📚 Density & Pressure | 密度与压强
Density and pressure are two essential concepts in IGCSE Edexcel Physics. Density describes how much mass is packed into a given volume and helps to identify substances, while pressure explains how forces are distributed over surfaces or transmitted through fluids. Mastering these topics allows you to analyse situations ranging from floating objects to hydraulic machines and to tackle experiments involving measurement of density and fluid pressure.
密度和压强是 IGCSE Edexcel 物理中两个核心概念。密度描述单位体积内所含质量的多少，可用于鉴别物质；压强则说明力如何分布在表面上或在流体中传递。掌握这些主题能让你分析从物体浮沉到液压机械的各种现象，并能应对涉及密度测量和流体压强的实验问题。
1. Understanding Density | 理解密度
Density (ρ) is defined as mass (m) per unit volume (V). It can be expressed by the equation ρ = m / V. The SI unit of density is kilogram per cubic metre (kg/m³), although grams per cubic centimetre (g/cm³) is also commonly used in the laboratory. Density is a characteristic property of a material: pure water has a density of 1000 kg/m³ (or 1.0 g/cm³) at 4 °C, while most metals have much higher densities.
密度 (ρ) 定义为单位体积 (V) 的质量 (m)，可用公式 ρ = m / V 表示。密度的国际单位是千克每立方米 (kg/m³)，但在实验室也常用克每立方厘米 (g/cm³)。密度是物质的一种特征性质：纯水在 4 °C 时的密度为 1000 kg/m³ (即 1.0 g/cm³)，而大多数金属的密度要大得多。
An object will float in a fluid if its average density is less than that of the fluid; it will sink if its density is greater. This principle explains why ships made of steel can float – their hollow shape gives the structure an overall lower density than water.
若物体的平均密度小于流体的密度，它就会漂浮；若大于，则会下沉。这就是为什么钢铁制成的轮船能够浮在水面上——中空的结构使船体的整体密度低于水。
2. Calculating Density | 计算密度
nsions of 10 cm × 5 cm × 4 cm. Its volume is 10 × 5 × 4 = 200 cm³. The density in g/cm³ is ρ = 600 g / 200 cm³ = 3.0 g/cm³. To obtain kg/m³, note that 1 g/cm³ = 1000 kg/m³, so 3.0 g/cm³ = 3000 kg/m³.
密度计算题往往需要转换单位并重组公式。例如，一块木头的质量为 600 g，尺寸为 10 cm × 5 cm × 4 cm。其体积为 10 × 5 × 4 = 200 cm³。以 g/cm³ 表示的密度为 ρ = 600 g / 200 cm³ = 3.0 g/cm³。若转换为 kg/m³，注意 1 g/cm³ = 1000 kg/m³，因此 3.0 g/cm³ = 3000 kg/m³。
When the mass is in kg and volume in m³, simply divide: a stone of mass 2.5 kg and volume 0.001 m³ has density ρ = 2.5 / 0.001 = 2500 kg/m³. Always check that the final units are consistent with the values given.
若质量以 kg 为单位、体积以 m³ 为单位，直接相除即可：一块质量为 2.5 kg、体积为 0.001 m³ 的石头，其密度为 ρ = 2.5 / 0.001 = 2500 kg/m³。任何计算都要确保最终单位与数据匹配。
3. Measuring Density: Regular Solids, Irregular Solids and Liquids | 测量密度：规则固体、不规则固体和液体
ngth × width × height for a cuboid). The density is then found by dividing mass by volume.
对于形状规则的固体，用天平称量质量，并用几何测量值计算体积（例如长方体的长 × 宽 × 高）。然后用质量除以体积得出密度。
id is lowered into the water, and the new volume V₂ is read. The volume of the solid is V₂ – V₁. Combined with the mass from the balance, density = mass / (V₂ – erflow) can may also be used to catch the displaced water and measure its volume directly.
对于形状不规则、无法简单计算体积的固体，采用排水法。先在量筒中加入适量水，记录初始体积 V₁。将固体轻轻放入水中，再读取体积 V₂。固体的体积即为 V₂ – V₁。结合天平测出的质量，密度 = 质量 / (V₂ – V₁)。也可以使用溢水罐 (Eureka can) 直接接取排开的水并测量其体积。
quid / volume. A density bottle is specifically designed to hold a precise volume when the stopper is inserted, which improves accuracy.
测量液体密度时，先称量空烧杯或密度瓶的质量，再加入已知体积的液体，测总质量。两者质量之差即为液体的质量；密度 = 液体质量 / 体积。密度瓶的瓶塞插入后可精确容纳固定体积的液体，有助于提高测量准确度。
4. Introduction to Pressure | 压强介绍
Pressure (P) is the force (F) acting perpendicularly on a surface per unit area (A). It is calculated by P = F / A where 1 Pa = 1 N/m². A larger force or a smaller contact area produces a higher pressure.
压强 (P) 是垂直作用在单位面积 (A) 上的力 (F)，由 P = F / A 计算。压强的国际单位是帕斯卡 (Pa)，1 Pa = 1 N/m²。力越大或接触面积越小，产生的压强就越大。
Everyday examples illustrate this: a sharp pin can easily pierce materials because the applied force is concentrated over a tiny area, creating very high pressure. Conversely, snowshoes prevent sinking into snow by spreading the same weight over a larger area, reducing the pressure.
日常生活中的例子说明了这一点：尖细的针容易刺穿物体，因为施加的力集中在极小的面积上，产生了很大的压强。相反，雪鞋可将相同的体重分散在较大的面积上，减小压强，避免陷入雪中。
5. Pressure in Solids | 固体中的压强
When a solid object rests on a surface, it exerts a pressure equal to its weight divided by the contact area. For a rectangular block, placing it on different faces changes the contact area and therefore the pressure, while the weight remains constant.
当固体放置于表面时，它对表面的压强等于其重量除以接触面积。对于一块长方体，以不同的面作为底面会使接触面积发生变化，压强也随之改变，而重量保持不变。
aller the area, the larger the pressure and the deeper the indentation into a soft surface.
例如，一块重 20 N 的砖，其三个面的面积分别为 0.02 m²、0.01 m² 和 0.005 m²，对应的压强分别为 20/0.02 = 1000 Pa、20/0.01 = 2000 Pa 和 20/0.005 = 4000 Pa。面积越小，压强越大，陷入松软表面的程度也越深。
In solid-on-solid contact, the force is transmitted in the same direction as the applied force; the pressure depends only on the normal component of the force and the contact area. This contrasts with fluids, which can transmit pressure in all directions.
在固体与固体的接触中，力沿着原来的方向传递；压强只取决于力的法向分量和接触面积。这与流体能在所有方向上传递压强不同。
6. Pressure in Fluids: Liquids and Gases | 流体中的压强：液体和气体
A fluid is a substance that can flow – both liquids and gases. In a fluid, the particles move freely and exert pressure in all directions by colliding with surfaces. In a liquid, pressure increases with depth because the weight of the liquid above adds to the force on lower layers. In a gas, pressure arises from the random impacts of molecules on the walls of a container.
流体是指能够流动的物质，包括液体和气体。在流体中，粒子自由运动，并通过与表面的碰撞在所有方向上产生压强。在液体中，压强随着深度增加，因为上方液体的重量加大了作用于下层液体的力。在气体中，压强源于分子对容器壁的无规则撞击。
An important characteristic of fluids is that a pressure applied at any point in a confined fluid is transmitted equally and undiminished to every other point within the fluid (Pascal’s principle). This is the basis of hydraulic brakes and lifting systems.
流体的一个重要特性是，施加在密闭流体中任一点的压强会等大地、不减弱地传递到流体的各点（帕斯卡原理）。这是液压刹车和举升系统的基础。
7. Pressure in Liquids: Deriving P = hρg | 液体中的压强：推导 P = hρg
is weight acts as a force over the area A at the bottom, so the pressure due to the liquid column is P = W / A = (ρ A h g) / A = h ρ g. This shows that liquid pressure depends only on depth, density and gravitational field strength, not on the cross-sectional area or total volume.
设想一个高度为 h、密度为 ρ、横截面积均匀为 A 的液柱。液体的体积 V = A h，质量 m = ρ V = ρ A h，重量 W = m g = ρ A h g。这个重量作为力作用在底部面积 A 上，因此液柱产生的压强为 P = W / A = (ρ A h g) / A = h ρ g。这表明液体压强只取决于深度、密度和重力场强度，与横截面积或总体积无关。
In the equation P = h ρ g, h is the vertical depth below the liquid surface, ρ is the liquid density (assumed uniform), and g is the acceleration due to gravity (9.8 m/s² or approximately 10 m/s²). At the same horizontal level, the pressure is the same throughout a stationary liquid, which explains why the surface of a liquid in a container is flat and horizontal.
在公式 P = h ρ g 中，h 是液面以下的竖直深度，ρ 是液体密度（假设均匀），g 是重力加速度（9.8 m/s² 或约 10 m/s²）。在同一水平面上，静止液体内各点的压强相等，这解释了容器中液面为什么是平的且水平的。
8. Atmospheric Pressure and Its Measurement | 大气压强及其测量
The Earth is surrounded by a thick layer of air, which exerts pressure on all surfaces on the ground due to its weight. Atmospheric pressure at sea level is about 1.01 × 10⁵ Pa (101 000 Pa), often called 1 atmosphere (1 atm). This pressure is equivalent to the weight of a column of mercury 760 mm high or a column of water about 10.3 m high.
地球周围包裹着一层厚厚的空气，空气因其重量对地面上所有的表面施加压强。海平面的大气压强约为 1.01 × 10⁵ Pa (101 000 Pa)，常称作 1 个标准大气压。这一压强相当于 760 mm 高的水银柱或约 10.3 m 高的水柱的重量所产生的压强。
The existence of atmospheric pressure can be demonstrated by filling a cup with water, covering it with a piece of card, and inverting it – the card remains in place because atmospheric pressure pushing upwards is greater than the weight of the water and the small pressure of trapped air. The famous Magdeburg hemispheres experiment also showed that a large force is needed to separate two evacuated hemispheres due to external air pressure.
大气压的存在可用覆杯实验演示：在杯中装满水，用卡片盖住杯口，倒置后卡片不掉落，因为下方大气向上的压强大于水的重量及杯内空气的微小压强。著名的马德堡半球实验同样表明，由于外部气压，需要很大的力才能拉开抽空的两个半球。
A mercury barometer is used to measure atmospheric pressure precisely. It consists of a vertical glass tube closed at one end and filled with mercury, inverted in a dish of mercury. The mercury column falls until the pressure due to its weight equals atmospheric pressure. The height of the column, typically around 760 mm at sea level, gives the pressure: Patm = h ρ g.
水银气压计可精确测量大气压。它由一根一端封闭并装满水银的竖直玻璃管组成，倒置插入水银槽中。水银柱降到其自身重量产生的压强与大气压相等时即保持平衡。该液柱的高度（海平面通常约 760 mm）即表示大气压：Patm = h ρ g。
9. Manometers and Barometers | U型管压力计与气压计
A U-tube manometer is a device used to measure the pressure of a gas or compare two pressures. One arm of the U-tube is connected to the gas supply, and the other is left open to the atmosphere. The liquid (often water or mercury) in the tube moves, creating a height difference h between the two surfaces. If the gas pressure is greater than atmospheric pressure, the liquid is pushed down on the gas side and up on the open side. The gas pressure can be found from Pgas = Patm + h ρ g, where ρ is the density of the manometer liquid.
U 型管压力计用于测量气体压强或比较两个压强。U 型管一端连接到待测气源，另一端与大气相通。管内的液体（通常是水或水银）会产生一个高度差 h。若气体压强大于大气压强，连接气体的一侧液面下降，开口侧液面上升。此时气体压强可由 Pgas = Patm + h ρ g 计算，其中 ρ 为管内液体的密度。
If the gas pressure is lower than atmospheric, the height difference appears on the opposite side, and the equation becomes Pgas = Patm – h ρ g. A barometer is essentially a manometer with one arm sealed and vacuum above the liquid, so it directly reads atmospheric pressure.
若气体压强低于大气压，则高度差出现在相反一侧，公式变为 Pgas = Patm – h ρ g。气压计本质上就是一侧密封并抽真空的 U 型管压力计，因此可直接读出大气压强。
10. Pascal’s Principle and Hydraulic Systems | 帕斯卡原理与液压系统
Pascal’s principle states that when pressure is applied to an enclosed fluid, that pressure is transmitted equally throughout the fluid without loss. In a hydraulic press, two pistons of different areas A₁ (small) and A₂ (large
Published by TutorHao | IGCSE Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图