IB Physics: Newton's Laws of Motion Explained | IB物理：牛顿运动定律详解

📚 IB Physics: Newton’s Laws of Motion Explained | IB物理：牛顿运动定律详解

Newton’s laws of motion form the cornerstone of classical mechanics. In the IB Physics curriculum (Topic 2: Mechanics), these laws are used to predict the motion of objects subjected to forces. We will break down each law, examine its mathematical formulation, and apply it to typical exam scenarios.

牛顿运动定律是经典力学的基石。在IB物理课程（Topic 2：力学）中，这些定律用于预测物体在受力作用下的运动。我们将逐一解析每条定律，探讨其数学表达式，并将其应用于典型的考试情境。

1. Newton’s First Law | 牛顿第一定律

Newton’s first law states: an object remains at rest or performs uniform motion in a straight line unless acted upon by a net external force.

牛顿第一定律指出：除非受到合外力作用，否则物体将保持静止或做匀速直线运动。

This law introduces the concept of inertia, the tendency of an object to resist changes in its state of motion.

该定律引入了惯性的概念，即物体抵抗其运动状态改变的趋势。

In the absence of a net force, the acceleration of the object is exactly zero.

在没有合外力时，物体的加速度恰好为零。

The law is valid only in inertial reference frames, where no fictitious forces appear.

该定律仅在惯性参考系中成立，在惯性参考系中不会出现惯性力。

An inertial reference frame is one that is either at rest or moving with constant velocity relative to the stars.

惯性参考系是相对于恒星静止或做匀速运动的参考系。

2. Inertia and Mass | 惯性与质量

Mass is a quantitative measure of inertia: the larger the mass, the more strongly an object resists acceleration under a given net force.

质量是惯性的定量量度：质量越大，物体在给定合外力作用下抵抗加速度的能力越强。

Inertial mass can be measured by applying a known net force F and measuring the resulting acceleration a:

惯性质量可以通过施加已知合外力F并测量由此产生的加速度a来测定：

m = F / a

This relationship shows that mass is the ratio of net force to acceleration.

该关系表明质量是合外力与加速度的比值。

Mass is a scalar quantity measured in kilograms (kg).
质量是标量，单位为千克（kg）。
Weight is a force and equals m g, where g is the gravitational field strength.
重力是力，等于m g，其中g为重力场强度。
Mass does not change with location, while weight depends on g.
质量不随位置改变，而重力则取决于g。

3. Newton’s Second Law | 牛顿第二定律

Newton’s second law states that the rate of change of momentum of an object is directly proportional to the net external force and takes place in the direction of that force.

牛顿第二定律指出：物体动量的变化率与合外力成正比，且方向与合外力方向一致。

For an object with constant mass, this reduces to the familiar equation:

对于质量恒定的物体，该定律简化为熟悉的方程：

F = m a

Where F is the net force (N), m is the mass (kg), and a is the acceleration (m·s⁻²).

其中F为合外力（N），m为质量（kg），a为加速度（m·s⁻²）。

The net force is the vector sum of all external forces acting on the object.

合外力是作用在物体上所有外力的矢量和。

Acceleration is directly proportional to net force and inversely proportional to mass.

加速度与合外力成正比，与质量成反比。

Unit definition: a net force of 1 newton imparts an acceleration of 1 m·s⁻² to a mass of 1 kg.

单位定义：1牛顿的合外力使1千克质量的物体产生1米每二次方秒的加速度。

4. Force, Mass, and Acceleration | 力、质量与加速度

To apply Newton’s second law effectively, you must resolve forces into components and use vector addition to find the net force.

有效应用牛顿第二定律需要将力分解为分量，并通过矢量加法求合力。

The table below summarises the key quantities involved:

下表总结了涉及的关键物理量：

Quantity	Symbol	Unit
Force	F	N = kg·m·s⁻²
Mass	m	kg
Acceleration	a	m·s⁻²
Momentum	p	kg·m·s⁻¹

When forces are not along the same line, draw a perpendicular axis system and resolve each force into x- and y-components.

当力不在同一直线上时，应画出垂直的坐标轴系统，并将每个力分解为x和y分量。

Newton’s second law is then applied separately in each direction: Fₓ = m aₓ and Fᵧ = m aᵧ.

然后分别在每个方向应用牛顿第二定律：Fₓ = m aₓ 和 Fᵧ = m aᵧ。

5. 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.

牛顿第三定律指出：如果物体A对物体B施加力，那么物体B对物体A施加大小相等、方向相反的力。

These two forces are called an action-reaction pair.

这一对力称为作用力与反作用力对。

Action-reaction forces always act on different objects, so they can never cancel each other out.

作用力与反作用力总是作用在不同的物体上，因此它们永远不会相互抵消。

Both forces are of the same physical type, such as gravitational, electric, or contact forces.

这一对力属于相同的物理类型，例如引力、电力或接触力。

They occur simultaneously; neither force exists without the other.

它们同时出现；没有其中一个力，另一个力也不存在。

6. Action-Reaction Pairs | 作用力与反作用力对

In IB exams, students often confuse action-reaction pairs with balanced forces. The key difference lies in whether the forces act on the same object or on different objects.

在IB考试中，学生常把作用力与反作用力对与平衡力混淆。关键区别在于力是作用在同一物体还是不同物体上。

Consider a book resting on a table:

以静止在桌面上的书为例：

The weight of the book and the normal force from the table are balanced forces; both act on the book, and their vector sum is zero.
书的重力和桌面的支持力是平衡力；两者都作用在书上，矢量和为零。
The action-reaction pair is: Earth pulls the book down with gravitational force, and the book pulls Earth up with an equal gravitational force.
作用力与反作用力对是：地球以引力向下拉书，而书以等大的引力向上拉地球。
Similarly, the book pushes the table down, and the table pushes the book up; these form another action-reaction pair.
同样，书向下压桌面，桌面向上支撑书；这构成另一对作用力与反作用力。

A common exam trap is to list weight and normal force as an action-reaction pair. Always check the objects on which the forces act.

常见的考试陷阱是将重力和支持力列为作用力与反作用力对。务必检查力作用的物体。

7. Free-Body Diagrams | 受力分析图

A free-body diagram is a simplified drawing showing a single object and all external forces acting on it, represented by arrows.

受力分析图是一种简化的图形，显示一个孤立物体以及作用在其上的所有外力，用箭头表示。

Follow these steps when constructing a free-body diagram:

画受力分析图时请遵循以下步骤：

Isolate the object and draw it as a point or a box.
隔离研究对象，将其画为一个点或一个方框。
Identify all contact forces and non-contact forces acting on the object.
确定作用在物体上的所有接触力和非接触力。
Draw each force vector starting from the centre of the object, with length proportional to magnitude.
从物体中心开始绘制每个力矢量，长度与大小成比例。
Add a coordinate system and resolve forces into components if necessary.
添加坐标系，并在需要时将力分解为分量。

Once the free-body diagram is complete, apply Newton’s second law to find the net force or acceleration.

完成受力分析图后，应用牛顿第二定律求解合外力或加速度。

8. Applications: Elevators and Inclined Planes | 应用：电梯与斜面

Elevator problems are a classic application of Newton’s second law. When an elevator accelerates upward, the normal force on a passenger increases.

电梯问题是牛顿第二定律的经典应用。当电梯加速上升时，乘客受到的支持力增大。

Consider a person of mass m standing on a scale inside an elevator. The scale reading (normal force N) satisfies:

考虑电梯内站在体重秤上、质量为m的人。体重秤读数（支持力N）满足：

N – m g = m a

For upward acceleration, N = m(g + a), so the apparent weight increases.

当向上加速时，N = m(g + a)，因此表观重量增加。

For downward acceleration, N = m(g – a), so the apparent weight decreases.

当向下加速时，N = m(g – a)，因此表观重量减小。

In free fall, a = g and N = 0, giving apparent weightlessness.

在自由落体中，a = g且N = 0，出现完全失重。

For an object on a frictionless inclined plane at angle θ, the weight component parallel to the plane is m g sin θ.

对于无摩擦斜面上、倾角为θ的物体，重力沿斜面方向的分量为m g sin θ。

The acceleration down the plane is therefore:

因此物体沿斜面下滑的加速度为：

a = g sin θ

The normal force is m g cos θ, perpendicular to the plane.

支持力为m g cos θ，垂直于斜面。

9. Friction Forces | 摩擦力

Friction is a contact force that opposes the relative sliding motion between two surfaces.

摩擦力是一种接触力，阻碍两个表面之间的相对滑动。

Static friction prevents an object from moving, while kinetic friction acts when the object is sliding.

静摩擦力阻止物体运动，滑动摩擦力在物体滑动时起作用。

The maximum static friction is given by:

最大静摩擦力为：

f_s,max = μ_s N

Where μ_s is the coefficient of static friction and N is the normal force.

其中μ_s为静摩擦系数，N为支持力。

Kinetic friction is given by:

滑动摩擦力为：

f_k = μ_k N

Generally, μ_s > μ_k, meaning it is harder to start sliding than to keep sliding.

通常μ_s > μ_k，即启动滑动比维持滑动更困难。

Friction does not depend on the contact area in the IB model; it depends on N and the surface characteristics.

在IB模型中，摩擦力与接触面积无关，它取决于N和表面特性。

10. Momentum and Newton’s Laws | 动量与牛顿定律

Newton’s second law can be written in terms of momentum p = m v:

牛顿第二定律可以用动量p = m v来表示：

F = Δp / Δt

Where Δp is the change in momentum and Δt is the time interval over which the force acts.

其中Δp是动量的变化量，Δt是力作用的时间间隔。

For constant mass, this is equivalent to F = m a, because a = Δv / Δt.

对于质量恒定的情况，由于a = Δv / Δt，该表达式等价于F = m a。

If the net external force is zero, then momentum is conserved:

如果合外力为零，则动量守恒：

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

This conservation principle is used to solve collision and explosion problems in IB Topic 2.

该守恒原理用于解决IB Topic 2中的碰撞和爆炸问题。

11. Common IB Exam Questions and Tips | 常见IB考题与技巧

Many IB mechanics problems require you to combine Newton’s laws with kinematics equations. Practise identifying forces and using consistent sign conventions.

许多IB力学问题需要你将牛顿定律

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IB Physics: Newton’s Laws of Motion Explained | IB物理：牛顿运动定律详解