Let’’s calculate:
When a body is falling down, it will have collisions with the molecules of the air. Assume the air will get an additional velocity same as the falling body. From Newton’’s Third Law, the total momentum the air molecules will get is equal to the force on the body exerted by the air multiplied by the time:
(Force)*(Time)=[(Density of air)*(Velocity)*(Time)*(Area)]*(Velocity)
where Area is that of the side facing downwards.
Then,cancel Time,
(Force)=[(Density of air)*(Area)]*(Velocity)^2
At equilibrium:
(Force)=(Mass)*g=(Density of body)*(Volume of body)*g
also =[(Density of air)*(Area)]*(Velocity)^2
Using: (Volume of body)/(Area)=(Height of body), then we get:
(Velocity)^2=[(Density of body)*(Height of body)*g]/(Density of air)
We can assume that the body density of Ant and Human are similar as that of water.
So (Velocity)^2 is totally proportional to the Height of body.
Now, Height of Ant is about 1mm, Height of human is 1.6m, 1600 times larger,
So the falling velocity of Human will be 40 times larger than that of Ant. Imagine it, 40 times larger not mentioning that the body of Ant is much strong than ours, it’’s indeed not surprising that falling from high enough will cause death for Human but very safe for Ant.
And if we consider the frictional force from the air, note that it will be proportional to the body surface area which is proportional to h^2, but don’’t forget the volum of body is proportional to h^3, so the frictional force is relatively much larger for Ant than for Human comparing with their body weight, which will even more slow down the falling velocity of Ant.

我记得好象流体如水，空气的阻力是跟速度3次方成正比的吧。
严格来讲，我觉得要考虑很多方面，比如形状，触地过程，这都会影响受力的。呵呵。

Come on, it’’s just a very simple model trying to explain the phenomena! You thought I did not consider about what you said? Then give me a better one and I’’ll admire you.

数学建模对于我就如同德语一样,我知道有这么个东西,但它到底是怎么回事就一点也不清楚.

[这个贴子最后由tycolion在 2002/04/24 09:23am 编辑]

引用:

下面引用由crushor在 2002/04/23 10:31pm 发表的内容：
数学建模对于我就如同德语一样,我知道有这么个东西,但它到底是怎么回事就一点也不清楚.

是物理模型。其实这只是让大家感觉感觉。关于这个问题，我相信流体力学和空气动力学已经给出相当完满的的解答，只是我不熟悉，相信大家也不感兴趣。

我来随便想想吧,反正也不懂.呵呵.
落地时的速度.照我的感觉,假设人从很高处往下落,能够到达匀速,(不考虑会不会被烧死冻死)这样应该达到很高的速度,(好象人的形状比较圆滑哦,密度也不小).而蚂蚁由于它的形状,密度,很容易到达匀速,我想它应该比雨滴的速度更小,而雨滴是3米/秒(好象是吧).
再考虑触地过程,人的骨骼是比较硬的,这就使触地时间变短,受力变大.即使人没骨头,就是个水袋子,我想也会由于内脏受力过大导致死亡的吧.相比较,蚂蚁的腿及身体可以使触地时间充分的长吧.

若把人体缩到蚂蚁的尺度,再和蚂蚁比劲对撞,你就知道谁的骨头硬了

蚂蚁乃用的是轻功。大比段誉的“凌波微步”佩服佩服！！

何止，乾坤大挪移都练到登峰造极了。。。

   Ft=mv 是没错，可是谁知道 t是多少啊，而且就算蚂蚁所受到的冲击力很小，比人受到的小得很多很多，可是你们好像都没有考虑到，蚂蚁很小啊。就算泰森打人一拳最多也不过晕倒，可是一个小孩子轻轻一按，蚂蚁就死了，我想这个总该考虑吧。
   我看耻这还和蚂蚁的生理结构有关，蚂蚁的壳有没有起到作用？说不定蚂蚁能在漂浮时保持足部先行落地，蚂蚁有6条腿，而且很长，可以分散冲击力，增加落地时间，正如皮蛋先生所说的蚂蚁使的是轻功啊！