Newton's Second Law · 牛顿第二定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| mass/mæs/ | 质量 | zhì liàng |
| Newton's second law/ˈnjuːtnz ˈsekənd lɔː/ | 牛顿第二定律 | niú dùn dì èr dìng lǜ |
| net force/net fɔːs/ | 合力 | hé lì |
| acceleration/əkˌseləˈreɪʃn/ | 加速度 | jiā sù dù |
| inertia/ɪˈnɜːʃə/ | 惯性 | guàn xìng |
| components/kəmˈpəʊnənts/ | 分量 | fèn liàng |
| pulley/ˈpʊli/ | 滑轮 | huá lún |
The same shove -- a feather flies, a fridge barely budges
- Give a feather a gentle push and it shoots off; push a fridge just as hard and it hardly moves.
- Same force, wildly different results -- the difference is mass 质量.
- One equation ties force, mass, and motion together.
- It is the engine of mechanics: give it the forces and the mass, and it hands you the motion.
同样一推——羽毛飞出去,冰箱却几乎不动
- 轻轻推一下羽毛,它就飞了出去;用同样的力推冰箱,它几乎纹丝不动。
- 力相同,结果却天差地别——区别在于质量。
- 有一个方程把力、质量和运动联系在一起。
- 它是力学的引擎:给它力和质量,它就把运动交给你。
Newton's second law
- Newton's second law 牛顿第二定律 states:
- The net force 合力 on an object equals its mass times its acceleration 加速度.
- Rearranged, $\vec{a} = \dfrac{\vec{F}_{net}}{m}$ -- the forces set the acceleration.
牛顿第二定律
- 牛顿第二定律指出:
- 物体所受的合力等于它的质量乘以加速度。
- 变形后为 $\vec{a} = \dfrac{\vec{F}_{net}}{m}$——力决定加速度。
A net force of $20\ \text{N}$ acts on a $4\ \text{kg}$ cart. What is its acceleration (in $\tfrac{\text{m}}{\text{s}^2}$)? · 一个 $20\ \text{N}$ 的合力作用在 $4\ \text{kg}$ 的小车上。它的加速度是多少($\tfrac{\text{m}}{\text{s}^2}$)?
$a = \dfrac{F_{net}}{m} = \dfrac{20}{4} = 5\ \tfrac{\text{m}}{\text{s}^2}$. · $a = \dfrac{F_{net}}{m} = \dfrac{20}{4} = 5\ \tfrac{\text{m}}{\text{s}^2}$。
Rearranging the second law: acceleration equals the net force divided by the . · 把第二定律变形:加速度等于合力除以。
$\vec{a} = \dfrac{\vec{F}_{net}}{m}$ -- the net force over the mass. · $\vec{a} = \dfrac{\vec{F}_{net}}{m}$——合力除以质量。
More force, less mass
- The one equation carries two rules:
- More net force → proportionally more acceleration.
- More mass → proportionally less acceleration (mass resists change -- its inertia 惯性).
- That is exactly why the light feather leaps and the massive fridge barely stirs.
力越大、质量越小
- 这一个方程包含两条规律:
- 合力越大 → 加速度成正比地越大。
- 质量越大 → 加速度成正比地越小(质量抵抗运动变化,这就是它的惯性)。
- 这正是为什么轻的羽毛飞出去、而重的冰箱几乎不动。
Keep the force the same but double the mass. The acceleration... · 保持力不变,但把质量加倍。加速度……
Since $a = F_{net}/m$, doubling $m$ halves $a$ -- mass and acceleration are inversely proportional. · 因为 $a = F_{net}/m$,质量加倍就使 $a$ 减半——质量与加速度成反比。
Select all · 所有 changes that would increase · 增加 an object's acceleration. · 选出所有会增大物体加速度的改变。
More net force or less mass both raise $a = F_{net}/m$; more mass lowers it, and cancelling forces gives zero net force. · 增大合力或减小质量都会提高 $a = F_{net}/m$;增大质量会降低它,而抵消的力则使合力为零。
It is the net force that counts
- An object usually feels several forces at once -- a push, gravity, friction.
- Only their vector sum, the net force, drives the acceleration.
- If the forces cancel to zero, there is no acceleration: the object stays at rest or keeps constant velocity.
起作用的是合力
- 物体通常同时受到好几个力——推力、重力、摩擦力。
- 只有它们的矢量和,也就是合力,才决定加速度。
- 如果各力抵消为零,就没有加速度:物体保持静止或匀速运动。
If all the forces on an object cancel, it cannot be moving. · 如果作用在物体上的所有力都抵消,它就不可能在运动。
Zero net force means zero acceleration, not zero velocity. A moving object simply keeps its constant velocity. · 合力为零意味着加速度为零,而不是速度为零。运动的物体只会保持匀速运动。
Splitting forces into components
- When forces point in awkward directions (say, on a ramp), split each into components 分量 along chosen axes.
- Apply $\sum F = ma$ separately in each direction.
- For connected objects on a pulley 滑轮, write the law for each mass and solve together.
把力分解成分量
- 当力指向不方便的方向(比如在斜坡上)时,把每个力沿选定的坐标轴分解成分量。
- 在每个方向上分别应用 $\sum F = ma$。
- 对于用滑轮连接的物体,给每个质量都写出该定律,再联立求解。
Free-body diagram: F = ma · 受力图:F = ma
The resultant of the forces, divided by the mass, gives the acceleration. Change a force and watch the acceleration respond. · 各力的合力除以质量,得到加速度。改变一个力,看看加速度如何变化。
A $2\ \text{kg}$ box is pulled with $30\ \text{N}$ while friction drags back $10\ \text{N}$. Find its acceleration (in $\tfrac{\text{m}}{\text{s}^2}$). · 一个 $2\ \text{kg}$ 的箱子被 $30\ \text{N}$ 拉动,同时摩擦力反向拉 $10\ \text{N}$。求它的加速度($\tfrac{\text{m}}{\text{s}^2}$)。
Net force $= 30 - 10 = 20\ \text{N}$, so $a = 20/2 = 10\ \tfrac{\text{m}}{\text{s}^2}$. Use the net force, not the $30\ \text{N}$ alone. · 合力 $= 30 - 10 = 20\ \text{N}$,所以 $a = 20/2 = 10\ \tfrac{\text{m}}{\text{s}^2}$。要用合力,而不是单独的 $30\ \text{N}$。
A net force of $20\ \text{N}$ acts on a $5\ \text{kg}$ box.
- Acceleration: $a = \dfrac{F_{net}}{m} = \dfrac{20}{5} = 4\ \tfrac{\text{m}}{\text{s}^2}$.
- Double the mass to $10\ \text{kg}$ with the same force, and the acceleration halves to $2\ \tfrac{\text{m}}{\text{s}^2}$.
一个 $20\ \text{N}$ 的合力作用在 $5\ \text{kg}$ 的箱子上。
- 加速度:$a = \dfrac{F_{net}}{m} = \dfrac{20}{5} = 4\ \tfrac{\text{m}}{\text{s}^2}$。
- 力不变、质量加倍到 $10\ \text{kg}$,加速度就减半为 $2\ \tfrac{\text{m}}{\text{s}^2}$。
Use the net force, not one force you happen to notice. A box pulled with $30\ \text{N}$ while friction drags back $10\ \text{N}$ has a net force of $30 - 10 = 20\ \text{N}$ -- so $a = 20/m$, not $30/m$.
要用合力,而不是你恰好注意到的某一个力。一个箱子被 $30\ \text{N}$ 拉动,同时摩擦力反向拉 $10\ \text{N}$,合力是 $30 - 10 = 20\ \text{N}$——所以 $a = 20/m$,不是 $30/m$。
Newton's second law is $\vec{F}_{net} = m\vec{a}$, or $\vec{a} = \dfrac{\vec{F}_{net}}{m}$: acceleration equals the net force divided by the mass. More force means more acceleration; more mass means less. Always add the forces as vectors first, then divide.
牛顿第二定律是 $\vec{F}_{net} = m\vec{a}$,即 $\vec{a} = \dfrac{\vec{F}_{net}}{m}$:加速度等于合力除以质量。力越大,加速度越大;质量越大,加速度越小。永远先把各力作为矢量相加,再相除。