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Консультация № 113912
14.12.2007, 00:29
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Задача из Иродова: Частица массы m движется в некоторой плоскости Р под действием постоянной по модулю силы F, которая поворачивается в этой плоскости с постоянной угдовой скоростью w. Считая, что в момент t=0 частица покоилась, найти
а) модуль ее скорости в зависимости от времени;
б) путь, проходимый частицей между двумя последовательными остановками, и среднюю скорость на этом пути.
все решебники перерыл и не нашел решения к этой задаче.Может вы мне хоть как то поможите))
Приложение:
на тему из механики
а) модуль ее скорости в зависимости от времени;
б) путь, проходимый частицей между двумя последовательными остановками, и среднюю скорость на этом пути.
все решебники перерыл и не нашел решения к этой задаче.Может вы мне хоть как то поможите))
Приложение:
на тему из механики
Обсуждение
Неизвестный
14.12.2007, 04:41
общий
это ответ
Здравствуйте, Hagen!
Fx = F cos(wt) ; Fy = F sin(wt)
Vx = (F/mw) sin(wt); Vy = (F/mw)(1 - cos(wt)) =>
V^2 = (F/mw)^2 * ( 2 - 2 cos(wt) ) = ((F/mw) * 2 sin(wt/2))^2 =>
a) |V| = |2(F/mw)sin(wt/2)|
точки остановок V=0 т.е wt/2 = k*pi или t= 2k*pi/w , где к=0,1,2,...
b) путь S = интеграл от |V|*dt на отрезке [0,2pi/w]
S = 8F/(m w^2)
средняя скорость = S/(2pi/w) = 4F/(pi*m*w)
Fx = F cos(wt) ; Fy = F sin(wt)
Vx = (F/mw) sin(wt); Vy = (F/mw)(1 - cos(wt)) =>
V^2 = (F/mw)^2 * ( 2 - 2 cos(wt) ) = ((F/mw) * 2 sin(wt/2))^2 =>
a) |V| = |2(F/mw)sin(wt/2)|
точки остановок V=0 т.е wt/2 = k*pi или t= 2k*pi/w , где к=0,1,2,...
b) путь S = интеграл от |V|*dt на отрезке [0,2pi/w]
S = 8F/(m w^2)
средняя скорость = S/(2pi/w) = 4F/(pi*m*w)
Форма ответа
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