Задача №31.28
Условие
Материальная точка A под действием силы тяжести движется по шероховатой винтовой поверхности, ось которой Oz вертикальна; поверхность задана уравнением z=aφ+f(r); коэффициент трения точки о поверхность равен k. Найти условие, при котором движение точки происходит на постоянном расстоянии от оси AB=r0, т.е. происходит по винтовой линии, а также найти скорость этого движения, предполагая, что a=const. Указание. Для решения задачи целесообразно воспользоваться системой естественных осей, проектируя уравнение движения на касательную, главную нормаль и бинормаль винтовой линии в точке A. На рисунке угол между нормальной компонентой N реакции винтовой поверхности и ортом главной нормали n° обозначен через β.Решение
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1.1
1.2
1.3
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1.5
2.1
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3.1
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24.1
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27.1
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28.1
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30.1
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31.1
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32.1
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33.1
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34.1
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38.1
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39.1
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43.1
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46.1
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47.1
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48.1
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49.1
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55.2
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