Forces, Motion and Newton's Laws | 力、运动与牛顿定律

📚 Forces, Motion and Newton’s Laws | 力、运动与牛顿定律

This revision guide explores the physics of forces and motion. It is a core topic for Edexcel IGCSE Science (Double Award). You need to describe forces, interpret distance-time and velocity-time graphs, and apply Newton’s laws to simple situations. These ideas connect to everyday events such as a car braking, a person pushing a trolley, or a rocket taking off.

本复习指南探讨力与运动的基本物理概念。这是 Edexcel IGCSE 科学（双奖）的核心考点。你需要能够描述力、解读距离-时间图像和速度-时间图像，并把牛顿定律应用于简单情境。这些原理与日常事件密切相关，例如汽车刹车、人推手推车或火箭发射。

1. What is a Force? | 什么是力？

A force is a push, pull or twist that acts on an object. Forces can affect how an object moves, how fast it moves, or the direction in which it moves. They can also change the shape of an object, for example when a spring is stretched or compressed.

力是施加在物体上的推、拉或扭转作用。力可以影响物体如何运动、运动有多快，或者运动的方向。力也可以改变物体的形状，例如拉伸或压缩弹簧。

A force is a vector quantity. This means it has both size and direction. The unit of force is the newton, which has the symbol N. If two forces act on the same object, we can combine them to find the resultant force.

力是矢量。这意味着力既有大小又有方向。力的单位是牛顿，符号为 N。如果有两个力作用在同一物体上，我们可以把它们合并求出合力。

Forces can produce different effects on an object:

力可以对物体产生不同的效果：

change the speed of the object: make it speed up or slow down | 改变物体的速率：使其加速或减速
change the direction of the object: make it turn or change path | 改变物体的方向：使其转向或改变路径
change the shape of the object: stretch, compress or bend it | 改变物体的形状：使其拉伸、压缩或弯曲

2. Contact and Non-Contact Forces | 接触力与非接触力

Forces can be grouped into contact forces and non-contact forces. Contact forces only act when two objects are physically touching. Non-contact forces can act through empty space without any contact between the objects.

力可分为接触力与非接触力。接触力只在两个物体实际接触时才起作用。非接触力可以穿过空间作用，不需要物体之间相互接触。

Contact forces 接触力	Non-contact forces 非接触力
friction 摩擦力	gravitational force 重力
air resistance 空气阻力	electrostatic force 静电力
tension in a rope 绳子中的张力	magnetic force 磁力
normal contact force 法向接触力	gravitational attraction between masses 质量之间的万有引力

In Edexcel IGCSE questions, you may be asked to name the force that causes a movement or to state whether a force is contact or non-contact. For example, a ball falling towards the Earth is affected by the non-contact force of gravity, while a book sliding on a table experiences the contact force of friction.

在 Edexcel IGCSE 考试中，可能会要求你指出引起某个运动的力，或者判断一个力是接触力还是非接触力。例如，一个球落向地球时受到重力这种非接触力的作用，而一本在桌面上滑动的书则受到摩擦力这种接触力的作用。

3. Balanced and Unbalanced Forces | 平衡力与非平衡力

When several forces act on an object, the overall force is called the resultant force. To find the resultant force, add forces acting in the same direction and subtract forces acting in opposite directions.

当多个力作用在同一物体上时，总作用力称为合力。求合力时，方向相同的力相加，方向相反的力相减。

If the resultant force is zero, the forces are balanced. A balanced force changes nothing about the motion of an object. If the object is stationary, it will stay stationary. If it is moving, it will continue to move at the same speed and in the same direction.

如果合力为零，这些力就是平衡力。平衡力不会改变物体的运动状态。如果物体静止，它将保持静止。如果物体正在运动，它将保持相同的速率和方向继续运动。

If the resultant force is not zero, the forces are unbalanced. An unbalanced force causes acceleration. This could mean speeding up, slowing down, or changing direction.

如果合力不为零，这些力就是不均衡力。非平衡力会使物体加速。这可能意味着加速、减速或改变方向。

For example, a car driving at a constant velocity on a straight, level road has engine force equal to friction and air resistance. The forces are balanced and the resultant force is zero. When the driver presses the accelerator harder, the engine force becomes larger and the car accelerates forwards.

例如，一辆汽车在平直路面上以恒定速度行驶时，发动机的驱动力与摩擦力和空气阻力相平衡。这些力是平衡的，合力为零。当司机踩下加速踏板时，驱动力变大，汽车向前加速。

4. Distance, Speed and Velocity | 距离、速率与速度

Before solving motion problems, you must understand the difference between distance and displacement, and between speed and velocity. Distance and speed are scalar quantities because they only have size. Displacement and velocity are vector quantities because they have both size and direction.

在解决运动问题之前，你必须理解距离与位移、速率与速度之间的区别。距离和速率是标量，因为它们只有大小。位移和速度是矢量，因为它们既有大小又有方向。

Speed is a measure of how fast an object is moving. It is defined as the distance travelled per unit time.

速率是用来表示物体运动有多快的量。它的定义是单位时间内通过的距离。

speed = distance ÷ time, v = s ÷ t

速率 = 距离 ÷ 时间， v = s ÷ t

Velocity is similar to speed but it must include the direction of motion. A car moving at 15 m/s north has a different velocity from a car moving at 15 m/s south, even though they have the same speed. In IGCSE questions, the symbol v is often used for speed or velocity, and s is used for distance or displacement.

速度与速率相似，但必须包含运动方向。一辆以 15 m/s 向北行驶的汽车与另一辆以 15 m/s 向南行驶的汽车速度不同，尽管它们的速率相同。在 IGCSE 试题中，v 通常表示速率或速度，s 表示距离或位移。

Common unit for speed is the metre per second, written as m/s. In some questions you may also see km/h.

速率的常用单位是米每秒，记为 m/s。有些题目中也会出现 km/h。

5. Acceleration | 加速度

Acceleration is the rate of change of velocity. It tells us how quickly an object is speeding up or slowing down. Acceleration is a vector quantity, and its unit is the metre per second squared, written as m/s².

加速度是速度的变化率。它表示物体加速或减速的快慢。加速度是矢量，单位是米每二次方秒，记为 m/s²。

For an object with initial velocity u and final velocity v, the change in velocity is v − u. If this change happens over a time t, then:

对于初速度为 u、末速度为 v 的物体，速度的变化量为 v − u。如果这一变化经历的时间为 t，则：

acceleration = (v − u) ÷ t, a = (v − u) ÷ t

加速度 = (末速度 − 初速度) ÷ 时间， a = (v − u) ÷ t

Sometimes the equation is written as a = Δv ÷ t, where Δv is the change in velocity.

这个公式有时也写成 a = Δv ÷ t，其中 Δv 表示速度变化量。

Worked example: a car moves from rest to 20 m/s in 4 s. What is its acceleration?

示例：一辆汽车从静止出发，在 4 s 内速度达到 20 m/s。它的加速度是多少？

a = (20 − 0) ÷ 4 = 5 m/s²

If an object slows down, the change in velocity is negative, so the acceleration is negative. This is sometimes called deceleration or retardation. For example, if a cyclist slows from 8 m/s to 2 m/s in 3 s, the acceleration is (2 − 8) ÷ 3 = −2 m/s².

如果物体减速，速度变化量为负值，所以加速度也是负值。这有时称为减速度或负加速度。例如，如果一个骑车人从 8 m/s 减速到 2 m/s，用时 3 s，那么加速度为 (2 − 8) ÷ 3 = −2 m/s²。

6. Distance-Time Graphs | 距离-时间图像

A distance-time graph shows how the distance travelled by an object changes with time. Time is plotted on the horizontal axis, and distance is plotted on the vertical axis.

距离-时间图像表示物体通过的距离随时间的变化。时间画在横轴上，距离画在纵轴上。

On a distance-time graph, the gradient of the line represents speed. The steeper the line, the greater the speed. A horizontal line means the object is not moving because the distance is not changing.

在距离-时间图像中，直线的斜率表示速率。直线越陡，速率越大。水平线表示物体没有运动，因为距离没有变化。

Horizontal line: object is stationary | 水平线：物体静止
Straight sloping line: object is moving at constant speed | 直线斜线：物体匀速运动
Steeper slope: higher speed | 斜率更大：速率更高
Curved line: speed is changing | 曲线：速率在变化

To calculate the speed from a distance-time graph, choose a point on the straight line and divide the change in distance by the change in time. If the graph is curved, the speed at a particular moment is the gradient of the tangent to the curve at that moment. This is normally an extension idea, but the concept can appear in IGCSE questions.

要从距离-时间图像中计算速率，可以在直线上取一点，用距离的变化量除以时间的变化量。如果图像是曲线，某一时刻的速率就是该时刻曲线上切线的斜率。这通常是拓展概念，但在 IGCSE 题目中也可能出现。

7. Velocity-Time Graphs | 速度-时间图像

A velocity-time graph shows how the velocity of an object changes with time. On the horizontal axis is time, and on the vertical axis is velocity.

速度-时间图像表示物体的速度随时间的变化。横轴是时间，纵轴是速度。

On a velocity-time graph, the gradient represents acceleration. A horizontal line means that velocity is not changing, so the object is moving at constant velocity. If the line has a positive gradient, the object is speeding up; if the gradient is negative, the object is slowing down.

在速度-时间图像中，斜率表示加速度。水平线表示速度不变，所以物体以恒定速度运动。如果斜率为正，物体在加速；如果斜率为负，物体在减速。

Horizontal line: constant velocity | 水平线：恒定速度
Positive slope: acceleration | 正斜率：加速
Negative slope: deceleration | 负斜率：减速
Area under the graph: distance travelled | 图像下方的面积：行驶距离

For a simple shape such as a triangle or rectangle, you can calculate the distance travelled by finding the area under the graph. For example, if a car moves at constant velocity 10 m/s for 5 s, the distance travelled is the rectangle area: 10 × 5 = 50 m.

对于三角形或矩形等简单图形，可以通过计算图像下方的面积来求物体行驶的距离。例如，如果一辆汽车以恒定速度 10 m/s 行驶了 5 s，那么行驶的距离就是矩形面积：10 × 5 = 50 m。

For a triangle area, use:

对于三角形面积，使用：

area = ½ × base × height

面积 = ½ × 底 × 高

8. Newton’s First Law | 牛顿第一定律

Newton’s first law of motion states that an object will remain at rest or continue to move at constant velocity unless acted on by a resultant force. If the resultant force on an object is zero, its motion does not change.

牛顿第一运动定律指出：除非受到合力的作用，否则物体将保持静止状态或匀速直线运动状态。如果物体所受合力为零，其运动状态不会改变。

This law explains why a pencil stays on a table until you push it. It also explains why a moving object glides on a smooth surface for a long time. Friction and air resistance are forces that always oppose motion, so they eventually bring moving objects to a stop.

这条定律解释了为什么铅笔在桌上静止不动，直到你推动它。它也解释了为什么在光滑表面运动的物体可以滑动很长时间。摩擦力和空气阻力总是妨碍运动的力，因此它们最终会使运动的物体停下来。

To keep an object moving at constant velocity, the driving force must balance the resisting forces. For example, a train moving at steady speed has the pulling force of the engine exactly balanced by friction and air resistance.

要保持物体以恒定速度运动，驱动力必须与阻力平衡。例如，一列火车匀速行驶时，发动机的牵引力正好与摩擦力和空气阻力相平衡。

9. Newton’s Second Law | 牛顿第二定律

Newton’s second law connects the resultant force on an object to its mass and acceleration. The larger the force, the larger the acceleration for a given mass. The larger the mass, the smaller the acceleration for a given force.

牛顿第二定律把物体所受的合力与它的质量和加速度联系起来。质量一定时，力越大，加速度越大。力一定时，质量越大，加速度越小。

resultant force = mass × acceleration, F = m × a

合力 = 质量 × 加速度， F = m × a

In this equation, F is the resultant force in newtons (N), m is the mass in kilograms (kg), and a is the acceleration in metres per second squared (m/s²).

在这个公式中，F 是合力，单位是牛顿（N）；m 是质量，单位是千克（kg）；a 是加速度，单位是米每二次方秒（m/s²）。

Worked example: a trolley has a mass of 3 kg and accelerates at 2 m/s². What is the resultant force acting on it?

示例：一辆手推车质量为 3 kg，以 2 m/s² 的加速度加速。作用在它上面的合力是多少？

F = 3 × 2 = 6 N

You can rearrange the equation to find mass or acceleration. For example, m = F ÷ a and a = F ÷ m. In calculations, always check that the units are consistent.

你可以重新排列公式来求质量或加速度。例如，m = F ÷ a，a = F ÷ m。在计算中，始终检查单位是否一致。

10. Newton’s Third Law | 牛顿第三定律

Newton’s third law states that if object A exerts a force on object B, then object B exerts an equal and opposite force on object A. These two forces are sometimes called action and reaction.

牛顿第三定律指出：如果物体 A 对物体 B 施加一个力，那么物体 B 也会对物体 A 施加一个大小相等、方向相反的力。这两个力有时称为作用力和反作用力。

The action and reaction forces always act on different objects. This is important because they do not cancel each other out. They are the same size, act along the same line, but push in opposite directions.

作用力和反作用力总是作用在不同的物体上。这一点很重要，因为这两个力不会相互抵消。它们大小相等，作用在同一直线上，但方向相反。

A good example is a rocket taking off. The rocket pushes hot gas downwards. The gas pushes the rocket upwards with an equal-sized force. The reaction force from the gas is what makes the rocket move. Another example is a person standing on the floor. The person pushes the floor downwards, while the floor pushes the person upwards.

火箭发射是一个很好的例子。火箭向下喷出高温气体，气体以大小相等的力向上推火箭。气体产生的反作用力使火箭向上运动。另一个例子是人站在地板上。人向下压地板，地板向上推人。

11. Mass and Weight | 质量与重力

Mass and weight are often confused, but they are different physical quantities. Mass is the amount of matter in an object. It is measured in kilograms (kg) and is a scalar quantity. Mass does not change with location.

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Forces, Motion and Newton’s Laws | 力、运动与牛顿定律