Newton's Third Law · 牛顿第三定律
You cannot push without being pushed back
- Shove a heavy wall and you feel it shove you — hard enough and you slide backward.
- Every force is one half of a pair; there is no such thing as a lone push.
- Newton's third law: if A pushes B, then B pushes A equally and oppositely.
- This is why rockets fly, swimmers move, and you can walk at all.
你无法推别人而不被推回
- 用力推一堵厚墙,你会感到它反过来推你——用力够大你就向后滑。
- 每一个力都是一对中的一半;根本不存在孤零零的一个推。
- 牛顿第三定律:如果 A 推 B,那么 B 等大反向地推 A。
- 这就是火箭飞行、游泳者前进、以及你能走路的原因。
The law in symbols
- For any interaction between two bodies: $\vec F_{A\to B} = -\,\vec F_{B\to A}$.
- Equal in size, opposite in direction — always, no exceptions.
- It holds whether the objects are still, moving, heavy, or light.
- The pair appears and disappears together, at the same instant.
用符号写出定律
- 对两个物体之间的任何相互作用:$\vec F_{A\to B} = -\,\vec F_{B\to A}$。
- 大小相等,方向相反——永远如此,没有例外。
- 无论物体是静止、运动、重、还是轻,它都成立。
- 这一对同时出现、同时消失,在同一瞬间。
You push a wall with a force of $50\ \text{N}$. With what force does the wall push back on you? · 你用$50\ \text{N}$的力推墙。墙以多大的力推回你？
By the third law the reaction is equal in size: the wall pushes back with $50\ \text{N}$. · 根据第三定律，反作用力大小相等：墙以$50\ \text{N}$的力推回你。
Newton's third law says forces come in equal-and-____ pairs. · 牛顿第三定律指出力成大小相等、____的对出现。
Equal in magnitude, opposite in direction: $\vec F_{A\to B} = -\vec F_{B\to A}$. · 大小相等，方向相反：$\vec F_{A\to B} = -\vec F_{B\to A}$。
The pair acts on different objects
- The two forces in the pair act on different bodies — one on A, one on B.
- That is why they do not cancel: cancellation only happens for forces on the same object.
- To find the motion of B, you only count the forces acting on B.
- The reaction force acts on A, so it never appears in B's free-body diagram.
这一对作用在不同物体上
- 这一对中的两个力作用在不同的物体上——一个在 A,一个在 B。
- 这就是它们不相消的原因:相消只发生在作用于同一物体的力之间。
- 要求 B 的运动,你只数作用在 B 上的力。
- 反作用力作用在 A 上,所以它绝不出现在 B 的受力图里。
The two forces of an action–reaction pair act on the same object. · 作用力与反作用力对的两个力作用在同一物体上。
They act on different objects — one on A, one on B. That is why they do not cancel. · 它们作用在不同的物体上——一个在A上，一个在B上。这就是它们不抵消的原因。
Why do the action and reaction forces not cancel each other out? · 为什么作用力和反作用力不互相抵消？
Forces only cancel when they act on the same · 相同 body. Action and reaction act on two different bodies. · 只有当力作用在同一个物体上时才会抵消。作用力和反作用力作用在两个不同的物体上。
Third law all around you
- Walking: your foot pushes the ground back; the ground pushes you forward.
- Swimming: you push water back; the water pushes you forward.
- Rockets: engines push gas down; the gas pushes the rocket up.
- In each case the small "reaction" is what actually drives you.
处处都是第三定律
- 走路:你的脚向后推地面;地面把你向前推。
- 游泳:你把水向后推;水把你向前推。
- 火箭:引擎把气体向下推;气体把火箭向上推。
- 每一种情形里,那个小小的"反作用"才是真正驱动你的力。
Third-law pairs · 第三定律配对
Newton's third-law forces are equal, opposite, and act on different objects. Sort each statement. · 牛顿第三定律的力大小相等、方向相反，且作用在不同物体上。对每个陈述进行排序。
A rocket pushes exhaust gas backward with $2000\ \text{N}$. With what force does the gas push the rocket forward, in $\text{N}$? · 火箭向后喷出气体$2000\ \text{N}$。气体以多大的力向前推火箭，单位为$\text{N}$？
The reaction is equal and opposite: the gas pushes the rocket forward with $2000\ \text{N}$ of thrust. · 反作用力大小相等方向相反：气体以$2000\ \text{N}$的推力向前推火箭。
Select all · 所有 examples that rely on Newton's third law. · 选择所有依赖牛顿第三定律的例子。
Swimming, walking and rockets all push on something that pushes back. A resting book still has third-law pairs, but its motion is not driven by them. · 游泳、行走和火箭都通过推某个东西来获得反推力。静置的书仍有第三定律配对，但其运动并非由它们驱动。
Action and reaction never cancel each other out, because they act on different objects. A common mistake is to say "the forces are equal and opposite, so nothing moves". They are equal and opposite — but on two separate bodies, so each body can still accelerate.
作用与反作用绝不会互相抵消,因为它们作用在不同的物体上。一个常见错误是说"力等大反向,所以什么都不动"。它们确实等大反向——但作用在两个不同的物体上,所以每个物体仍能加速。
A rocket engine pushes exhaust gas backward with $2000\ \text{N}$.
- By the third law, the gas pushes the rocket forward with $2000\ \text{N}$.
- That forward force on the rocket is the thrust that launches it.
一台火箭引擎以 $2000\ \text{N}$ 把废气向后推。
- 由第三定律,废气以 $2000\ \text{N}$ 把火箭向前推。
- 作用在火箭上的这个向前的力就是发射它的推力。
Newton's third law: $\vec F_{A\to B} = -\vec F_{B\to A}$ — forces come in equal-and-opposite pairs. The two act on different objects, so they never cancel. Walking, swimming and rockets all work by pushing on something that pushes back.
牛顿第三定律:$\vec F_{A\to B} = -\vec F_{B\to A}$——力成等大反向的对出现。这一对作用在不同的物体上,所以绝不相消。走路、游泳和火箭都靠推某个会推回来的东西而工作。