Gravitational Force · 引力
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| gravity/ˈɡrævɪti/ | 引力 | yǐn lì |
| weight/weɪt/ | 重量 | zhòng liàng |
| gravitational field strength/ˌɡrævɪˈteɪʃənl fiːld streŋθ/ | 重力场强度 | zhòng lì chǎng qiáng dù |
The apple and the Moon feel the same pull
- Legend says a falling apple made Newton wonder: does the same pull reach the Moon?
- It does. One law of gravity 引力 governs both the apple and the orbit.
- Near Earth we feel it as weight 重量 — the downward force $mg$.
- Farther out, the same law becomes the universal $F = \dfrac{GMm}{r^2}$.
苹果和月球感受到同一种拉力
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传说落下的苹果让牛顿产生疑问:同样的拉力会不会一直伸到月球?
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确实如此。一条引力定律既支配苹果,也支配轨道。
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在地球附近,我们把它感受为重力——向下的力 $mg$。
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更远处,同一条定律变成普遍的 $F = \dfrac{GMm}{r^2}$。
Weight near a surface
- Weight is the gravitational force on an object: $W = mg$, straight down.
- Here $g$ is the gravitational field strength 重力场强度, about $9.8\ \tfrac{\text{N}}{\text{kg}}$ at Earth's surface.
- So a $1\ \text{kg}$ mass weighs about $9.8\ \text{N}$.
- Weight is a force (newtons); mass is the amount of matter (kilograms).
表面附近的重力
- 重力是作用在物体上的引力:$W = mg$,竖直向下。
- 这里 $g$ 是引力场强度,在地球表面约为 $9.8\ \tfrac{\text{N}}{\text{kg}}$。
- 所以一个 $1\ \text{kg}$ 的质量重约 $9.8\ \text{N}$。
- 重力是一个力(牛顿);质量是物质的多少(千克)。
Gravity on different worlds · 不同星球上的重力
Switch the planet and watch how a weaker or stronger g bends the same launch differently. · 切换行星，观察较弱或较强的g如何以不同角度弯曲相同的抛射轨迹。
What is the weight of a $5\ \text{kg}$ bag on Earth, where $g = 9.8\ \tfrac{\text{N}}{\text{kg}}$? Answer in $\text{N}$. · 质量为 $5\ \text{kg}$ 的袋子在地球上的重量是多少，其中 $g = 9.8\ \tfrac{\text{N}}{\text{kg}}$？答案单位为 $\text{N}$。
$W = mg = 5 \times 9.8 = 49\ \text{N}$.
On a distant planet a $10\ \text{kg}$ rock weighs $25\ \text{N}$. What is $g$ there, in $\tfrac{\text{N}}{\text{kg}}$? · 在遥远的行星上，一块 $10\ \text{kg}$ 的岩石重 $25\ \text{N}$。那里的 $g$ 是多少，单位为 $\tfrac{\text{N}}{\text{kg}}$？
$g = W/m = 25/10 = 2.5\ \tfrac{\text{N}}{\text{kg}}$.
Universal gravitation
- Every mass attracts every other mass: $F = \dfrac{G M m}{r^2}$.
- $M$ and $m$ are the two masses, $r$ the distance between their centres, $G$ a constant.
- The bigger the masses, the stronger the pull; the farther apart, the weaker.
- This one formula holds apples, moons, planets and galaxies together.
万有引力
- 每个质量都吸引每个其他质量:$F = \dfrac{G M m}{r^2}$。
- $M$ 和 $m$ 是两个质量,$r$ 是它们中心之间的距离,$G$ 是一个常数。
- 质量越大,拉力越强;相距越远,越弱。
- 这一个公式把苹果、月球、行星和星系维系在一起。
Select all · 所有 changes that would make the gravitational force between two objects stronger. · 选择所有能使两个物体间万有引力增强的变化。
$F = GMm/r^2$ grows with either mass and shrinks with distance. Moving them apart weakens it. · $F = GMm/r^2$ 随质量增加而随距离减小。将它们分开会减弱它。
The inverse-square law
- Gravity falls off as $\dfrac{1}{r^2}$ — the inverse-square law.
- Double the distance and the force drops to a quarter; triple it and it drops to a ninth.
- That is also why $g$ is weaker on a mountain top than at sea level.
- Field strength links to the law by $g = \dfrac{GM}{r^2}$.
平方反比定律
- 引力按 $\dfrac{1}{r^2}$ 衰减——平方反比定律。
- 距离加倍,力降到四分之一;距离变三倍,降到九分之一。
- 这也是山顶的 $g$ 比海平面弱的原因。
- 场强与定律的联系是 $g = \dfrac{GM}{r^2}$。
If the distance between two masses doubles, the gravitational force between them becomes: · 如果两个质量之间的距离加倍，它们之间的万有引力变为：
Gravity is inverse-square: $F \propto 1/r^2$, so doubling $r$ gives $1/2^2 = 1/4$ the force. · 重力是平方反比定律：$F \propto 1/r^2$，因此将 $r$ 加倍会导致力变为原来的 $1/2^2 = 1/4$。
Gravitational force is proportional to $1/r^{\_\_}$. Fill in the power. · 重力与 $1/r^{\_\_}$ 成正比。填入幂次。
It is an inverse-square law: $F \propto 1/r^2$. · 它是逆-平方定律：$F \propto 1/r^2$。
Weight is not mass. Mass ($\text{kg}$) never changes; weight ($\text{N}$) depends on the local $g$. On the Moon ($g \approx 1.6\ \tfrac{\text{N}}{\text{kg}}$) your mass is unchanged but you weigh about one-sixth as much.
**重力不是质量。**质量($\text{kg}$)永不改变;重力($\text{N}$)取决于当地的 $g$。在月球上($g \approx 1.6\ \tfrac{\text{N}}{\text{kg}}$),你的质量不变,但你的重量约为六分之一。
An object has the same weight everywhere in the universe. · 物体在宇宙任何地方的重量都相同。
Weight · 重力 $W = mg$ depends on the local $g$. Mass stays fixed, but weight changes from planet to planet. · 重量$W = mg$W=mg取决于当地的$g$重力加速度。质量保持不变，但重量随行星而异。
Find the weight of a $5\ \text{kg}$ bag on Earth ($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$).
- $W = mg = 5 \times 9.8 = 49\ \text{N}$, pointing straight down.
Take the same bag to the Moon and its weight drops to about $8\ \text{N}$ — but its mass is still $5\ \text{kg}$.
求一个 $5\ \text{kg}$ 的包在地球上($g = 9.8\ \tfrac{\text{N}}{\text{kg}}$)的重力。
- $W = mg = 5 \times 9.8 = 49\ \text{N}$,竖直向下。
把同一个包带到月球,它的重力降到约 $8\ \text{N}$——但它的质量仍是 $5\ \text{kg}$。
Gravity gives weight $W = mg$ near a surface and follows the universal law $F = GMm/r^2$ in general. It is an inverse-square force (double $r$ → quarter $F$), and $g = GM/r^2$. Mass (kg) is fixed; weight (N) changes with $g$.
引力在表面附近给出重力 $W = mg$,一般情况下遵循万有引力定律 $F = GMm/r^2$。它是平方反比力(距离加倍 → 力四分之一),且 $g = GM/r^2$。质量(kg)固定;重力(N)随 $g$ 改变。