Pressure (压力)
Pressure is defined as the force acting per unit
area. When a force is applied to a surface, the
pressure experienced depends on both the
magnitude of the force and the area over which it
is distributed. This relationship is expressed by the
formula:
Examples of Pressure Calculations (压
力计算示例)
Example 1: A 500 N force is applied to an area of 2
m². Calculate the pressure.
Solution: P = F/A = 500 N / 2 m² = 250 Pa
Pressure = Force / Area
Example 2: A woman weighing 600 N stands on one
P = F/A
heel with an area of 1 cm² (0.0001 m²). Calculate
压力 = 力 / 面积
the pressure on the floor.
The standard unit of pressure in the International
Solution: P = F/A = 600 N / 0.0001 m² = 6,000,000 Pa
System of Units (SI) is the pascal (Pa), which is
= 6 MPa
equivalent to one newton per square meter (N/m²).
To put this in perspective, the average atmospheric
pressure at sea level is approximately 101,325 Pa
or 101.325 kPa.
Understanding pressure is crucial for explaining
many everyday phenomena. For instance, snow
shoes have a large surface area to reduce the
pressure on snow, preventing the wearer from
sinking. Similarly, knives have sharp edges to
concentrate force over a small area, increasing
pressure and making cutting easier.
When studying pressure in solids, remember that
increasing the area over which a force acts will
decrease the pressure, while decreasing the area
will increase the pressure. This principle explains
why walking on soft sand is easier with flat shoes
than with high heels.
Key Points to
Remember (要记住的
要点)
Standard Units (标准
单位)
Pressure increases when
standard unit of pressure
Pascal (Pa) = N/m² is the
Practical
Applications (实际应
用)
Understanding pressure
helps explain the design of
the same force is applied
many everyday objects like
over a smaller area
pins, knives, and
snowshoes
Pressure in Liquids (液体中的压力)
Pressure in liquids behaves differently from pressure in solids due to the fluid nature of liquids. A key principle is that pressure in a liquid increases
with depth. This occurs because liquids have weight, and the deeper you go, the more liquid there is above you, creating greater pressure.
The Formula for Liquid Pressure (液体压力公式)
Pressure = Density × Gravity × Depth
P = ρgh
压力 = 密度 × 重力加速度 × 深度
Where:
•
P is pressure (Pa)
•
ρ (rho) is the density of the liquid (kg/m³)
•
g is the acceleration due to gravity (9.8 m/s²)
•
h is the depth below the surface (m)
This formula shows that three factors affect liquid pressure: the density
of the liquid, the acceleration due to gravity, and the depth. For the
same depth, a denser liquid (like mercury) will exert more pressure than
Practical Applications (实际应用)
a less dense liquid (like water).
The principles of liquid pressure have numerous real-world applications:
•
Dam design: Engineers must account for increasing water pressure
with depth when designing dams
•
Submarine construction: Submarines must withstand enormous
pressures in deep water
•
Hydraulic systems: These systems use the transmission of pressure
through liquids to multiply force
Hydraulic systems like car brakes and hydraulic lifts work based on
Pascal's principle, which states that pressure applied to an enclosed
fluid is transmitted equally in all directions.
Sample Problems (样题)
Example 1: Calculate the pressure at a depth of 5 meters in a swimming pool. (Water density = 1000 kg/m³)
Solution: P = ρgh = 1000 kg/m³ × 9.8 m/s² × 5 m = 49,000 Pa = 49 kPa
Example 2: A submarine is at a depth where the water pressure is 350,000 Pa. If water density is 1025 kg/m³, calculate the depth of the submarine.
Solution: h = P/(ρg) = 350,000 Pa ÷ (1025 kg/m³ × 9.8 m/s²) = 34.8 m
Common Misconceptions (常见误解)
Test Yourself (自我测试)
Key Terminology (关键术语)
•
•
Why does a dam need to be thicker at
•
Hydrostatic pressure (静水压力)
the bottom than at the top?
•
Pascal's principle (帕斯卡原理)
Explain why scuba divers must equalize
•
Fluid dynamics (流体动力学)
•
Pressure gradient (压力梯度)
The shape of the container does not
affect the pressure at a given depth
•
Pressure acts equally in all directions,
•
not just downward
•
Water pressure is not directly related to
the amount of water, but to the depth
and density
pressure in their ears as they descend
•
Calculate the pressure 10 meters below
the surface of a lake
Pressure in Gases (气体中的压力)
Gas pressure operates on different principles than pressure in solids or liquids. In gases, pressure results from countless
molecular collisions against surfaces. When gas molecules strike the walls of their container, they exert tiny forces. With billions of
molecules hitting the surface every second, these forces combine to create measurable pressure.
Atmospheric Pressure (大气压力)
The air around us exerts pressure called atmospheric pressure. This pressure results from the weight of all the air in the
atmosphere pressing down on Earth's surface. At sea level, standard atmospheric pressure is approximately 101,325 Pa (101.3
kPa), often expressed as 1 atmosphere (atm).
Atmospheric pressure decreases with altitude because there is less air above pressing down. This explains why airplane cabins
must be pressurized and why it's harder to breathe on tall mountains.
Weather Systems (天气系统)
High and low pressure systems determine weather patterns. Air moves from high-pressure areas to low-pressure areas,
creating winds. Barometers measure these atmospheric pressure changes to help forecast weather conditions.
Balloons (气球)
When you inflate a balloon, you pump air molecules inside. These molecules collide with the balloon's inner surface,
creating pressure that pushes outward, expanding the balloon until the outward gas pressure balances with the elastic
resistance of the balloon material.
Tires (轮胎)
Vehicle tires rely on gas pressure for proper functioning. The pressurized air inside provides the necessary rigidity while still
allowing for shock absorption. When temperature rises, the air molecules move faster, increasing pressure—explaining
why tire pressure increases on hot days.
Measuring Gas Pressure (气体压力的测量)
Several instruments are used to measure gas pressure:
•
Barometers (气压计): Measure atmospheric pressure using mercury or aneroid mechanisms
•
Manometers (压力计): Measure the pressure of gases in containers relative to atmospheric pressure
•
Pressure gauges (压力表): Used for measuring tire pressure and other contained gas systems
Sample Problems (样题)
Example 1: A container of gas exerts a pressure of 120 kPa. If
Example 2: The pressure in a car tire is measured at 220 kPa at
the volume is reduced to half its original size (with
15°C. If the temperature rises to 35°C, what will be the new
temperature constant), what will be the new pressure?
pressure? (Assuming the volume remains constant)
Solution: According to Boyle's Law, P₁V₁ = P₂V₂
Solution: Using the formula P₁/T₁ = P₂/T₂, where T is in Kelvin:
If V₂ = V₁/2, then P₂ = P₁ × (V₁/V₂) = 120 kPa × 2 = 240 kPa
T₁ = 15 + 273 = 288 K
T₂ = 35 + 273 = 308 K
P₂ = P₁ × (T₂/T₁) = 220 kPa × (308 K/288 K) = 235.3 kPa
Density (密度)
Density is a fundamental property of matter that describes how much mass is
contained in a given volume. It is a measure of how "compact" or "concentrated" the
matter is. Materials with high density, like lead, have their particles packed closely
together, while materials with low density, like cork, have particles that are more
spread out.
Density = Mass / Volume
ρ = m/V
密度 = 质量 / 体积
The standard unit for density in the SI system is kilograms per cubic meter (kg/m³).
However, in the laboratory, density is often expressed in grams per cubic centimeter
(g/cm³). These units are related: 1 g/cm³ = 1000 kg/m³.
Calculating Density (计算密度)
To calculate density, you need to measure both the mass and volume of an object.
Mass can be measured directly using a balance, while volume can be determined in
different ways depending on the object's shape:
Examples of Densities (密度实例)
•
For regular shapes (cubes, spheres), use geometric formulas
•
For irregular solids, use water displacement
•
For liquids, measure the volume directly in a graduated cylinder
Material (材料)
Density (密度) (g/cm³)
Air (空气)
0.0013
Cork (软木)
0.24
Ice (冰)
0.92
Water (水)
1.00
Aluminum (铝)
2.70
Iron (铁)
7.87
Lead (铅)
11.34
Gold (金)
19.32
Applications of Density: Buoyancy and Floating (密度应用：浮力和漂浮)
Density plays a crucial role in determining whether objects float or sink in fluids. The principle of buoyancy states that:
•
If an object's density is less than the fluid's density, it will float
•
If an object's density is greater than the fluid's density, it will sink
•
If the densities are equal, the object will remain suspended within the fluid
This principle explains why ice (density 0.92 g/cm³) floats in water (density 1.00 g/cm³), and why ships made of steel can float despite steel having a higher density than water.
Ships are designed with hollow spaces, reducing their average density to less than that of water.
Find Mass
Find Volume
Find Density
m=ρ×V
V=m÷ρ
ρ=m÷V
Practice Problems (练习题)
Example 1: A block of wood has a mass of 400 g and a volume of 500 cm³. Calculate its density.
Solution: ρ = m/V = 400 g / 500 cm³ = 0.8 g/cm³
Example 2: A piece of metal has a density of 8.96 g/cm³ and a volume of 15 cm³. Calculate its mass.
Solution: m = ρ × V = 8.96 g/cm³ × 15 cm³ = 134.4 g
Example 3: An object has a mass of 35 g and a density of 2.5 g/cm³. Calculate its volume.
Levers (杠杆)
A lever is a simple machine consisting of a rigid bar that pivots on a fixed point called a fulcrum. Levers are among the oldest and most fundamental
mechanical devices, used to amplify force or change its direction. From bottle openers to see-saws, levers are everywhere in our daily lives and
understanding them is essential to grasping basic mechanical principles.
Three Classes of Levers (三类杠杆)
1
First Class Levers (第一类杠杆)
2
Second Class Levers (第二类杠杆)
3
Third Class Levers (第三类杠杆)
The fulcrum is positioned between the
The load is positioned between the
The effort is positioned between the
effort (force applied) and the load
fulcrum and the effort. Examples include
fulcrum and the load. Examples include
(resistance). Examples include scissors,
wheelbarrows, nutcrackers, and bottle
tweezers, fishing rods, and human
seesaws, and crowbars. These levers can
openers. These levers always amplify
forearms. These levers always amplify
either amplify force or distance,
force at the expense of distance.
distance at the expense of force.
depending on the position of the
fulcrum.
Mechanical Advantage of Levers (杠杆的机械优势)
The mechanical advantage (MA) of a lever is the ratio of output force to input force. It indicates how much a lever multiplies the applied force.
Mechanical Advantage = Output Force / Input Force
机械优势 = 输出力 / 输入力
For a lever, the mechanical advantage can also be calculated from the distances:
Mechanical Advantage = Effort Distance / Load Distance
机械优势 = 施力距离 / 负重距离
Where effort distance is the distance from the fulcrum to where force is applied, and load distance is the distance from the fulcrum to the load.
Real-World Applications (实际应用)
Construction Equipment (建筑设备)
Hand Tools (手动工具)
Human Body (人体)
Cranes and excavators utilize lever principles
Many common tools like hammers, pliers, and
Our bodies contain numerous natural levers.
to lift heavy objects with relatively small inputs
wrenches employ lever mechanisms to
Our arms are third-class levers with muscles
of force. The long arm of a crane acts as a
amplify force. A longer wrench handle
providing the effort, joints acting as fulcrums,
lever, with the pivot point serving as the
provides greater torque with the same applied
and hands/objects being the load.
fulcrum.
force.
Worked Example (例题)
Problem: A 10N force is applied to a lever 0.8m from the fulcrum. If the load is 0.2m on the other side of the fulcrum, calculate:
1. The mechanical advantage of the lever
2. The maximum load that can be lifted
Solution:
1. Mechanical Advantage = Effort Distance / Load Distance = 0.8m / 0.2m = 4
2. Load Force = Input Force × Mechanical Advantage = 10N × 4 = 40N
This means the lever multiplies the applied force by 4, allowing a 10N input force to lift a 40N load.
Calculating Moments (力矩的计算)
A moment is the turning effect of a force. When you push or pull on an object in a
way that makes it rotate, you're creating a moment. The size of the moment
depends on two factors: the force applied and the perpendicular distance from
the pivot point (fulcrum) to the line of action of the force.
Moment = Force × Perpendicular Distance
M=F×d
力矩 = 力 × 垂直距离
The standard unit for moments is the newton-meter (Nm). A larger moment will
produce a greater turning effect.
Direction of Moments (力矩的方向)
Moments can act in a clockwise or counterclockwise direction:
•
Clockwise moments (顺时针力矩): Forces that would turn the object in a
clockwise direction
•
Counterclockwise moments (逆时针力矩): Forces that would turn the object in
a counterclockwise direction
When calculating multiple moments acting on an object, it's important to assign a
positive sign to one direction (typically counterclockwise) and a negative sign to
the other direction (typically clockwise).
Principle of Moments (力矩原理)
For an object to be in rotational equilibrium (not rotating), the sum of all
clockwise moments must equal the sum of all counterclockwise moments. This is
known as the principle of moments:
Sum of clockwise moments = Sum of counterclockwise moments
顺时针力矩之和 = 逆时针力矩之和
This principle is fundamental for solving problems involving balanced objects,
such as seesaws, cranes, and bridges.
Example Problems (例题)
Example 1: Basic Moment Calculation
Example 2: Principle of Moments
Example 3: Multiple Forces
Problem: A force of 30N is applied perpendicular
Problem: A seesaw has a 300N child sitting 1.5m
Problem: A beam has three forces acting on it:
to a lever arm at a distance of 0.5m from the
from the pivot on one side. Where should a 400N
50N downward at 2m from the pivot, 30N upward
pivot. Calculate the moment.
child sit on the other side to balance the seesaw?
at 1m from the pivot, and an unknown force F
Solution: Moment = Force × Distance = 30N ×
Solution: Using the principle of moments: 300N ×
0.5m = 15Nm
1.5m = 400N × d d = (300N × 1.5m) ÷ 400N =
acting downward at 3m from the pivot. If the
beam is balanced, find F.
1.125m The 400N child should sit 1.125m from
Solution: Taking clockwise as positive: Clockwise
the pivot.
moments: 50N × 2m = 100Nm Counterclockwise
moments: 30N × 1m + F × 3m = 30Nm + 3F Since
the beam is balanced: 100Nm = 30Nm + 3F 3F =
70Nm F = 23.33N
Identify the pivot point
Determine the point around which rotation would occur
Measure distances
Find the perpendicular distance from the pivot to each force
Calculate individual moments
Multiply each force by its perpendicular distance
Apply the principle of moments
Set up the equation balancing clockwise and counterclockwise moments
Understanding moments is crucial for analyzing structures and machines where rotational forces are involved. Engineers use these principles when designing bridges,
buildings, and various mechanical devices to ensure stability and proper function. In daily life, we apply these principles when using tools like wrenches, opening doors,
or balancing objects.
Review and Practice Questions (复习和练习题)
Key Concepts Summary (关键概念总结)
Pressure (压力)
Liquid Pressure (液体压力)
•
P = F/A
•
P = ρgh
•
Units: Pascal (Pa)
•
Increases with depth
•
Pressure inversely proportional to area
•
Acts equally in all directions
Density (密度)
Moments (力矩)
•
ρ = m/V
•
M=F×d
•
Units: kg/m³ or g/cm³
•
Units: Newton-meter (Nm)
•
Determines floating/sinking
•
Clockwise = Counterclockwise for balance
Mixed Practice Questions (综合练习题)
1.
A 750N force is applied to an area of 0.5m². Calculate the pressure exerted. (750N ÷ 0.5m² = 1500 Pa)
2.
Calculate the pressure at a depth of 15m in seawater (density 1025 kg/m³). (P = 1025 × 9.8 × 15 = 150,675 Pa)
3.
A substance has a mass of 560g and a volume of 80cm³. Calculate its density and determine if it will float in water. (ρ = 560g ÷ 80cm³ = 7g/cm³. It will sink in water.)
4.
A lever has a mechanical advantage of 5. If the effort force is 200N, what load can it lift? (Load = 200N × 5 = 1000N)
5.
Calculate the moment produced by a 25N force acting at a perpendicular distance of 0.4m from a pivot. (M = 25N × 0.4m = 10Nm)
6.
A seesaw has a 350N child sitting 1.2m from the pivot. Where should a 280N child sit to balance the seesaw? (d = (350N × 1.2m) ÷ 280N = 1.5m)
Exam Success Tips (考试成功技巧)
Review Formulas Regularly
Practice Calculations
Create flashcards with key formulas and review them daily. Understanding the
Regularly solve different types of problems. Pay attention to units and show
relationship between variables in each formula is crucial.
your working clearly to earn full marks.
Time Management
Draw Diagrams
During the exam, allocate time based on the marks for each question. If stuck,
Use clear, labeled diagrams to illustrate your understanding, especially for
move on and return later if time permits.
lever classes and moment problems.
Key Terms Glossary (关键术语词汇表)
English
中文
Definition
Pressure
压力
Force per unit area
Density
密度
Mass per unit volume
Buoyancy
浮力
Upward force exerted by a fluid on an immersed
object
Lever
杠杆
A rigid bar that pivots around a fixed point (fulcrum)
Fulcrum
支点
The pivot point of a lever
Moment
力矩
The turning effect of a force
Mechanical Advantage
机械优势
Ratio of output force to input force
Pascal
帕斯卡
The SI unit of pressure (N/m²)
For additional learning resources, consider using the physics simulations available at PhET Interactive Simulations (phet.colorado.edu), Khan Academy's physics courses, and
the supplementary materials provided with the "Complete Physics for Cambridge Secondary 1 Oxford" textbook. Regular practice with past papers will also help familiarize
you with the exam format and question styles.