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Консультация № 195187
09.04.2019, 11:21
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Шар массой m1, летящий со скоростью v1=5 м/с, ударяет неподвижный шар массой m2. Удар прямой, неупругий. Определить скорость и шаров после удара, а также долю ω кинетической энергии летящего шара, израсходованной на увеличение внутренней энергии этих шаров. Рассмотреть два случая: 1) m1=2 кг, m2=8 кг; 2) m1=8 кг, m2=2 кг.
Шар массой m1, летящий со скоростью v1=5 м/с, ударяет неподвижный шар массой m2. Удар прямой, неупругий. Определить скорость и шаров после удара, а также долю ω кинетической энергии летящего шара, израсходованной на увеличение внутренней энергии этих шаров. Рассмотреть два случая: 1) m1=2 кг, m2=8 кг; 2) m1=8 кг, m2=2 кг.
Обсуждение
13.04.2019, 14:22
общий
это ответ
Здравствуйте, sasha181999_9!
До столкновения импульс системы, состоящей из двух шаров, равен m1v1, после столкновения -- (m1+m2)u. По закону сохранения импульсы до и после столкновения векторно равны. Тогда m1v1=(m1+m2)u, u=m1v1/((m1+m2). Направление вектора u совпадает с направлением вектора v[sub]1[/sub]. В случае 1) u=2*5/(2+8)=1 (м/с); в случае 2) u=8*5/(8+2)=4 (м/с).
Кинетическая энергия системы шаров до удара составляет m1v12/2, после удара -- (m1+m2)u2/2. На увеличение внутренней энергии шаров после удара расходуется доля, равная [$969$]=(m1v12/2-(m1+m2)u2/2)/(m1v12/2)=1-(m1+m2)u2/(m1v12). В случае 1) [$969$]=1-(2+8)*12/(2*52)=1-10/50=1-1/5=4/5=0,8; в случае 2) [$969$]=1-(8+2)*42/(8*52)=1-160/200=1-4/5=1/5=0,2.
До столкновения импульс системы, состоящей из двух шаров, равен m1v1, после столкновения -- (m1+m2)u. По закону сохранения импульсы до и после столкновения векторно равны. Тогда m1v1=(m1+m2)u, u=m1v1/((m1+m2). Направление вектора u совпадает с направлением вектора v[sub]1[/sub]. В случае 1) u=2*5/(2+8)=1 (м/с); в случае 2) u=8*5/(8+2)=4 (м/с).
Кинетическая энергия системы шаров до удара составляет m1v12/2, после удара -- (m1+m2)u2/2. На увеличение внутренней энергии шаров после удара расходуется доля, равная [$969$]=(m1v12/2-(m1+m2)u2/2)/(m1v12/2)=1-(m1+m2)u2/(m1v12). В случае 1) [$969$]=1-(2+8)*12/(2*52)=1-10/50=1-1/5=4/5=0,8; в случае 2) [$969$]=1-(8+2)*42/(8*52)=1-160/200=1-4/5=1/5=0,2.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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