Mass, weight and density · 质量、重量与密度
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| mass/mæs/ | 质量 | zhì liàng |
| weight/weɪt/ | 重力 | zhòng lì |
| density/ˈdensɪti/ | 密度 | mì dù |
| matter/ˈmætə/ | 物质 | wù zhì |
| gravity/ˈɡrævɪti/ | 引力 | yǐn lì |
| gravitational field strength/ˌɡrævɪˈteɪʃənl fiːld streŋθ/ | 重力场强度 | zhòng lì chǎng qiáng dù |
| displacement/dɪˈspleɪsmənt/ | 排水法 | pái shuǐ fǎ |
Same you, lighter on the Moon
- An astronaut on the Moon can leap high and feels light.
- Yet they are made of exactly the same stuff as on Earth.
- The puzzle is solved by two different ideas: mass 质量 and weight 重力. Then we measure density 密度.
同样的你,在月球上更轻
- 一个月球上的宇航员能跳得高并感觉轻。
- 然而他们由与在地球上完全相同的东西构成。
- 这个谜题由两个不同的想法解决:质量和重量。然后我们测量密度。
Mass
- Mass is the amount of matter 物质 in an object.
- It is measured in kilograms (kg).
- Mass does not change when you move the object — to the Moon, into space, anywhere.
- A balance compares an unknown mass with known masses.
质量
- 质量(mass)是一个物体中物质的量。
- 它以千克(kg)测量。
- 当你移动物体时质量不变化——到月球、进入太空、任何地方。
- 一个天平(balance)把一个未知质量与已知质量比较。
Weight and mass · 重量与质量
W = mg
Weight is proportional to mass — the gradient is the gravitational field strength g (about 10 N/kg on Earth). · 重量与质量成正比——斜率是引力场强度 g(在地球上约 10 N/kg)。
Weight
- Weight is the force of gravity 引力 on a mass. It is measured in newtons (N).
- Weight can change: it is smaller on the Moon because the Moon's gravity is weaker.
- Gravitational field strength 重力场强度 is the force per unit mass:
- So weight is $W = mg$. On Earth $g \approx 9.8\ \text{N/kg}$ — the same number as the acceleration of free fall.
A falling object speeds up until air resistance grows to equal its weight
重量
- 重量(weight)是一个质量上的重力。它以牛顿(N)测量。
- 重量能变化:它在月球上更小,因为月球的引力更弱。
- 引力场强度(gravitational field strength)是每单位质量的力:
- 所以重量是 $W = mg$。在地球上 $g \approx 9.8\ \text{N/kg}$——与自由落体加速度相同的数字。
一个下落的物体加速,直到空气阻力增长到等于它的重量
Floating and density · 浮动与密度
Change the object's density and the liquid: it floats if it's less dense, and the denser it is the more sits underwater. Iron sinks in water but floats on mercury. · 改变物体的密度和液体:如果它密度更小它就浮,而它越密集越多沉在水下。铁在水中沉但在水银上浮。
An astronaut travels from Earth to the Moon. What happens to their mass · 质量 and weight · 重量? · 一个宇航员从地球到月球。他们的质量和重量会怎样?
Mass (amount of matter) never changes. Weight is the force of gravity, and the Moon's gravity is weaker, so the weight is smaller. · 质量(物质的量)从不变化。重量是重力,而月球的引力更弱,所以重量更小。
A bag has a mass of $5.0\ \text{kg}$. What is its weight on Earth, in N? (Use $g = 9.8\ \text{N/kg}$.) · 一个袋子有 $5.0\ \text{kg}$ 的质量。它在地球上的重量是多少,以 N 计?(用 $g = 9.8\ \text{N/kg}$。)
$W = mg = 5.0 \times 9.8 = 49\ \text{N}$. · $W = mg = 5.0 \times 9.8 = 49\ \text{N}$。
Density
- Density is the mass packed into each unit of volume:
- The symbol $\rho$ is the Greek letter "rho". The unit is $\text{kg/m}^3$ or $\text{g/cm}^3$.
- To measure it: find the mass with a balance, find the volume, then divide.
- Regular solid (a box): measure the sides and calculate the volume.
- Irregular solid (a stone): lower it into water in a measuring cylinder — the rise in water level is its volume (the displacement 排水法 method).
密度
- 密度(density)是塞进每单位体积的质量:
- 符号 $\rho$ 是希腊字母"rho"。单位是 $\text{kg/m}^3$ 或 $\text{g/cm}^3$。
- 要测量它:用一个天平找质量,找体积,然后除。
- 规则固体(一个盒子):测量边并计算体积。
- 不规则固体(一块石头):把它放进一个量筒里的水中——水位的上升是它的体积(排水(displacement)法)。
A metal block has a mass of $240\ \text{g}$ and a volume of $30\ \text{cm}^3$. What is its density, in g/cm³? · 一个金属块有 $240\ \text{g}$ 的质量和 $30\ \text{cm}^3$ 的体积。它的密度是多少,以 g/cm³ 计?
$\rho = \dfrac{m}{V} = \dfrac{240}{30} = 8.0\ \text{g/cm}^3$. · $\rho = \dfrac{m}{V} = \dfrac{240}{30} = 8.0\ \text{g/cm}^3$。
How do you find the volume of a small, oddly-shaped stone? · 你如何找出一块小的、奇形状的石头的体积?
The stone pushes the water up. The rise in the water level equals the stone's volume — the displacement method. · 石头把水推上去。水位的上升等于石头的体积——排水法。
Water in a measuring cylinder reads $50\ \text{cm}^3$. After a stone is added it reads $74\ \text{cm}^3$. What is the volume of the stone, in cm³? · 一个量筒中的水读 $50\ \text{cm}^3$。加入一块石头后它读 $74\ \text{cm}^3$。石头的体积是多少,以 cm³ 计?
The volume is the rise in level: $74 - 50 = 24\ \text{cm}^3$. · 体积是水位的上升:$74 - 50 = 24\ \text{cm}^3$。
Floating and sinking
- An object floats if its density is less than the density of the liquid.
- It sinks if its density is greater.
- Ice floats on water because ice is slightly less dense than water.
浮和沉
- 一个物体如果它的密度小于液体的密度就浮。
- 如果它的密度大于就沉。
- 冰浮在水上,因为冰比水密度稍小。
An object floats on a liquid if its density is less than the density of the liquid. · 一个物体如果它的密度小于液体的密度就浮在液体上。
Less dense than the liquid → it floats; denser than the liquid → it sinks. · 比液体密度小 → 它浮;比液体密集 → 它沉。
You've got it
- mass = amount of matter (kg), never changes; weight = force of gravity (N), $W = mg$
- $g = \dfrac{W}{m} \approx 9.8\ \text{N/kg}$ on Earth
- density $\rho = \dfrac{m}{V}$; find an odd shape's volume by displacement
- floats if its density is less than the liquid's
你掌握了
- 质量 = 物质的量(kg),从不变化;重量 = 重力(N),$W = mg$
- 在地球上 $g = \dfrac{W}{m} \approx 9.8\ \text{N/kg}$
- 密度 $\rho = \dfrac{m}{V}$;用排水找一个奇形状的体积
- 如果它的密度小于液体的就浮