齿轮齿数比的问题
- 时间:2020-04-06 17:58:42
- 分类:数学世界
- 阅读:147 次
有甲、乙、丙三个互相咬合的齿轮,当甲齿轮转了2圈时,乙齿轮正好转了3圈,丙齿轮正好转了4圏,这三个齿轮齿数之比是多少?
分析:齿数越多,转的圈数越少;齿数越少,转的圈数越多。转的圈数与齿数成反比,所以,甲、乙、丙三个齿轮齿数之比为4:3:2,这恐怕是最容易想到的答案了,但很遗憾,这是错误的答案。我们可以这样检验:如果答案真是4:3:2的话,我们可以将齿数的份数与圈数相乘,结果得到8份、9份、8份,而实际上这三个齿轮的齿数份数与圈数的积应该是相等的。
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