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Консультация № 174302
16.11.2009, 22:31
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Помогите с решением задачки, плз
С наклонной плоскости высотой h=3м скатывается без трения однородный цилиндр. Найдите скорость поступательного движения цилиндра у основания наклонной плоскости и расстояние, которое пройдёт цилиндр от основания наклонной плоскости до полной остановки, двигаясь по горизонтальной поверхности. Коэффициент трения при движении по горизонтальной поверхности равен 0,1.
Заранее бооольшое спасибо!
С наклонной плоскости высотой h=3м скатывается без трения однородный цилиндр. Найдите скорость поступательного движения цилиндра у основания наклонной плоскости и расстояние, которое пройдёт цилиндр от основания наклонной плоскости до полной остановки, двигаясь по горизонтальной поверхности. Коэффициент трения при движении по горизонтальной поверхности равен 0,1.
Заранее бооольшое спасибо!
Обсуждение
16.11.2009, 23:19
общий
это ответ
Здравствуйте, Михай64766.
Дано:
h=3 м
[$956$]=0,1
Найти:
v, l
Решение:
Согласно закону сохранения механической энергии
Еп=Ек (1)
Еп=mgh (2)
Ек=Ек пост + Ек вр = mv2/2 + J[$969$]2/2 (3)
Момент инерции цилиндра
J=mR2/2 (4)
Квадрат угловой скорости
[$969$]2=v2/R2 (5)
Следовательно (подставим (4) и (5) в (3))
Ек=(3/4)*mv2 (6)
Подставим (2) и (6) в (1) и выразим v
v=[$8730$]((4/3)*g*h)=6,3 м/с
Далее
Работа силы трения равна изменению механической энергии, т.е., поскольку в конце пути цилиндр останавливается, следовательно
А=Е
Тогда
[$956$]*mg*l = mg*h
Следовательно
l=h/[$956$]=3/0.1=30 м
Удачи
Дано:
h=3 м
[$956$]=0,1
Найти:
v, l
Решение:
Согласно закону сохранения механической энергии
Еп=Ек (1)
Еп=mgh (2)
Ек=Ек пост + Ек вр = mv2/2 + J[$969$]2/2 (3)
Момент инерции цилиндра
J=mR2/2 (4)
Квадрат угловой скорости
[$969$]2=v2/R2 (5)
Следовательно (подставим (4) и (5) в (3))
Ек=(3/4)*mv2 (6)
Подставим (2) и (6) в (1) и выразим v
v=[$8730$]((4/3)*g*h)=6,3 м/с
Далее
Работа силы трения равна изменению механической энергии, т.е., поскольку в конце пути цилиндр останавливается, следовательно
А=Е
Тогда
[$956$]*mg*l = mg*h
Следовательно
l=h/[$956$]=3/0.1=30 м
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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