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Консультация № 180043
26.09.2010, 13:05
45.00 руб.
0
1
1
Грузик, привязанный к шнуру длиной L=50 см, описывает окружность в горизонтальной плоскости. Какой угол (в градусах) образует шнур с вертикалью, если частота вращения n=1 c-1?
Обсуждение
26.09.2010, 14:47
общий
это ответ
Здравствуйте, Посетитель - 337752.
Прошу прощения, но в своем решении я обозначил длину нити маленькой буквой l. так, как выполнил рисунок. На рисунке большая L - это длина окружности - в процессе решения не пригодилась.
Дано:
l=50 см = 0,5 м
n= 1 c-1
Найти: [$945$]
Решение:
(см.рис.)
Начнем с центростремительного (нормального) ускорения
an=v2/R (1)
Кроме того, как видно из рисунка
an/g = R/(l*cos[$945$])
Следовательно
an= g*R/(l*cos[$945$]) (2)
g - ускорение свободного падения, R - радиус окружности, описываемой грузиком.
Приравняем правые части выражений (1) и (2) и выразим квадрат скорости движения
v2 = g*R2/(l*cos[$945$]) (3)
Линейная скорость грузика связана с угловой скоростью и частотой вращения следующими формулами
v = [$969$]*R = 2*pi*n*R (4)
Тогда
g/cos[$945$] = 4*pi2*n2
Следовательно
cos[$945$] = g/(4*pi2*n2*l)
после подстановки получаем
cos[$945$]~0.5
[$8658$] [$945$]~60[$186$]
Удачи
Прошу прощения, но в своем решении я обозначил длину нити маленькой буквой l. так, как выполнил рисунок. На рисунке большая L - это длина окружности - в процессе решения не пригодилась.
Дано:
l=50 см = 0,5 м
n= 1 c-1
Найти: [$945$]
Решение:
(см.рис.)
Начнем с центростремительного (нормального) ускорения
an=v2/R (1)
Кроме того, как видно из рисунка
an/g = R/(l*cos[$945$])
Следовательно
an= g*R/(l*cos[$945$]) (2)
g - ускорение свободного падения, R - радиус окружности, описываемой грузиком.
Приравняем правые части выражений (1) и (2) и выразим квадрат скорости движения
v2 = g*R2/(l*cos[$945$]) (3)
Линейная скорость грузика связана с угловой скоростью и частотой вращения следующими формулами
v = [$969$]*R = 2*pi*n*R (4)
Тогда
g/cos[$945$] = 4*pi2*n2
Следовательно
cos[$945$] = g/(4*pi2*n2*l)
после подстановки получаем
cos[$945$]~0.5
[$8658$] [$945$]~60[$186$]
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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