Balancing a pencil or any other top-heavy object on its tip is quite a precarious task.It's easy to see why top-heavy objects are unstable.They just want to fall down.Any little nudge will put it off balance.With gravity happy to pull its center of mass even more off balance.And the more off-balanced it is.the more gravity pulls until...
将铅笔或任何头重的物体平衡在尖端都是在拼人品。显然 头重的物体很不稳定，它们就喜欢趴体。极小的推力就会使其失衡。而重力很乐意使其质心更偏离平衡点，越偏离平衡 重力作用越明显 直到...
Physicists call this kind of tipping an inverted pendulum,because it's kind like an upside down pendulum,And careful mathematical analysis of inverted pendulums will tell you the obvious:they are really unstable.
In fact,these equations predict that if a perfectly balanced pencil with a perfectly sharp tip were to get nudged off balance by just 1/10,000 of the width of an atom,it would take only 3 seconds to fall over.There are indeed acrobats who can balance poles with other acrobats on top.and robots that can balance and,catch and throw upright sticks and people who make seemingly impossible artistic rock stacks,But in all these cases,keeping the objects balanced either requires an active stabilization effort,or else carefully taking advantage of the fact that the balancing point isn't actually a point.
实际上 这些等式说明，如果一个尖端极其锐利 处于完美平衡的铅笔受到推力失衡，偏离原子长度的万分之一，倒下只需不到三秒。的确有杂技演员可以平衡顶端站人的杆子，有机器人可以平衡 抛掷或接住竖直棒，有人可以堆出看似不可能的石堆。但这些情况中 保持物体平衡，要么需要动态平衡支持，要么谨慎地利用算不上点的“平衡点”。
So the question is this:Can you balance a pencil sharpened to a perfect single atom wide tip on its tip,without active stabilization?Well to start,you'd better get rid of all the air bumping on the sides of the pencil.since the kinetic energy of a typical oxygen molecule is enough to destabilize the pencil.
那么 问题在此，你能否将一只铅笔平衡在其原子大小的尖端，而不需要动态平衡吗？一开始 你最好排空碰撞着铅笔各面的空气。因为单是氧原子的动能就足以让铅笔失衡.
Remember,if the pencil gets off center by even 1/10,000 the width of an atom,it will fall down in under 3 seconds.And you'd better cool the pencil and table down as close to absolute zero as you can,since the thermal jiggling of their atoms when they are hotter will similarly jiggle the pencil off balance.
But even then,matter at very small scales has a spread out wave-like nature,which means you can't have both the pencil perfectly upright and not moving at the same time.And while this quantum effect is never a real life inhibitor of precarious pencil balancing,it means you never even could succeed.
即使这样 十分微小的物质具有类似于波的本质，也就是说 铅笔完全竖直与保持平衡不动，不可同时兼得。尽管量子效应不会对你拼人品平衡铅笔带来真实影响。者却意味着 你永远做不到。
However,it's still fun to see how long you can keep a pencil balanced on a finger tip.The shorter the pencil,the harder it is,My best time for a standard 19cm pencil was 1.3s.Think you can beat it?
不过 看看你能用指尖平衡铅笔多长时间也很有意思。铅笔越短 难度越大。我的标准19厘米铅笔最好记录是1。3秒。你行你上啊？