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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: на тренировках по ушу спортсмен массой 75 кг выполняет хлопок внешней стороны стопы по ладони перед лицом, способом маха-прямая нога движется вертикально до хлопка. Определить максимальный момент импульса, если время подъема прямой ноги 0,2 с. Массу ноги принять равной 1/3 от всей массы.Угол подъема ноги равен 145 градусов. Плечо момента силы вращения бедра принять равным 0,5 с.
Подозреваю, что всё-таки тут и вправду должно быть 0,5 м. Но тут есть и ещё одна проблема с условием - плечо момента силы и масса позволяют найти момент инерции точечной массы, но в общем случае к этому нужно добавить ещё и момент инерции тела относительно центра массы. И в случае ноги это точно соизмеримая величина (но нам не дано данных для её расчёта... можно попробовать принять равномерное распределение массы по всей длине). И ещё такой вопрос - каким считать движение? Тут уж Вам нужно выбрать вариант: 1) Постоянная угловая скорость 2) постоянное угловое ускорение (подозреваю, что имеется ввиду этот вариант, если спрашивается максимальный момент) 3) постоянный момент силы со стороны спортсмена (с поправкой на силу тяжести - но это сложнее рассчитать)
Здравствуйте, Сидорова Наталья! Попробуем разобраться в условии. Массу ноги принимаем m=25 кг. Плечо момента силы (расстояние от оси вращения до центра массы), видимо, равно r=0,5 м Время подъёма ноги t=0,2 с. Угол подъёма [$966$]=145[$186$]=2,53 радиана. Характер движения не уточнён, можем принять его за равноускоренное вращение. Тогда угловая скорость меняется от 0 до [$969$]max за время t, при этом осуществляется поворот на [$966$]=t[$183$]([$969$]max+0)/2=[$969$]maxt/2 отсюда находим максимальную угловую скорость [$969$]max=2[$966$]/t=2[$183$]2,53рад/0,2с=25,3 рад/с Но чтобы найти момент импульса необходимо определить момент инерции, и тут несколько недостаточно данных. Точнее, данных достаточно, если массу предположить точечной. В этом случае момент инерции J=mr2=25кг[$183$](0,5м)2=6,25 кг[$183$]м2 и момент импульса равен L=[$969$]maxJ=6,25кг[$183$]м2[$183$]25,3рад/с=158 кг[$183$]м2/с=158 Дж[$183$]с
Но на самом деле это лишь момент импульса, связанный с движением центра массы. К нему ещё добавляется момент импульса, связанный с вращением относительно центра массы, однако нам не дано распределение массы ноги по её длине. Если предположить равномерное распределение массы (а ось вращения принять находящейся на конце), то общая длина будет l=2r (поскольку центр массы очевидно в середине длины) и линейная плотность равна m/l=m/2r Далее есть 2 варианта определения полного момента инерции (которые, как мы сейчас убедимся, дают идентичный результат): а) складываем момент инерции точечной массы и момент инерции относительно центра массы J=mr2+-rr[$8747$](m/2r)x2dx=mr2+[$8747$](m/6r)(r3-(-r)3)=mr2+mr2/3=(4/3)mr2 б) интегрируем сразу относительно оси на конце J=02r[$8747$](m/2r)x2dx=(m/6r)[$183$](2r)3=(4/3)mr2 В этом случае момент импульса также на треть больше, чем в предположении точечной массы: L=[$969$]maxJ=(4/3)[$969$]maxmr2=211 Дж[$183$]с
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