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Здравствуйте! У меня возникли сложности с таким вопросом: На массивную тележку, движущуюся вверх по наклонной плоскости со скоростью u =0,05м/с , падает мешок с песком, движущийся по вертикали со скоростью v = 0,75м/с. Наклонная плоскость образует с горизонтом угол a=30 . При каком коэффициенте трения скольжения мешок не будет проскальзывать по тележке? Длительность соударения очень мала.
Здравствуйте, irinasoboleva76! Принимая, что поверхность тележки параллельна наклонной плоскости, скорость мешка относительно неё раскладывается на следующие составляющие: Параллельно поверхности: vx=v[$183$]sin[$945$]+u Перпендикулярно поверхности: vy=v[$183$]cos[$945$] При коротком времени соударения трудно говорить о силах взаимодействия - поэтому лучше говорить об интеграле силы по времени взаимодействия (что соответствует импульсу) Так при неупругом ударе сила реакции, перпендикулярная поверхности, гасит перпендикулярную поверхности составляющую импульса T[$8747$]Fнdt=mvy где m - масса мешка Если коэффициент трения скольжения равен [$956$], максимальное значение силы трения составляет Fт=[$956$]Fн Максимальный импульс, направленный параллельно поверхности, который за время удара может погасить сила трения равен T[$8747$]Fтdt=T[$8747$][$956$]Fнdt=[$956$][$183$]T[$8747$]Fнdt=[$956$]mvy С другой стороны, импульс, направленный вдоль поверхности равен mvx, поэтому условие минимального коэффициента трения, при котором мешок не будет скользить T[$8747$]Fтdt=mvx [$956$]mvy=mvx [$956$]=vx/vy=(v[$183$]sin[$945$]+u)/(v[$183$]cos[$945$])=0,654
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