IGCSE Physics: Force and Deformation & Hooke's Law | 力与形变的关系及胡克定律

📚 IGCSE Physics: Force and Deformation & Hooke’s Law | 力与形变的关系及胡克定律

When a force is applied to an object, it may change the object’s shape, length, or volume. This relationship between force and deformation is central to understanding elasticity, and Hooke’s Law provides a simple yet powerful model for how springs and other elastic materials behave. In this article, we will explore the key concepts, definitions, and calculations you need for your Edexcel IGCSE Physics exam.

当力作用于物体时，物体可能会改变形状、长度或体积。力与形变之间的关系是理解弹性的核心，而胡克定律则为弹簧和其他弹性材料的行为提供了一个简单而有力的模型。在本文中，我们将探讨Edexcel IGCSE物理考试所需的关键概念、定义和计算方法。

1. What Is Deformation? | 什么是形变？

Deformation refers to the change in shape or size of an object due to an applied force. When you stretch a spring, compress a sponge, or bend a ruler, you are causing deformation. Deformation can be temporary or permanent depending on the material and the size of the force.

形变是指物体在外力作用下发生的形状或尺寸变化。当你拉伸弹簧、压缩海绵或弯曲尺子时，你就是在引起形变。形变可以是暂时的，也可以是永久的，这取决于材料和外力的大小。

Elastic deformation: the object returns to its original shape when the force is removed.

弹性形变：当外力撤去后，物体恢复到原来的形状。
Plastic deformation: the object does not return to its original shape when the force is removed.

塑性形变：当外力撤去后，物体不能恢复到原来的形状。

In IGCSE Physics, you need to distinguish between these two types of deformation and understand that a spring can behave elastically up to a certain limit.

在IGCSE物理中，你需要区分这两种形变类型，并理解弹簧在一定限度内可以表现为弹性形变。

2. Forces and Extension | 力与伸长量

When a force is applied to a spring, it stretches. The amount by which the spring’s length increases is called its extension. If you hang weights on a spring, the extension increases as the force increases. For small forces, the extension is directly proportional to the force.

当力作用于弹簧时，弹簧会被拉长。弹簧长度增加的量称为伸长量。如果你在弹簧下端悬挂重物，伸长量会随着力的增大而增大。在小力作用下，伸长量与力成正比。

extension = new length − original length

伸长量 = 新长度 − 原长度

Unit of extension: metre (m) or centimetre (cm).

伸长量的单位：米（m）或厘米（cm）。
Force is measured in newtons (N).

力的单位是牛顿（N）。

3. Hooke’s Law Statement | 胡克定律的内容

Hooke’s Law states that the extension of an elastic object is directly proportional to the force applied to it, provided that the limit of proportionality is not exceeded.

胡克定律指出：在比例极限内，弹性物体的伸长量与施加在其上的力成正比。

F = k × e

F = force applied (N)

F = 施加的力（N）
k = spring constant (N/m)

k = 弹簧常数（N/m）
e = extension (m)

e = 伸长量（m）

Here is an example: if a spring has a spring constant of 100 N/m and is stretched by 0.2 m, the force applied is F = 100 × 0.2 = 20 N.

例如：如果一根弹簧的弹簧常数为100 N/m，被拉伸了0.2 m，则施加的力为 F = 100 × 0.2 = 20 N。

4. The Spring Constant k | 弹簧常数 k

The spring constant measures the stiffness of a spring. A spring with a large spring constant is stiff and requires a large force to stretch it by a given amount. A spring with a small spring constant is soft and stretches easily.

弹簧常数衡量弹簧的“硬度”。弹簧常数大的弹簧较硬，需要较大的力才能拉伸一定长度；弹簧常数小的弹簧较软，容易拉伸。

k = F ÷ e

The unit of the spring constant is newtons per metre (N/m). In exam questions, you may need to rearrange Hooke’s Law to find k or e.

弹簧常数的单位是牛顿每米（N/m）。在考试题中，你可能需要重新排列胡克定律来求 k 或 e。

5. Force–Extension Graphs | 力-伸长量图像

A graph of force against extension for a spring that obeys Hooke’s Law is a straight line passing through the origin. The gradient of this line is equal to the spring constant k.

对于遵守胡克定律的弹簧，其力-伸长量图像是一条过原点的直线。这条直线的斜率等于弹簧常数 k。

Straight-line portion: elastic region where Hooke’s Law applies.

直线部分：弹性区域，胡克定律适用。
Curved portion: the spring has exceeded the limit of proportionality and no longer obeys Hooke’s Law.

弯曲部分：弹簧已超过比例极限，不再遵循胡克定律。

You should be able to describe and interpret these graphs, and identify the limit of proportionality from the graph.

你应该能够描述并解读这些图像，并从图像中识别比例极限。

6. Limit of Proportionality and Elastic Limit | 比例极限与弹性极限

The limit of proportionality is the point on a force–extension graph beyond which extension is no longer directly proportional to force. The elastic limit is the point beyond which the object does not return to its original length when the force is removed.

比例极限是力-伸长量图像上伸长量不再与力成正比的那个点。弹性极限是当力撤去后物体不能恢复原长的那个点。

Before the elastic limit: elastic deformation (reversible).

在弹性极限之前：弹性形变（可逆）。
After the elastic limit: plastic deformation (permanent).

在弹性极限之后：塑性形变（永久）。

For a typical metal wire, the limit of proportionality and the elastic limit are very close. For rubber, the graph is not a straight line, so Hooke’s Law does not apply.

对于典型的金属丝，比例极限和弹性极限非常接近。对于橡胶，其图像不是直线，因此胡克定律不适用。

7. Work Done in Stretching a Spring | 拉伸弹簧所做的功

Stretching a spring requires energy. The work done in stretching a spring is equal to the energy stored in the spring as elastic potential energy. For a spring obeying Hooke’s Law, the work done is given by:

拉伸弹簧需要能量。拉伸弹簧所做的功等于弹簧储存的弹性势能。对于遵循胡克定律的弹簧，所做的功为：

E = ½ × k × e²

E = elastic potential energy (J)

E = 弹性势能（J）
k = spring constant (N/m)

k = 弹簧常数（N/m）
e = extension (m)

e = 伸长量（m）

Alternatively, work done equals the area under the force–extension graph, which for a straight line is a triangle: ½ × base × height = ½ × e × F.

另一种方法：所做的功等于力-伸长量图像下的面积。对于直线图像，这是三角形面积：½ × 底 × 高 = ½ × e × F。

8. Experimental Method: Finding the Spring Constant | 实验方法：求弹簧常数

In the school laboratory, you will often carry out an experiment to determine the spring constant of a spring. The standard method is as follows:

在学校的实验室中，你经常会通过实验来测量弹簧的弹簧常数。标准方法如下：

Set up a spring suspended from a clamp stand with a ruler alongside it.

将弹簧悬挂在铁架台上，旁边放置一把尺子。
Measure the original length of the spring with no load.

记录无负载时弹簧的原长。
Add a known mass to the spring and record the new length.

在弹簧下端挂一个已知质量的物体，记录新长度。
Repeat with increasing masses, recording force and extension each time.

不断增加质量，记录每次的力和伸长量。
Plot a graph of force against extension.

绘制力-伸长量图像。
Use the gradient of the straight-line portion to find k.

利用直线部分的斜率求出 k。

Remember that force = mass × gravitational field strength (F = mg), where g ≈ 9.8 N/kg on Earth.

记住：力 = 质量 × 重力场强度（F = mg），地球上 g ≈ 9.8 N/kg。

9. Typical Exam-Style Question | 典型考试题

Let us work through a common exam question. A spring has an original length of 0.10 m. When a force of 5.0 N is applied, it stretches to a new length of 0.15 m. Calculate the spring constant.

让我们做一道常见考试题。一根弹簧原长为 0.10 m。当施加 5.0 N 的力时，它的新长度为 0.15 m。计算弹簧常数。

Step 1: Calculate extension: e = 0.15 − 0.10 = 0.05 m.

第一步：计算伸长量：e = 0.15 − 0.10 = 0.05 m。

Step 2: Use Hooke’s Law: k = F ÷ e = 5.0 ÷ 0.05 = 100 N/m.

第二步：使用胡克定律：k = F ÷ e = 5.0 ÷ 0.05 = 100 N/m。

Note that the answer must include the correct unit N/m.

注意答案必须包含正确的单位 N/m。

10. Common Mistakes to Avoid | 易错点提醒

Students often make the following mistakes when answering questions about Hooke’s Law:

学生在回答胡克定律相关问题时经常犯以下错误：

Using the new length instead of the extension in the formula F = ke. Always subtract the original length first.

在公式 F = ke 中使用了新长度而不是伸长量。务必先减去原长。
Forgetting to convert units. If extension is given in cm, convert to metres before calculating with standard units.

忘记换算单位。如果伸长量以厘米为单位，请先换算成米再使用标准单位计算。
Swapping the spring constant and force. Remember k is measured in N/m, while F is measured in N.

混淆弹簧常数和力。记住 k 的单位是 N/m，而 F 的单位是 N。
Ignoring the condition “provided the limit of proportionality is not exceeded.” Hooke’s Law is not universal for all materials.

忽略“在比例极限内”的条件。胡克定律并非适用于所有材料。

11. Real-World Applications | 实际应用

Hooke’s Law is used in many everyday devices. Car suspension springs compress when the car hits a bump, and the spring constant determines how smooth the ride is. Mattresses, trampolines, and pogo sticks all rely on elastic deformation and Hooke’s Law to store and release energy.

胡克定律在许多日常设备中都有应用。汽车悬挂弹簧在汽车遇到颠簸时会压缩，弹簧常数决定了乘坐的平顺程度。床垫、蹦床和弹簧高跷都依靠弹性形变和胡克定律来储存和释放能量。

Spring scales used in laboratories and kitchens measure force based on how much a spring stretches. The heavier the object, the greater the extension, and the scale is calibrated using Hooke’s Law.

实验室和厨房中使用的弹簧秤根据弹簧的伸长量来测量力。物体越重，伸长量越大，秤的刻度就是根据胡克定律标定的。

12. Quick Revision Summary | 快速复习总结

Here is a concise summary of the most important points for your exam:

以下是考试中最重要的要点总结：

Quantity	Symbol	Unit	Formula
Force	F	N	F = k × e
Extension	e	m	e = F ÷ k
Spring constant	k	N/m	k = F ÷ e
Elastic potential energy	E	J	E = ½ × k × e²

Always read the question carefully, check whether you need the new length or the extension, and ensure your units are consistent. With practice, Hooke’s Law problems become straightforward.

请务必仔细阅读题目，确认你需要的是新长度还是伸长量，并确保单位一致。多加练习，胡克定律问题就会变得非常简单。

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IGCSE Physics: Force and Deformation & Hooke’s Law | 力与形变的关系及胡克定律