📚 Year 9 WJEC Physics: Case Study Practical Exercises | Year 9 WJEC 物理：案例分析实战演练
Case studies are a vital part of WJEC Physics. They test your ability to apply scientific knowledge to real experimental data, making calculations, drawing graphs, and evaluating the reliability of results. This guide walks you through three complete case study exercises, showing exactly how to handle data, analyse motion, and forces and resistance, and pick up maximum marks in your assessments.
案例分析是 WJEC 物理的重要组成部分。它考查你将科学知识应用于真实实验数据的能力，包括计算、绘图和评估结果的可靠性。本指南将带你完整完成三个案例研究练习，展示如何处理数据、分析运动、力与电阻，并在评估中获取最高分。
1. What WJEC Case Studies Ask You to Do | WJEC 案例分析考查什么
A WJEC case study is not a memory test. You are given a real scenario - a spring, a trolley, a resistor - together with a set of measurements, and you are asked to do what a working scientist does: process the numbers, plot the graph, and judge how trustworthy the final answer is.
WJEC 案例分析并不是记忆测试。试卷会给出一个真实情境——弹簧、小车或电阻器——再配上一组测量数据，然后要求你像真正的科学家一样工作：处理数据、绘制图像，并判断最终结果的可信程度。
Nearly every case study rewards the same four skills: accurate calculation with correct units, careful graph plotting, correct interpretation of the gradient or intercept, and a reasoned evaluation of error and uncertainty.
几乎每一份案例分析试卷都会奖励同样的四项技能：带正确单位的准确计算、细致的图像绘制、对斜率或截距的正确解读，以及对误差和不确定度的有理有据的评估。
Marks are also awarded for method. If you write the equation first, substitute the numbers second, and give the answer with a unit third, you protect yourself against arithmetic slips and you show the examiner exactly how you reached your value.
方法分同样重要。如果你先写公式、再代入数值、最后给出带单位的结果，就能减少计算失误，并向考官清楚地展示你是如何得到答案的。
2. Case Study 1: Investigating Hooke's Law | 案例一：探究胡克定律
Hooke's Law states that the extension of a spring is directly proportional to the force applied to it, provided the elastic limit of proportionality is not exceeded. Written as an equation:
胡克定律指出：在不超过比例极限的前提下，弹簧的伸长量与所受的外力成正比。用等式表示为：
F = k × e
Here F is the force in newtons (N), e is the extension in metres (m), and k is the spring constant in newtons per metre (N/m). The spring constant is a measure of stiffness: a stiff spring has a large value of k and stretches only a little under a large load.
其中 F 是力，单位为牛顿 (N)；e 是伸长量，单位为米 (m)；k 是弹簧常数，单位为牛顿每米 (N/m)。弹簧常数衡量弹簧的劲度：k 越大，弹簧越硬，在较大载荷下也只被拉长一点点。
Extension means the increase in length, not the total length. This is the single most common mistake in this practical:
伸长量指的是长度的增加量，而不是弹簧的总长度。这是本实验中最常见的错误：
e = new length − natural length
Beyond the limit of proportionality the graph bends and the relationship stops being linear. Push the spring even further and you reach the elastic limit, after which the spring is permanently stretched and will not return to its natural length.
一旦超过比例极限，图像就会弯曲，这种正比关系不再成立。若继续拉伸，就会到达弹性极限，此后弹簧被永久拉长，无法恢复到原来的自然长度。
3. Experimental Setup and Data Collection | 实验装置与数据收集
To investigate Hooke's Law, a student suspends a spring from a clamp stand. A metre ruler is placed vertically next to the spring. A pointer attached to the bottom of the spring helps to read the scale accurately, because a thin pointer is easier to line up with a scale mark than the coils of the spring itself.
为了探究胡克定律，一名学生把弹簧悬挂在铁架台上，并在弹簧旁边竖直放置一把米尺。弹簧下端附有一个指针，用来更准确地读数，因为细指针比弹簧线圈本身更容易与刻度线对齐。
The student measures the natural length of the spring with no load, then adds 100 g slotted masses one at a time. After each mass is added, the student waits for the spring to stop moving before recording the new length. Readings are taken with the eye level with the pointer to avoid parallax error.
学生先测量空载时弹簧的自然长度，然后每次增加一个 100 g 的槽码。每加一个槽码后，都要等弹簧完全静止再记录新的长度。读数时视线要与指针齐平，以避免视差误差。
A safety mat or a box is placed underneath the masses, because a slotted mass falling from a stretched spring can cause injury. Goggles are also sensible if the spring is under a large tension.
实验下方要放置软垫或箱子，因为槽码从被拉伸的弹簧上掉落可能造成伤害。如果弹簧张力较大，佩戴护目镜也是明智之举。
The independent variable is the load (the weight hanging on the spring); the dependent variable is the extension; the control variables are the same spring, the same ruler position, and the same waiting time before each reading.
自变量是载荷（挂在弹簧上的重量）；因变量是伸长量；控制变量包括使用同一根弹簧、米尺位置不变，以及每次读数前等待相同的时间。
4. Recording Results and Calculating Extension | 记录结果与计算伸长量
s who plot mass in grams instead of weight in newtons lose the mark for correct variables.
每个槽码的重量必须用 W = m × g 计算，取 g = 9.8 N/kg。因此 100 g 的槽码重量为 0.100 × 9.8 = 0.98 N。如果学生用"克"表示的质量代替"牛顿"表示的重量作图，就会失去使用正确变量的分数。
A typical set of results is shown below. Note that extension is calculated by subtracting the natural length from each new length.
下面是一组典型的实验结果。注意，伸长量是用每次的新长度减去自然长度得到的。
| Mass / g | Weight / N | Length / cm | Extension / cm |
| 0 | 0.00 | 12.0 | 0.0 |
| 100 | 0.98 | 14.5 | 2.5 |
| 200 | 1.96 | 17.0 | 5.0 |
| 300 | 2.94 | 19.5 | 7.5 |
| 400 | 3.92 | 22.0 | 10.0 |
| 500 | 4.90 | 24.5 | 12.5 |
| 600 | 5.88 | 29.5 | 17.5 |
Up to 500 g the extension increases by exactly 2.5 cm for every 100 g added, so the relationship is linear. At 600 g the extension jumps to 17.5 cm instead of the expected 15.0 cm, which shows that the limit of proportionality has been passed.
在 500 g 以内，每增加 100 g，伸长量正好增加 2.5 cm，说明两者成线性关系。而在 600 g 时，伸长量跳到 17.5 cm，而不是预期的 15.0 cm，说明已经超过了比例极限。
5. Plotting the Graph and Finding the Spring Constant | 绘图与求弹簧常数
equal to the spring constant k, because gradient = change in force ÷ change in extension.
正确的图像应把伸长量放在横轴、力放在纵轴。按这种安排，最佳拟合直线的斜率就等于弹簧常数 k，因为斜率 = 力的变化量 ÷ 伸长量的变化量。
oose two points on the line of best fit that are far apart, never two data points that happen to lie close together.
作图前要先把伸长量由厘米换算成米：12.5 cm = 0.125 m，2.
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