Forces and Free-Body Diagrams · 力与受力图
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| force/fɔːs/ | 力 | lì |
| contact forces/ˈkɒntækt ˈfɔːsɪz/ | 接触力 | jiē chù lì |
| field forces/fiːld ˈfɔːsɪz/ | 场力 | chǎng lì |
| free-body diagram/friː ˈbɒdi ˈdaɪəɡræm/ | 受力图 | shòu lì tú |
| components/kəmˈpəʊnənts/ | 分量 | fèn liàng |
| net force/net fɔːs/ | 合力 | hé lì |
The forces you cannot see
- A book lies still on a table -- so nothing is happening, right?
- Wrong: gravity pulls it down and the table pushes it up, in perfect balance.
- Every object is a tug-of-war of hidden forces.
- To solve any mechanics problem, you first have to draw those forces.
你看不见的那些力
- 一本书静静躺在桌上——所以什么都没发生,对吧?
- 错了:重力把它往下拉,同时桌子把它往上推,完美平衡。
- 每个物体都是一场看不见的力的拔河。
- 要解任何力学问题,你首先得把这些力画出来。
What a force is
- A force 力 is a push or a pull one object exerts on another, measured in newtons.
- Contact forces 接触力 need touching -- the normal force, friction, tension.
- Field forces 场力 act at a distance -- gravity is the everyday one.
什么是力
- 力是一个物体对另一个物体的推或拉,以牛顿为单位。
- 接触力需要接触——法向力、摩擦力、张力。
- 场力隔空作用——重力就是日常见到的那种。
Which of these is a field · 场 force (acts without contact)? · 下列哪一个是场力(无需接触即可作用)?
Gravity is a field force acting at a distance; friction, normal, and tension all require contact. · 重力是隔空作用的场力;摩擦力、法向力和张力都需要接触。
Select all · 所有 contact forces. · 选出所有接触力。
Normal, friction, and tension all need contact; gravity is a field force. · 法向力、摩擦力和张力都需要接触;重力是场力。
Draw a free-body diagram
- A free-body diagram 受力图 shows the object as a single dot.
- Every force on it becomes an arrow, pointing the right way, labeled.
- Draw only the forces acting on the object -- never the forces it exerts on other things.
画受力图
- 受力图把物体画成一个点。
- 作用在它上面的每个力都变成一个箭头,方向正确,并标注。
- 只画作用在该物体上的力——绝不画它对别的物体施加的力。
Build a free-body diagram · 搭建一张受力图
Add each force as an arrow and read off the net force and resulting acceleration. · 把每个力作为箭头加上去,读出合力和由此产生的加速度。
The force an object exerts on your hand belongs on that object's free-body diagram. · 物体对你手施加的力,应该画在该物体的受力图上。
A free-body diagram shows forces on the object. The force it pushes back on your hand goes on your hand's diagram. · 受力图画的是作用在物体上的力。它反推你手的那个力应画在你手的图上。
Resolve into components
- Forces rarely line up with your axes, so split each into components 分量.
- On a ramp, tilt the axes along and across the slope.
- Gravity then splits into $mg\sin\theta$ down the slope and $mg\cos\theta$ into it.
分解成分量
- 力很少正好对齐你的坐标轴,所以把每个力分解成分量。
- 在斜坡上,把坐标轴倾斜到沿坡和垂直于坡的方向。
- 重力于是分解为沿坡向下的 $mg\sin\theta$ 和压入坡面的 $mg\cos\theta$。
On a ramp of angle $\theta$, the component of gravity along the slope is $mg\,____\,\theta$. · 在倾角为 $\theta$ 的斜坡上,重力沿坡的分量是 $mg\,____\,\theta$。
The along-slope pull is $mg\sin\theta$; the into-slope part is $mg\cos\theta$. · 沿坡的分量是 $mg\sin\theta$;压入坡面的分量是 $mg\cos\theta$。
Add them to a net force
- The net force 合力 is the vector sum of every arrow.
- Add components axis by axis: $\sum F_x$ and $\sum F_y$ separately.
- That net force is what $\sum F = ma$ then turns into acceleration.
相加得到合力
- 合力是所有箭头的矢量和。
- 逐轴相加分量:$\sum F_x$ 和 $\sum F_y$ 分别计算。
- 这个合力就是 $\sum F = ma$ 随后转化成的加速度。
Forces on a box (rightward positive):$+15\ \text{N}$, $-6\ \text{N}$, $+1\ \text{N}$. What is the net horizontal force (in N)? · 箱子受的力(向右为正):$+15\ \text{N}$、$-6\ \text{N}$、$+1\ \text{N}$。水平合力是多少(单位 N)?
$15 - 6 + 1 = 10\ \text{N}$ to the right -- just add the components with their signs. · $15 - 6 + 1 = 10\ \text{N}$,方向向右——把带符号的分量相加即可。
If every force on an object cancels, its net force is zero. · 如果作用在物体上的每个力都抵消,它的合力就为零。
Balanced forces sum to zero, so there is no net force and no acceleration. · 平衡的力相加为零,所以没有合力,也没有加速度。
A $2\ \text{kg}$ box on the floor is pushed right with $12\ \text{N}$; friction resists with $4\ \text{N}$.
- Horizontal net force: $12 - 4 = 8\ \text{N}$ to the right.
- Vertical: the normal force and gravity cancel, so $\sum F_y = 0$.
一个 $2\ \text{kg}$ 的箱子在地板上被向右推 $12\ \text{N}$;摩擦力反抗 $4\ \text{N}$。
- 水平合力:向右 $12 - 4 = 8\ \text{N}$。
- 竖直方向:法向力和重力抵消,所以 $\sum F_y = 0$。
A free-body diagram shows forces on the object only. The force the box pushes back on your hand belongs on your hand's diagram, not the box's -- mixing them up is the most common mistake in all of mechanics.
受力图只画作用在物体上的力。箱子反推你手的那个力,应画在你手的受力图上,而不是箱子的——把它们弄混,是整个力学中最常见的错误。
A free-body diagram draws every force on an object as a labeled arrow. Split them into components along your axes, then add to get the net force ($\sum F_x$, $\sum F_y$). Only forces on the object appear -- that net force drives its acceleration.
受力图把物体上的每个力都画成一个带标注的箭头。把它们沿坐标轴分解成分量,再相加得到合力($\sum F_x$、$\sum F_y$)。只有作用在物体上的力才出现——这个合力驱动它的加速度。