Name: 大多數碰撞都祕密地發生在一個維度上 (Most Collisions Are Secretly in One Dimension)
Uploaded: 2022-06-09T17:55:23.000Z
Duration: 3 min 44 s

When two things crash into each other, it  seems like it should be a messy affair,  

當兩件事情相互碰撞時，似乎應該是一件混亂的事情。

where just about anything can happen.  I mean, that's kind of our everyday  

在那裡，任何事情都可能發生。  我的意思是，這就是我們的日常。

experience of collisions! But there's actually  a magic simplicity underlying the complexity. 

碰撞的經驗!但實際上，在複雜的背後有一個神奇的簡單性。

In fact, if you have just two things  colliding along just one direction,  

事實上，如果你只有兩個東西沿著一個方向碰撞。

then there's only one possible outcome! I mean,  sure, after the collision each object could in  

那麼就只有一個可能的結果！我的意思是，在碰撞之後，每個物體都可以在一個特定的時間內，在一個特定的地點，在一個特定的地點，在一個特定的地點，在一個特定的地點，在一個特定的地點。我的意思是，當然，在碰撞之後，每個物體可以在

principle have any possible velocity to the left  or right - which is to say, there are two unknown  

原則上有任何可能的速度向左或向右--也就是說，有兩個未知的

variables. But conservation of momentum provides  one equation those variables have to satisfy.  

變量。但動量守恆提供了一個這些變量必須滿足的方程式。  

And conservation of energy provides another  equation those variables have to satisfy.  

而能量守恆則提供了這些變量必須滿足的另一個方程式。  

And in our universe, two independent equations  for two unknown variables will uniquely  

而在我們的宇宙中，兩個未知變量的兩個獨立方程將唯一地

determine those variables. So for each possible  combination of masses and incoming velocities,  

決定這些變量。是以，對於品質和傳入速度的每個可能的組合。

there's only one possible outcome  of a 1D collision. For example. 

一個一維碰撞只有一個可能的結果。比如說。

Two identical objects coming in at the  same velocity? They bounce off each other. 

兩個相同的物體以相同的速度衝過來？它們會相互反彈。

One of those objects not moving?  One stops and the other starts. 

其中一個物體不動？  一個停止，另一個開始。

One object twenty times as big and not moving?  The little one bounces back with 90% the speed,  

一個物體是它的20倍大，而且不動？  小的那個以90%的速度反彈回來。

and the big one starts moving with 10% the speed. And so on... 

而大的那個開始以10%的速度移動。以此類推...

Oh, “but what if energy isn't conserved?”  Well, yeah, maybe some of the energy of  

哦，"但如果能量不是守恆的呢？"  嗯，是的，也許有些能量的

the colliding objects doesn't stay as  kinetic energy but turns into heat,  

碰撞的物體不會以動能的形式存在，而會變成熱能。

or sound, or rotational energy, or whatever, so  the conservation of energy equation isn't valid.  

或聲音，或旋轉能量，或其他，所以能量守恆方程是無效的。  

Except, you can simply put the lost energy  into the conservation of energy equation and  

除了，你可以簡單地將損失的能量放入能量守恆方程中，然後

it becomes valid again. So there are still two  equations and two unknowns, and therefore only  

它又變得有效。所以仍然有兩個方程和兩個未知數，是以只有

one possible outcome of the collision as far as  the objects' velocities are concerned. Though  

就物體的速度而言，碰撞的一個可能結果。雖然

it's typically really hard to keep track of lost  energy and so the outcome of these collisions can  

通常情況下，很難跟蹤損失的能量，是以這些碰撞的結果可以

seem surprising - but from the Universe's  perspective, they are uniquely determined. 

似乎令人驚訝--但從宇宙的角度來看，它們是獨一無二的決定。

And what about in two or three dimensions where  most collisions aren't perfectly one dimensional?  

那麼在二維或三維空間中，大多數碰撞並不是完全一維的呢？  

Well, the truth is, they secretly are! Most of  the time, collisions in 2D or 3D result in a  

好吧，事實是，他們暗地裡是這樣的!大多數情況下，二維或三維的碰撞會導致

net force between the objects which is only in one  direction - typically perpendicular to the surface  

物體之間的淨力只在一個方向上，通常是垂直於表面的。

where the objects collide, though if the surface  is complicated or there's friction it might be a  

物體碰撞的地方，但如果表面複雜或有摩擦，它可能是一個

different direction. Since there are no net forces  in directions perpendicular to the net force,  

不同的方向。由於在與淨力垂直的方向上沒有淨力。

the motion of the objects in those perpendicular  directions is unaffected by the collision!  

物體在這些垂直方向上的運動不受碰撞的影響!  

So even though a collision happens in 2D, if  you find the right direction the collision  

是以，即使碰撞發生在2D中，如果你找到正確的方向，碰撞就會發生。

will be the same as a one dimensional collision  in that direction, and in the other direction,  

將與該方向上的一維碰撞相同，而在另一方向上的一維碰撞。

the objects just pass by each other, unaffected.  Which means that even in two or three dimensions,  

物體只是互相擦肩而過，不受影響。  這意味著，即使在二維或三維空間，也是如此。

once you know the secret direction, the outcome  of collisions is again uniquely determined! 

一旦你知道了祕密的方向，碰撞的結果又是唯一確定的！"。

And that's the magic of collisions: even  though they look complicated and random,  

而這就是碰撞的魔力：儘管它們看起來很複雜，很隨機。

they're secretly not. The combination of  conservation of momentum and conservation  

他們祕密地不是。動量守恆和守恆的結合

of energy and the fact that most collisions are  secretly in one dimension means that the outcome  

的能量，而且大多數碰撞是祕密地在一個維度上進行的，這意味著結果是

of almost any collision between two objects is  completely determined - as long as you know the  

幾乎任何兩個物體之間的碰撞都是完全確定的--只要你知道

incoming masses and velocities, the amount of  kinetic energy lost to heat and sound and so on,  

傳入的品質和速度，損失為熱和聲音的動能數量等等。

and the direction of the one secret dimension.  And, as long as you're ignoring quantum mechanics. 

和一個祕密維度的方向。  而且，只要你忽略了量子力學。

Since most big and complicated collisions are  actually made up of lots of two-object collisions,  

因為大多數大型複雜的碰撞實際上是由很多雙物體的碰撞組成的。

that means big complicated collisions  are also completely determined!  

這意味著大的複雜的碰撞也是完全確定的!  

Which is why it's really easy for  computers to simulate lots of collisions. 

這就是為什麼計算機真的很容易模擬出大量的碰撞。

If you've made it this far into a video about  the physics of collisions, I bet you're pretty  

如果你對一個關於碰撞物理學的視頻看了這麼久，我打賭你肯定很

curious, and so you may also be curious  about out Brilliant, this video's sponsor.  

好奇，所以你可能也會對這個視頻的贊助商--Out Brilliant感到好奇。  

Brilliant is a fun, interactive science and  math learning platform for curious people young  

輝煌是一個有趣的、互動的科學和數學學習平臺，適合好奇心強的年輕人。

and old, professional and beginner. Brilliant  is based off the principle that active problem  

輝煌是基於主動解決問題的原則。輝煌是基於這樣的原則：積極的問題

solving is the fastest path towards mastery  of a new concept or skill - not just lectures  

解決問題是掌握新概念或技能的最快途徑--而不僅僅是講課。

alone - and they have interactive courses ranging  from logic to fundamentals of computer science  

獨自一人--他們有互動課程，從邏輯學到計算機科學的基礎知識。

to quantum mechanics to infinity and beyond  (literally - they have courses about infinity)!  

到量子力學，再到無窮大，甚至更遠（字面意思是--他們有關於無窮大的課程）!  

To gain a deeper understanding of science  and mathematics and to sign up for free,  

為了更深入地瞭解科學和數學，並免費註冊。

go to Brilliant.org/MinutePhysics.  The first 200 people will get 20%  

去Brilliant.org/MinutePhysics。  前200人將獲得20%的

off an annual Premium subscription with full  access to all of Brilliant's courses and puzzles.  

贈送年度高級訂閱，可以完全訪問Brilliant的所有課程和謎題。  

Again, that's Brilliant.org/MinutePhysics -  and thanks to Brilliant for their support.

同樣，這就是Brilliant.org/MinutePhysics--感謝Brilliant的支持。