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Консультация № 200867
19.05.2021, 14:51
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Здравствуйте, уважаемые эксперты! Очень срочно; пожалуйста, ответьте на вопрос:
Человек массой m = 60 кг стоит на корме лодки M = 40 кг и длиной L = 10 м, которая причалила к пристани (точка O). Расстояние от носа лодки до ее центра масс по горизонтали l1 = 6 м. Человек переходит на нос лодки. Определите расстояние на которое сместится центр масс системы. Ответ дайте в метрах.
Человек массой m = 60 кг стоит на корме лодки M = 40 кг и длиной L = 10 м, которая причалила к пристани (точка O). Расстояние от носа лодки до ее центра масс по горизонтали l1 = 6 м. Человек переходит на нос лодки. Определите расстояние на которое сместится центр масс системы. Ответ дайте в метрах.
Обсуждение
19.05.2021, 15:52
общий
Считаем лодку привязанной к пристани и не в состоянии двигаться (в противном случае положение центра масс системы "человек+лодка" останется неизменным).
По определению координаты центра масс системы (например, до перехода) равны: r= (m1*r1 + m2*r2)/(m1+m2), где m1 и m2 - массы человека и лодки, а r1 и r2 - их координаты (по сути, векторы с началом в начале координат).
Аналогично, после перехода (использую заглавные буквы): R= (m1*R1 + m2*R2)/(m1+m2)
Вычитаю одно из другого: R-r = (m1*R1 + m2*R2)/(m1+m2) - (m1*r1 + m2*r2)/(m1+m2) = m1*(R1 - r1)/(m1+m2), т.к. лодка была неподвижна и r2=R2
или в терминах этой задачи = m*L/(m + M), т.е. даже не зависит от положения центр масс лодки.
Если подставить числа, то получается 6 м, т.е. центр тяжести "человек + лодка" сместится на 6 метров.
По определению координаты центра масс системы (например, до перехода) равны: r= (m1*r1 + m2*r2)/(m1+m2), где m1 и m2 - массы человека и лодки, а r1 и r2 - их координаты (по сути, векторы с началом в начале координат).
Аналогично, после перехода (использую заглавные буквы): R= (m1*R1 + m2*R2)/(m1+m2)
Вычитаю одно из другого: R-r = (m1*R1 + m2*R2)/(m1+m2) - (m1*r1 + m2*r2)/(m1+m2) = m1*(R1 - r1)/(m1+m2), т.к. лодка была неподвижна и r2=R2
или в терминах этой задачи = m*L/(m + M), т.е. даже не зависит от положения центр масс лодки.
Если подставить числа, то получается 6 м, т.е. центр тяжести "человек + лодка" сместится на 6 метров.
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