Fluids and Newton's Laws · 流体与牛顿定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| buoyant force/ˈbɔɪənt fɔːs/ | 浮力 | fú lì |
A steel ship floats, but a steel nail sinks
- Drop a steel nail in water and it sinks at once. Yet a ship made of thousands of tonnes of steel floats.
- The ship wins by pushing aside a huge volume of water — enough to hold its weight up.
- The upward push from a fluid is the buoyant force 浮力.
- It obeys a beautifully simple rule discovered by Archimedes.
钢制的船能浮,钢钉却下沉
- 把一颗钢钉丢进水里,它立刻下沉。可一艘由几千吨钢造成的船却浮着。
- 船靠推开巨大体积的水取胜——足以托起它的重量。
- 来自流体的向上的推力就是浮力。
- 它遵守阿基米德发现的一条美妙而简单的规则。
Archimedes' principle
- The buoyant force equals the weight of the fluid displaced: $F_b = \rho_{\text{fluid}} V g$.
- It comes from pressure being larger at the bottom of an object than the top.
- $V$ is the submerged volume, and $\rho_{\text{fluid}}$ the fluid's density.
- Push aside more fluid, or a denser fluid, and you get a bigger upward force.
阿基米德原理
- 浮力等于排开流体的重量:$F_b = \rho_{\text{fluid}} V g$。
- 它来自物体底部的压强比顶部大。
- $V$ 是浸没的体积,$\rho_{\text{fluid}}$ 是流体的密度。
- 推开更多流体,或更致密的流体,你就得到更大的向上的力。
A block of volume $0.002\ \text{m}^3$ is submerged in water ($\rho = 1000\ \tfrac{\text{kg}}{\text{m}^3}$, $g = 10\ \tfrac{\text{m}}{\text{s}^2}$). What is the buoyant force, in $\text{N}$? · 体积为$0.002\ \text{m}^3$的物块完全浸没在水中（$\rho = 1000\ \tfrac{\text{kg}}{\text{m}^3}$, $g = 10\ \tfrac{\text{m}}{\text{s}^2}$）。受到的浮力是多少$\text{N}$？
$F_b = \rho V g = 1000 \times 0.002 \times 10 = 20\ \text{N}$.
Archimedes' principle says the buoyant force equals: · 阿基米德原理指出，浮力等于：
$F_b = \rho_{\text{fluid}} V g$ — the weight of the fluid the object pushes aside. · $F_b = \rho_{\text{fluid}} V g$——物体排开的流体的重力。
Float or sink? Compare the forces
- Compare the buoyant force (up) with the object's weight (down) — a Newton's-law balance.
- If buoyancy can equal the weight, the object floats; if not, it sinks.
- Equivalently, compare densities: less dense than the fluid ⇒ floats; denser ⇒ sinks.
- A ship floats because its overall (average) density, hull plus air, is low.
浮还是沉?比较力
- 比较浮力(向上)和物体的重量(向下)——一个牛顿定律的平衡。
- 如果浮力能等于重量,物体就浮;如果不能,它就沉。
- 等价地,比较密度:比流体密度小 ⇒ 浮;更大 ⇒ 沉。
- 船能浮是因为它整体(平均)的密度——船体加空气——很低。
Will it float? · 它会漂浮吗？
Compare an object's density with the fluid's and see how buoyancy decides float or sink. · 比较物体密度与流体密度，观察浮力如何决定沉浮。
An object floats in a fluid when the object is: · 当物体满足什么条件时，会在流体中漂浮？
Less dense than the fluid ⇒ buoyancy can support its weight ⇒ it floats. · 比流体密度小 ⇒ 浮力足以支撑其重力 ⇒ 物体漂浮。
A steel ship floats because its overall average density (steel plus air) is less than water's. · 钢船之所以漂浮，是因为其整体平均密度（钢加空气）小于水。
The hollow hull traps air, lowering the ship's average density below that of water. · 空心船体截留了空气，使船的平均密度低于水。
Select all · 所有 things that increase the buoyant force on a fully submerged object. · 选择所有能增加完全浸没物体所受浮力的因素。
$F_b = \rho_{\text{fluid}} V g$ grows with volume, fluid density and $g$. Colour is irrelevant. · $F_b = \rho_{\text{fluid}} V g$随体积、流体密度和$g$增大。颜色无关紧要。
Why it feels lighter underwater
- Lift a rock underwater and it feels lighter — the buoyant force helps you.
- Its apparent weight is the real weight minus the buoyant force.
- Fully submerged, a denser-than-water object still sinks, but with reduced apparent weight.
- Buoyancy is just Newton's laws applied to the pressure of the surrounding fluid.
为什么在水下感觉更轻
- 在水下举一块石头,它感觉更轻——浮力在帮你。
- 它的视重是真实重量减去浮力。
- 完全浸没时,比水密度大的物体仍会沉,但视重减小了。
- 浮力只是把牛顿定律应用于周围流体的压强。
The apparent weight of a submerged object is its real weight minus the ____ force. · 浸没物体的视重等于其实际重力减去____力。
Apparent weight $=$ real weight $-$ buoyant force, so things feel lighter underwater. · 视重$=$实际重力$-$浮力，因此物体在水下感觉更轻。
Buoyancy depends on the volume of fluid displaced and the fluid's density — not on the object's own density or weight directly. Floating vs sinking is decided by comparing the buoyant force to the weight (or the object's density to the fluid's).
浮力取决于排开流体的体积和流体的密度——而非直接取决于物体自身的密度或重量。浮还是沉,由比较浮力与重量(或物体密度与流体密度)决定。
A block of volume $0.002\ \text{m}^3$ is fully submerged in water ($\rho = 1000\ \tfrac{\text{kg}}{\text{m}^3}$, $g = 10\ \tfrac{\text{m}}{\text{s}^2}$).
- $F_b = \rho V g = 1000 \times 0.002 \times 10 = 20\ \text{N}$.
If the block weighs more than $20\ \text{N}$ it sinks; less, and it rises and floats.
一个体积 $0.002\ \text{m}^3$ 的方块完全浸没在水中($\rho = 1000\ \tfrac{\text{kg}}{\text{m}^3}$,$g = 10\ \tfrac{\text{m}}{\text{s}^2}$)。
- $F_b = \rho V g = 1000 \times 0.002 \times 10 = 20\ \text{N}$。
如果方块重量超过 $20\ \text{N}$ 就下沉;更轻,它就上浮并漂浮。
The buoyant force equals the weight of the fluid displaced: $F_b = \rho_{\text{fluid}} V g$ (Archimedes' principle). An object floats if this can balance its weight — equivalently, if it is less dense than the fluid — and sinks if not. Underwater objects have a reduced apparent weight.
浮力等于排开流体的重量:$F_b = \rho_{\text{fluid}} V g$(阿基米德原理)。如果它能平衡物体的重量,物体就浮——等价地,如果物体比流体密度小——否则沉。水下物体有减小的视重。