密度与压强

Q: 考试中会提供密度和压强的相关公式吗？

不会，本考试不提供公式表，三个核心公式（、、）都需要考生自行记忆。

Q: 计算时我应该使用多大的g值？

根据爱德思IGCSE物理的考试要求，除非题目明确给出其他数值，否则一律使用 N/kg进行计算。

Q: 压强计算时如何将cm²转换为m²？

将cm²转换为m²需要乘以，例如： cm² = m² = m²。

物理· 第5部分，大纲考点5.1、5.3-5.7（2017版大纲）· 20 分钟阅读

1. 密度：定义、公式与单位换算★★☆☆☆⏱ 4 min

📘 定义

密度

$ρ = \frac{m}{V}$

密度是物质单位体积的质量，是材料的固有特性，与物质的总质量和总体积无关。

例:

Water has a density of 1000 kg/m³, or 1 g/cm³.

所有密度计算都遵循关系式 $ρ = m / V$ ，其中 $ρ$ 为密度， $m$ 为质量， $V$ 为体积。你需要仔细进行单位换算以避免常见错误：1 g/cm³ = 1000 kg/m³，1 cm³ = $1 0^{- 6}$ m³。

📐 例题

已知铝块质量为2700 kg，体积为1 m³，计算铝的密度，结果分别以kg/m³和g/cm³为单位给出。

1
步骤1：回忆密度计算公式
$\rho = \frac{m}{V}$
2
步骤2：代入以国际单位制给出的已知数值
$\rho = \frac{2700}{1} = 2700 \text{ kg/m}^3$
3
步骤3：将结果除以1000，换算为以g/cm³为单位的数值
$\rho = \frac{2700}{1000} = 2.7 \text{ g/cm}^3$

2. 密度的实验探究★★★☆☆⏱ 5 min

考试会考察你对三类物质（规则固体、不规则固体、液体）密度测量实验方法的书面描述。所有方法都遵循同一核心原理：分别测量质量和体积，再通过 $ρ = m / V$ 计算密度。

Regular solid: Measure mass using a top-pan balance. Measure dimensions using a ruler, calculate volume using the appropriate geometric formula, then compute density.
Irregular solid: Measure mass using a top-pan balance. Fill a eureka can to the spout with water, place a measuring cylinder under the spout, submerge the solid fully, measure displaced water volume, then compute density.
Liquid: Measure mass of an empty beaker, add a known volume of liquid from a measuring cylinder, remeasure total mass, subtract to find liquid mass, then compute density.

📐 例题

一名学生使用排水法测量小石块的密度，已知石块质量为150 g，排开水的体积为60 cm³，计算该石块的密度，单位为kg/m³。

1
步骤1：将质量换算为kg，体积换算为m³
$m = 150 \text{ g} = 0.15 \text{ kg}; V = 60 \text{ cm}^3 = 6 \times 10^{-5} \text{ m}^3$
2
步骤2：代入密度公式计算
$\rho = \frac{0.15}{6 \times 10^{-5}} = 2500 \text{ kg/m}^3$

Exam tip:

想要拿到AO3实验类题目的分数，一定要提到多次测量取平均值以减小随机误差，并且在使用排水法时要确认物体完全浸没在水中。

3. 固体压强：单位面积受力★★★☆☆⏱ 4 min

📘 定义

压强

$p = \frac{F}{A}$

压强是垂直作用在物体表面单位面积上的力，单位为帕斯卡（Pa），其中1 Pa = 1 N/m²。

例:

A sharp knife cuts more easily than a blunt one because the force acts over a smaller area, producing higher pressure.

压强计算中， $p$ 代表压强（单位Pa）， $F$ 代表垂直作用在表面上的力（单位N）， $A$ 代表力的作用面积（单位m²）。记住将cm²转换为m²时要乘以 $1 0^{- 4}$ ，例如50 cm² = 0.005 m²。

📐 例题

一个质量为50 kg的箱子放在地面上，底面积为0.2 m²，取 $g = 10$ N/kg，计算箱子对地面的压强。

1
步骤1：计算箱子的重力（即作用在地面上的力）
$F = mg = 50 \times 10 = 500 \text{ N}$
2
步骤2：代入压强公式计算
$p = \frac{F}{A} = \frac{500}{0.2} = 2500 \text{ Pa}$

4. 静止流体中的压强★★☆☆☆⏱ 3 min

静止的流体（液体和气体）在任意一点产生的压强都沿各个方向大小相等。这就是为什么无论水瓶上的小孔朝向哪个方向，水都会垂直于瓶身表面向外喷出。

✓ 快速检测

A scuba diver is 10 m below the surface of the sea. Which direction does the water pressure act on the diver's goggles?
- Only downwards
- Only upwards
- Equally in all directions
- Only sideways
显示答案
Equally in all directions —
Pressure in a static fluid acts equally in all directions at the same depth, so the goggles experience pressure from all sides.

5. 流体压强差计算★★★★☆⏱ 4 min

📘 定义

流体压强差

$p = h ρ g$

静态流体内两点之间的压强差仅取决于两点间的竖直高度差、流体密度以及重力场强度，与容器的形状或横截面积无关。

例:

The pressure at the bottom of a 1 m tall water tank is 10,000 Pa higher than the pressure at the top, regardless of how wide the tank is.

进行此类计算时， $p$ 代表压强差（单位：帕斯卡，符号Pa）， $h$ 代表两点间的竖直高度差（深度，单位：米，符号m）， $ρ$ 代表流体密度（单位：千克每立方米，符号kg/m³），除非另有说明，否则取 $g = 10$ N/kg。

📐 例题

计算泳池水面与水面下方2 m处某点的压强差。已知水的密度为1000 kg/m³，取 $g = 10$ N/kg。

1
步骤1：回忆流体压强差公式
$p = h\rho g$
2
步骤2：代入已知数值
$p = 2 \times 1000 \times 10 = 20000 \text{ Pa} = 20 \text{ kPa}$

Exam tip:

若容器倾斜，公式中的 $h$ 必须取竖直高度，不能取斜向长度。容器的形状不会影响压强差，只有竖直深度会对其产生影响。

6. 常见陷阱

错误做法:

Using g = 9.81 N/kg for calculations

原因:

The Edexcel IGCSE specification explicitly states to use g = 10 N/kg unless the question says otherwise, so using 9.81 will lead to incorrect answers and lost marks.

正确做法:

Always use g = 10 N/kg unless a different value is given in the question.

错误做法:

Forgetting to convert cm² to m² for pressure calculations, using cm² directly in the formula

原因:

Pressure is in pascals, which is N/m², so area must be in m². Using cm² will give a value 10,000 times larger than the correct answer.

正确做法:

Multiply any area given in cm² by $1 0^{- 4}$ to convert to m² before substituting into $p = F / A$ .

错误做法:

Using the volume of the container instead of displaced volume for irregular solid density calculations

原因:

The displacement method uses the volume of water pushed out by the solid, which equals the volume of the solid itself, not the total volume of the container.

正确做法:

Measure only the volume of water that flows out of the eureka can or the increase in water level in the measuring cylinder when the solid is submerged.

错误做法:

Assuming pressure in a fluid only acts downwards

原因:

Pressure in a static fluid acts equally in all directions at a given depth, so objects under water experience pressure from all sides, not just above.

正确做法:

State that pressure acts equally in all directions when describing fluid pressure in exam answers.

错误做法:

Converting g/cm³ to kg/m³ by multiplying by 100 instead of 1000

原因:

1 g/cm³ = 1000 kg/m³, as 1 kg = 1000 g and 1 m³ = 1,000,000 cm³, so the conversion factor is 1000.

正确做法:

Multiply density in g/cm³ by 1000 to get density in kg/m³, or divide kg/m³ by 1000 to get g/cm³.

7. 速查表

Formula	Variables	Units to Use	Key Note
$ρ = m / V$	$ρ$ = density, $m$ = mass, $V$ = volume	$ρ$ : kg/m³ or g/cm³; $m$ : kg or g; $V$ : m³ or cm³	1 g/cm³ = 1000 kg/m³; match units to required output
$p = F / A$	$p$ = pressure, $F$ = force, $A$ = area	$p$ : Pa (N/m²); $F$ : N; $A$ : m²	Convert cm² to m²: × $1 0^{- 4}$ ; use only contact area
$p = h ρ g$	$p$ = pressure difference, $h$ = vertical height, $ρ$ = fluid density, $g$ = gravitational field strength	$p$ : Pa; $h$ : m; $ρ$ : kg/m³; $g$ : 10 N/kg	Independent of container shape; use vertical depth, not diagonal length

8. 常见问题

考试中会提供密度和压强的相关公式吗？

不会，本考试不提供公式表，三个核心公式（ $ρ = m / V$ 、 $p = F / A$ 、 $p = h ρ g$ ）都需要考生自行记忆。

计算时我应该使用多大的g值？

根据爱德思IGCSE物理的考试要求，除非题目明确给出其他数值，否则一律使用 $g = 10$ N/kg进行计算。

压强计算时如何将cm²转换为m²？

将cm²转换为m²需要乘以 $1 0^{- 4}$ ，例如： $200$ cm² = $200 \times 1 0^{- 4}$ m² = $0.02$ m²。

深入阅读

syllabus爱德思IGCSE物理（4PH1）官方大纲可查阅第5部分获取该主题的完整指导内容

下一步

Now that you have mastered density and pressure for Edexcel IGCSE Physics, you are ready to move on to the next topics in the Solids, Liquids and Gases unit. Next, you will learn about specific heat capacity and changes of state, which build on your understanding of mass and energy transfers in materials. Following that, you will cover the gas laws, including the relationship between pressure, volume and temperature of gases, which extends your knowledge of pressure in fluids. Make sure you practise as many exam-style questions on density and pressure as possible to reinforce your recall of the three core formulae and unit conversion skills, as these are frequently tested in both Paper 1 and Paper 2 of the exam, as well as in the Double Award specification.