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Консультация № 169824
24.06.2009, 17:07
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Здравствуйте,уважаемые эксперты.помогите,пожалуйста,решить задачу:
какой должен быть коэффициент трения резины о внутреннюю поверхность конуса с углом у вершины 2[$946$],чтобы мотоциклист мог двигаться по окружности радиусом R с угловой скоростью [$969$].
заранее благодарен.
какой должен быть коэффициент трения резины о внутреннюю поверхность конуса с углом у вершины 2[$946$],чтобы мотоциклист мог двигаться по окружности радиусом R с угловой скоростью [$969$].
заранее благодарен.
Обсуждение
25.06.2009, 06:44
общий
Здравствуйте, уважаемый G-buck!
Перейдем в систему отсчета, вращающуюся вокруг оси конуса с угловой скоростью мотоциклиста. Тогда задача похожа на известную о соскальзывании бруска с наклонной поверхности, только добавляется еще неинерциальная центробежная сила.
Используя эту подсказку, можете сами взяться решить задачу.
На всякий случай, привожу свой вариант решения. Давно не решал физику, поэтому в ответе не уверен.
Сила реакции опоры
N = m*g*sin(β) + m*ω^2*R*cos(β)
Сила трения
F = k*N
Разложение сил в направлении образующей конуса
k*[m*g*sin(β) + m*ω^2*R*cos(β)] + m*ω^2*R*sin(β) = m*g*cos(β)
k = [g*cos(β) - ω^2*R*sin(β)]/[g*sin(β) + ω^2*R*cos(β)]
Перейдем в систему отсчета, вращающуюся вокруг оси конуса с угловой скоростью мотоциклиста. Тогда задача похожа на известную о соскальзывании бруска с наклонной поверхности, только добавляется еще неинерциальная центробежная сила.
Используя эту подсказку, можете сами взяться решить задачу.
На всякий случай, привожу свой вариант решения. Давно не решал физику, поэтому в ответе не уверен.
Сила реакции опоры
N = m*g*sin(β) + m*ω^2*R*cos(β)
Сила трения
F = k*N
Разложение сил в направлении образующей конуса
k*[m*g*sin(β) + m*ω^2*R*cos(β)] + m*ω^2*R*sin(β) = m*g*cos(β)
k = [g*cos(β) - ω^2*R*sin(β)]/[g*sin(β) + ω^2*R*cos(β)]
Форма ответа
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