Forces & Shape | 力与形变

📚 Forces & Shape | 力与形变

A force is a push or pull that can change the motion or shape of an object. In IGCSE Physics, we explore how forces cause deformation, and we distinguish between elastic and plastic behaviour. Understanding Hooke’s Law and interpreting force-extension graphs are essential skills for the Edexcel specification.

力是一种推或拉的作用，可以改变物体的运动状态或形状。在IGCSE物理中，我们将探讨力如何引起形变，并区分弹性与塑性行为。理解胡克定律以及解读力-伸长图像是Edexcel考纲中的核心技能。

1. What is a Force? | 什么是力？

A force is a vector quantity, meaning it has both magnitude and direction. Forces can be contact forces, such as friction, tension, and normal reaction, or non-contact forces like gravitational, electrostatic, and magnetic forces. The unit of force is the newton (N).

力是一个矢量，既有大小又有方向。力可以是接触力，如摩擦力、张力和法向反作用力，也可以是非接触力，如引力、静电力和磁力。力的单位是牛顿（N）。

2. Effects of Forces on Shape | 力对形状的影响

Forces can change the speed of an object, its direction of motion, or its shape. When a force is applied to a solid object, it may stretch, compress, or bend. The change in shape is called deformation. The ability of a material to return to its original shape after the force is removed depends on its elastic properties.

力可以改变物体的速度、运动方向或形状。当力作用于固体时，物体可能被拉伸、压缩或弯曲。形状的改变称为形变。材料在去除外力后恢复原状的能力取决于其弹性特性。

3. Elastic and Plastic Deformation | 弹性与塑性形变

Elastic deformation is temporary: the object returns to its original shape and size when the force is removed. Plastic (or inelastic) deformation is permanent: the object does not fully regain its original shape. Everyday examples include a stretched rubber band (elastic) and a crumpled aluminium can (plastic).

弹性形变是暂时的：移除外力后，物体恢复原来的形状和大小。塑性（非弹性）形变是永久的：物体无法完全恢复原状。日常例子包括拉伸的橡皮筋（弹性）和捏扁的铝罐（塑性）。

4. Introducing Hooke’s Law | 胡克定律简介

Hooke’s Law states that the extension of an elastic object, such as a spring, is directly proportional to the force applied, provided the limit of proportionality is not exceeded. Mathematically, this is expressed as:

F = k × x

where F is the applied force (N), k is the spring constant (N/m), and x is the extension (m).

胡克定律指出，在比例极限内，弹性物体（如弹簧）的伸长量与其所受的力成正比。数学表达式为：F = k × x，其中 F 是作用力（N），k 是弹簧常数（N/m），x 是伸长量（m）。

5. Spring Constant and Stiffness | 弹簧常数与刚度

The spring constant k measures the stiffness of a spring. A larger k value means a stiffer spring that requires a greater force to produce the same extension. The unit of k is newtons per metre (N/m). In force-extension graphs, a steeper straight-line gradient indicates a larger spring constant.

弹簧常数 k 衡量弹簧的刚度。k 值越大，弹簧越硬，产生相同伸长量需要更大的力。k 的单位是牛顿每米（N/m）。在力-伸长图中，更陡的直线斜率表示更大的弹簧常数。

6. The Limit of Proportionality | 比例极限

The limit of proportionality is the point beyond which Hooke’s Law no longer applies. Up to this limit, force and extension are directly proportional, producing a straight-line graph through the origin. After this point, the graph curves, and the spring may enter the plastic region.

比例极限是胡克定律不再成立的点。在此极限之内，力与伸长量成正比，图像为一条通过原点的直线。超过该点后，图线弯曲，弹簧可能进入塑性区域。

7. Force-Extension Graph for a Spring | 弹簧的力-伸长图像

A typical force-extension graph for a spring shows a straight line passing through the origin, obeying F = kx. As the force increases, the graph reaches the limit of proportionality (P), where the line begins to curve. Further loading may reach the elastic limit, after which permanent deformation occurs. Key features include:

Linear region: Hooke’s Law obeyed, gradient = k.
Limit of proportionality (P): the point where the graph starts to curve.
Elastic limit: beyond this point the spring is permanently deformed.

典型的弹簧力-伸长图像是一条通过原点的直线，遵循 F = kx。随着力增大，图线到达比例极限（P），开始弯曲。继续加载可能到达弹性极限，之后发生永久形变。主要特征包括：

线性区：遵守胡克定律，斜率 = k。
比例极限（P）：图线开始弯曲的点。
弹性极限：超过此点弹簧被永久形变。

8. Elastic Limit and Permanent Set | 弹性极限与永久变形

The elastic limit is the maximum force a material can experience and still return to its original length. If the force exceeds the elastic limit, the material undergoes plastic deformation and retains a permanent extension when unloaded. On a graph, the unloading path does not return to the origin.

弹性极限是材料能承受且仍能恢复原长的最大力。如果超过弹性极限，材料发生塑性变形，卸载后会保留一定的永久伸长量。在图像上，卸载路径不会回到原点。

9. Extension and Compression | 拉伸与压缩

Hooke’s Law applies to both extension (tensile forces) and compression. For a spring, compression reduces its length, and the extension x takes a negative value. The force-compression graph is similar: a straight line through the origin for small compressions, with the same spring constant k.

胡克定律适用于拉伸（拉力）和压缩。对弹簧而言，压缩会缩短其长度，伸长量 x 取负值。力-压缩图像类似：小压缩范围内为通过原点的直线，并具有相同的弹簧常数 k。

10. Investigating Hooke’s Law Experiment | 探究胡克定律实验

A standard experiment involves suspending a spring from a clamp, adding known masses, and measuring the extension with a ruler. The procedure:

Measure the original length of the spring (without load).
Add a mass, calculate the force (weight = mg, using g = 9.8 N/kg or 10 N/kg), and record the new length.
Extension = new length – original length.
Repeat for increasing masses, ensuring not to overstretch the spring.
Plot a graph of force (y-axis) against extension (x-axis).

The straight-line section confirms Hooke’s Law, and the gradient equals the spring constant k.

标准实验使用铁架台悬挂弹簧，添加已知砝码，用直尺测量伸长量。步骤如下：

测量弹簧原长（无负载）。
添加砝码，计算力（重量 = mg，g 取 9.8 N/kg 或 10 N/kg），记录新长度。
伸长量 = 新长度 – 原长。
逐渐增加砝码重复测量，注意不要过度拉伸弹簧。
绘制力（y轴）对伸长量（x轴）的图像。

直线部分验证了胡克定律，斜率等于弹簧常数 k。

11. Real-Life Applications of Hooke’s Law | 胡克定律的实际应用

Hooke’s Law is used in designing springs for vehicle suspensions, measuring instruments like spring balances, and many engineering structures. Understanding the elastic limit helps prevent material failure. Elastic bands, diving boards, and bungee cords rely on controlled elastic deformation.

胡克定律应用于车辆悬架弹簧、弹簧秤等测量仪器以及许多工程结构的设计。了解弹性极限有助于防止材料失效。橡皮筋、跳板、蹦极绳索都依赖于可控的弹性形变。

12. Summary and Key Equations | 总结与关键公式

Forces can change the shape of objects, leading to elastic or plastic deformation. Hooke’s Law (F = kx) describes the linear relationship for many materials within the limit of proportionality. The spring constant k indicates stiffness. Interpreting force-extension graphs, identifying the limit of proportionality and the elastic limit, and performing the standard experiment are all crucial for IGCSE Edexcel Physics.

力可以改变物体的形状，导致弹性或塑性形变。胡克定律（F = kx）描述了许多材料在比例极限内的线性关系。弹簧常数 k 表示刚度。解读力-伸长图像，识别比例极限和弹性极限，并进行标准实验，都是IGCSE Edexcel物理的重要内容。

Published by TutorHao | Physics Revision Series | aleveler.com

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Forces & Shape | 力与形变