·[$960$]/3 рад.
Решение (я стараюсь использовать имена переменных, как в Ответе для облегчения сравнения):
Импульс первого шара до соударения: P0 = m1·V1 = 0,1·15 = 1,5 кг·м/с.
Импульсы первого и второго шаров после соударения P1 = m1·U1 , P2 = m2·U2 соответственно.
По теореме косинусов для параллелограмма геометрической суммы 2х векторов:
P02 = P12 + P22 + 2·P1·P2·cos([$945$]) .
По Закону сохранения кинетической энергии :
m1·V12 / 2 = m1·U12 / 2 + m2·U22 / 2
Умножаем обе части этого уравнения на 2·m1 и получаем P02 = P12 + P22·m1 / m2
Я люблю вычислять и решать системы уравнений в популярном приложении Маткад (ссылка) . Маткад избавляет меня от ошибок. Маткад-скриншот с чертежом прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ: скорости шаров после удара равны 11,34 м/с и 5,67 м/с соответственно.
Дано: m1 = 0,1 кг, m2 = 0,3 кг, V1 = 15 м/с , [$945$] = 120° = 2·[$960$]/3 рад.
Решение (я стараюсь использовать имена переменных, как в Ответе для облегчения сравнения):
Импульс первого шара до соударения: P0 = m1·V1 = 0,1·15 = 1,5 кг·м/с.
Импульсы первого и второго шаров после соударения P1 = m1·U1 , P2 = m2·U2 соответственно.
По теореме косинусов для параллелограмма геометрической суммы 2х векторов:
P02 = P12 + P22 + 2·P1·P2·cos([$945$]) .
По Закону сохранения кинетической энергии :
m1·V12 / 2 = m1·U12 / 2 + m2·U22 / 2
Умножаем обе части этого уравнения на 2·m1 и получаем P02 = P12 + P22·m1 / m2
Я люблю вычислять и решать системы уравнений в популярном приложении Маткад (ссылка) . Маткад избавляет меня от ошибок. Маткад-скриншот с чертежом прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ: скорости шаров после удара равны 11,34 м/с и 5,67 м/с соответственно.
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