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Консультация № 186593
11.09.2012, 01:01
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Колесо радиуса R = 10 см вращается согласно уравнению φ(t)=7+4t+3t2 . Найти для точек находящихся на ободе колеса в момент времени t = 5 с: угловой путь, угловую скорость, угловое ускорение, линейную скорость, нормальное ускорение, тангенциальное ускорение, полное ускорение.
Колесо радиуса R = 10 см вращается согласно уравнению φ(t)=7+4t+3t2 . Найти для точек находящихся на ободе колеса в момент времени t = 5 с: угловой путь, угловую скорость, угловое ускорение, линейную скорость, нормальное ускорение, тангенциальное ускорение, полное ускорение.
Обсуждение
11.09.2012, 06:24
общий
это ответ
Здравствуйте, Massimo!
Угловой путь.
[$966$](5)=7+4*5+3*52=102 (рад)
Угловая скорость.
Скорость точки - это производная пути по времени
v=[$969$]*R=R*d[$966$]/dt=R*(7+4t+3t2)'=R*(4+6t), где
[$969$]=d[$966$]/dt - угловая скорость
[$969$]=4+6t
[$969$](5)=4+6*5=34 (рад/с)
Линейная скорость.
v=R*(4+6t)
v=0.1*(4+6*5)=3.4 (м/с)
Угловое ускорение.
Тангенсальное ускорение - это первая производная скорости:
a[$964$]=dv/dt=R*(4+6t)'=6R
a[$964$]=[$949$]*R, где [$949$] - угловое ускорение
[$949$]=a[$964$]/R=6 (рад/с2)
Тангенсальное ускорение.
a[$964$]=6R=6*0.1=0.6 (м/с2)
Нормальное ускорение.
Нормальное ускорение вычисляется по формуле:
an=v2/R=[$969$]2*R=(4+6t)2*R
an=(4+6*5)2*0.1=115.6 (м/с2)
Полное ускорение.
a=[$8730$](a[$964$]2+an2)=[$8730$](0.62+115.62)[$8776$]115.6 (м/с2)
Будут вопросы обращайтесь в минифорум.
Удачи
Угловой путь.
[$966$](5)=7+4*5+3*52=102 (рад)
Угловая скорость.
Скорость точки - это производная пути по времени
v=[$969$]*R=R*d[$966$]/dt=R*(7+4t+3t2)'=R*(4+6t), где
[$969$]=d[$966$]/dt - угловая скорость
[$969$]=4+6t
[$969$](5)=4+6*5=34 (рад/с)
Линейная скорость.
v=R*(4+6t)
v=0.1*(4+6*5)=3.4 (м/с)
Угловое ускорение.
Тангенсальное ускорение - это первая производная скорости:
a[$964$]=dv/dt=R*(4+6t)'=6R
a[$964$]=[$949$]*R, где [$949$] - угловое ускорение
[$949$]=a[$964$]/R=6 (рад/с2)
Тангенсальное ускорение.
a[$964$]=6R=6*0.1=0.6 (м/с2)
Нормальное ускорение.
Нормальное ускорение вычисляется по формуле:
an=v2/R=[$969$]2*R=(4+6t)2*R
an=(4+6*5)2*0.1=115.6 (м/с2)
Полное ускорение.
a=[$8730$](a[$964$]2+an2)=[$8730$](0.62+115.62)[$8776$]115.6 (м/с2)
Будут вопросы обращайтесь в минифорум.
Удачи
5
Большое спасибо!!!
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