滑轮组如何受力分析的问题?

2025-03-15 17:51:36
推荐回答(1个)
回答1:

LZ您好

您的问题是两个问题。

  • 考虑绳重

不以滑轮组,就讨论一个定滑轮。

显然,您拉的这一段绳子(长度为u)重力向下,它会帮你拉另一段绑重物的绳子。

所以在匀速运动的情况下,将有受力平衡

F+G(绳)u/L=G(绳)(L-u-πR)/L+G重 [假设方向垂直向下]

而u显然是一个关于t的函数,您越拉绳子需要的力F就越小。

所以这个F最后会得到一个关于t的函数。

现在放回滑轮组,结论就简单了

设滑轮组中,从滑轮或者重物出发,向下的绳子长u

则F+G(绳)u/L=G(绳)(L-u-S)/L+G重

而u和S具体多长,那就是数学几何的问题了(嗯,和公切线长,弧长有关呢)

  • 考虑摩擦

请注意滑轮组的摩擦是滑轮与轮轴的摩擦(不是绳子与滑轮的摩擦!绳子与滑轮的摩擦是有益摩擦,他不存在则绳子在滑轮上打滑。)这部分摩擦力应加到重物上(同被多段绳子分摊)

  • 注意,上述情况建立的前提是匀速运动,如果是匀加速拉滑轮,还要考虑滑轮自身转动惯量(克服惯性问题~)等。

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