Gravitational Force · 引力
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| mass/mæs/ | 质量 | zhì liàng |
| Newton's law of universal gravitation/ˈnjuːtnz lɔː ɒv ˌjuːnɪˈvɜːsl ˌɡrævɪˈteɪʃn/ | 万有引力定律 | wàn yǒu yǐn lì dìng lǜ |
| weight/weɪt/ | 重量 | zhòng liàng |
| gravitational field/ˌɡrævɪˈteɪʃənl fiːld/ | 引力场 | yǐn lì chǎng |
The apple and the Moon
- The same force that drops an apple also holds the Moon in its orbit.
- Newton's leap: every mass pulls on every other mass.
- The pull is usually far too weak to feel -- until one of the masses is planet-sized.
- One equation covers falling apples, orbiting moons, and whole galaxies.
苹果与月亮
- 让苹果落下的那个力,同样让月亮维持在轨道上。
- 牛顿的飞跃:每一个质量都吸引每一个其他质量。
- 这种吸引通常太弱、感觉不到——除非其中一个质量有行星那么大。
- 一个方程涵盖了下落的苹果、绕行的月亮,以及整个星系。
Universal gravitation
- Newton's law of universal gravitation 万有引力定律 gives the attraction between two masses:
- It grows with the masses and falls off with the square of the distance $r$ between them.
- $G$ is the tiny universal gravitational constant.
万有引力
- 万有引力定律给出两个质量之间的吸引力:
- 它随质量增大而增大,并随两者间距离 $r$ 的平方而减小。
- $G$ 是微小的万有引力常量。
Select all · 所有 ways to increase the gravitational force between two objects. · 选择所有能增加两物体间引力的方法。
More mass or less distance both raise $F_g = Gm_1m_2/r^2$; more distance lowers it. · 更大的质量或更小的距离都会使 $F_g = Gm_1m_2/r^2$ 增大；更大的距离会使其减小。
Mass versus weight
- Mass 质量 is how much matter an object has -- the same everywhere in the universe.
- Weight 重量 is the gravitational force on that mass, $F_g = mg$ -- it changes with location.
- On the Moon your mass is unchanged, but your weight is about one-sixth.
质量与重量
- 质量是物体含有多少物质——在宇宙各处都相同。
- 重量是作用在该质量上的引力,$F_g = mg$——它随位置改变。
- 在月球上你的质量不变,但重量约为六分之一。
An astronaut has a mass of $70\ \text{kg}$. What is her weight on Earth (in N, use $g = 9.8$)? · 一名宇航员的质量为 $70\ \text{kg}$。她在地球上的体重是多少（单位：N，使用 $g = 9.8$）？
$F_g = mg = 70 \times 9.8 = 686\ \text{N}$.
An astronaut's mass is smaller on the Moon than on Earth. · 宇航员在月球上的质量小于在地球上。
Mass is intrinsic and unchanged everywhere. It is the weight · 重量 (about one-sixth on the Moon) that differs. · 质量是本征属性，无处不在都不变。变化的是重量（在月球上约为六分之一）。
A rock weighs $60\ \text{N}$ on Earth ($g = 9.8$). What is its mass (in kg)? · 一块石头在地球上重$60\ \text{N}$（$g = 9.8$）。它的质量是多少（单位为kg）？
$m = F_g/g = 60/9.8 \approx 6.12\ \text{kg}$ -- and that mass stays the same on the Moon. · $m = F_g/g = 60/9.8 \approx 6.12\ \text{kg}$ —— 并且该质量在月球上保持不变。
The gravitational field
- Near a planet, the gravitational field 引力场 strength is $g = \dfrac{GM}{r^2}$.
- This $g$ is exactly the one in $F_g = mg$.
- A spherical planet pulls as if all its mass sat at its center.
引力场
- 在行星附近,引力场强度为 $g = \dfrac{GM}{r^2}$。
- 这个 $g$ 正是 $F_g = mg$ 里的那个。
- 球形行星的吸引,就好像它全部质量都集中在中心。
The gravitational field strength near a planet is $g = GM/r^{____}$. · 行星附近的引力场强度为 $g = GM/r^{____}$。
$g = GM/r^2$ -- the inverse-square law again. · $g = GM/r^2$ —— 再次应用平方反比定律。
It weakens with distance
- Because of the $1/r^2$, gravity drops fast as you move away.
- Double your distance from a planet's center and $g$ falls to a quarter.
- Satellites orbit far out, where the pull is gentler than at the surface.
它随距离减弱
- 由于 $1/r^2$,离得越远,引力下降得越快。
- 与行星中心的距离加倍,$g$ 就降到四分之一。
- 卫星在很远处绕行,那里的引力比在表面时温和。
Gravity falls off with distance · 重力随距离衰减
The gravitational force between two masses gets weaker as they move apart (an inverse-square law). · 两个质量之间的引力随着它们分离而减弱（平方反比定律）。
You move to twice your original distance from a planet's center. The gravitational force on you becomes... · 你移动到距行星中心两倍于原始距离的位置。作用于你的引力变为...
Gravity goes as $1/r^2$, so doubling $r$ divides the force by $2^2 = 4$. · 引力与 $1/r^2$ 成正比，因此将 $r$ 加倍会使力除以 $2^2 = 4$。
A $10\ \text{kg}$ rock has the same mass on Earth and the Moon.
- On Earth ($g = 9.8$): weight $= mg = 98\ \text{N}$.
- On the Moon ($g = 1.6$): weight $= 16\ \text{N}$.
- Mass is fixed; only the weight changes with the local field.
一块 $10\ \text{kg}$ 的石头在地球和月球上质量相同。
- 在地球上($g = 9.8$):重量 $= mg = 98\ \text{N}$。
- 在月球上($g = 1.6$):重量 $= 16\ \text{N}$。
- 质量固定;只有重量随当地场而改变。
Do not confuse mass and weight. A scale in kilograms reads your mass; the downward pull in newtons is your weight. An astronaut floating in orbit is weightless in feel, yet their mass -- and inertia -- is completely unchanged.
不要把质量和重量弄混。以千克为单位的秤读出你的质量;以牛顿为单位的向下拉力是你的重量。在轨道上漂浮的宇航员感觉失重,但他们的质量——以及惯性——完全没变。
Universal gravitation: $F_g = \dfrac{G m_1 m_2}{r^2}$ -- every mass attracts every other, falling off as $1/r^2$. Mass is intrinsic; weight $= mg$ depends on the local gravitational field $g = GM/r^2$. Move twice as far out and $g$ drops to a quarter.
万有引力:$F_g = \dfrac{G m_1 m_2}{r^2}$——每个质量吸引每个其他质量,并按 $1/r^2$ 减小。质量是内在的;重量 $= mg$ 取决于当地的引力场 $g = GM/r^2$。距离加倍到两倍,$g$ 就降到四分之一。