International A-Level Physics Example Responses: PH03 Unit 3 Practical Investigation | 国际A-Level物理示例答案：PH03单元3实验探究

📚 International A-Level Physics Example Responses: PH03 Unit 3 Practical Investigation | 国际A-Level物理示例答案：PH03单元3实验探究

In Edexcel International A-Level Physics, Unit 3 (PH03) focuses entirely on practical skills. You will not be tested on new theory; instead, you must show that you can plan experiments, process data, plot graphs, determine gradients and intercepts, calculate uncertainties, and critically evaluate results. This article walks you through each required skill, using a classic investigation – measuring the acceleration of free fall, g, by timing a falling object – as a running example. The structure mimics a full example response, so you can see exactly what examiners expect.

在爱德思国际A-Level物理中，单元3（PH03）完全专注于实验技能。你不会被考查新的理论知识；相反，你必须展示你能设计实验、处理数据、画图、求斜率和截距、计算不确定度，并批判性地评估结果。本文将以一个经典实验——通过测定下落物体的时间来测量自由落体加速度 g——作为贯穿始终的例子，带你逐一掌握每项技能。本文结构模拟一份完整的示例答案，让你清晰看到考官的期待。

1. Planning the Experiment and Identifying Variables | 实验设计与变量识别

Begin by clearly stating the aim: to determine the acceleration of free fall, g. You must identify the independent variable (the quantity you change), the dependent variable (what you measure), and all control variables. For a free-fall experiment using a ball dropped from rest, height h is the independent variable, and the time of fall t is the dependent variable. Control variables include the mass and shape of the ball, and releasing the ball from rest each time. Using the equation of motion h = ½ g t² (since initial velocity u = 0), a straight-line relationship can be obtained by plotting 2h against t². The gradient of this line will equal g.

首先要清楚说明实验目的：测定自由落体加速度 g。你必须识别出自变量（你改变的量）、因变量（你测量的量）以及所有控制变量。对于从静止释放小球的下落实验，高度 h 是自变量，下落时间 t 是因变量。控制变量包括小球的质量和形状，以及每次从静止释放。利用运动方程 h = ½ g t²（因为初速度 u = 0），通过绘制 2h 与 t² 的图像可以得到线性关系，该直线的斜率就等于 g。

In your plan, list the apparatus: metre rule, clamp stand, electromagnet or release mechanism, metal ball, trapdoor or timer connected to a switch, and a data logger or stopwatch. Mention that the height should be measured from the bottom of the ball to the trapdoor, using a set square to ensure the metre rule is vertical. State the range and intervals of the independent variable – for example, heights from 0.200 m to 1.500 m in steps of about 0.200 m. Always repeat each measurement at least three times and take the mean time to reduce random errors. Conduct a preliminary trial to check the apparatus works and that timing can be done reliably.

在你的计划中，列出所需器材：米尺、铁架台、电磁铁或释放装置、金属球、与开关连接的活板门或计时器，以及数据采集器或秒表。要提及高度应从球底部到活板门的距离测量，并使用直角尺确保米尺竖直。说明自变量的范围和间隔——例如，高度从 0.200 m 到 1.500 m，以约 0.200 m 为步长。每个测量值至少重复三次，并取时间平均值以减少随机误差。进行一次预试验，检查仪器是否正常工作，计时是否可靠。

2. Recording Data in a Well-Designed Table | 用设计良好的表格记录数据

Your table must have clear headings with units and show repeat readings. All raw data should be recorded to the correct precision – for a metre stick typically to the nearest mm, and for a digital timer to the nearest 0.01 s if possible. Do not forget to include a column for the mean time t and for calculated quantities such as t². The layout below is a model answer format.

你的表格必须有清晰的标题和单位，并显示重复读数。所有原始数据都应以正确的精度记录——米尺通常精确到毫米，数字计时器如果可能精确到 0.01 s。别忘了包括平均时间 t 和诸如 t² 等计算量的列。下面的布局是一个标准答案格式。

Height h / m	Time t₁ / s	t₂ / s	t₃ / s	Mean t / s	t² / s²	2h / m
0.200	0.19	0.20	0.20	0.197	0.0388	0.400
0.400	0.28	0.29	0.28	0.283	0.0801	0.800
0.600	0.35	0.34	0.35	0.347	0.1204	1.200
0.800	0.40	0.41	0.40	0.403	0.1624	1.600
1.000	0.45	0.45	0.44	0.447	0.1998	2.000

Notice that the number of decimal places in the mean time is consistent with the raw readings, and t² is given to the same number of significant figures as the data allows (usually one more than the raw data during calculation). The column for 2h is included for direct plotting. Headings must include the quantity and the unit separated by a solidus or brackets – e.g., Height, h / m.

注意，平均时间的小数位数与原始读数一致，t² 的有效数字位数与原始数据允许的位数一致（计算时通常比原始数据多一位）。包含 2h 列是为了直接作图。表头必须包含物理量和单位，用斜线或括号分隔——例如高度 h / m。

3. Plotting the Graph Accurately | 精确绘制图像

Plot a graph of 2h (on the y‑axis) against t² (on the x‑axis). Use a sharp pencil, draw axes with linear scales, and label them with the quantity and unit, e.g. 2h / m and t² / s². The scales should be chosen so that the plotted points occupy more than half of the graph paper in both directions. Do not use an awkward scale like 1:3 or 1:7; stick to 1, 2, 5, or 10 per division. Plot the points as small crosses or circled dots, then draw a single straight line of best fit – not through the origin unless the data clearly demand it. The line should have an even spread of points above and below it. Include a title and, if necessary, a small sketch showing the line does not pass through the origin.

绘制 2h（y 轴）与 t²（x 轴）的图像。用削尖的铅笔画坐标轴，采用线性刻度，并标注物理量与单位，例如 2h / m 和 t² / s²。刻度选择应使描点占据图形纸两个方向的一半以上。不要使用像 1:3 或 1:7 这类不便的刻度；坚持每格代表 1, 2, 5 或 10。将数据点画成小叉号或带圈圆点，然后作一条最佳拟合直线——除非数据明确要求，否则不要强制通过原点。直线上方和下方的点应均匀分布。包含图标题，必要时示意直线不经过原点。

An example response would state: ‘The graph of 2h vs t² is a straight line through the origin, confirming that h ∝ t², consistent with the equation h = ½ g t². The gradient of this line gives g.’ If a data point deviates significantly, circle it as an anomaly and do not include it in the line of best fit. Examiners reward clear annotation on the graph.

典型的回答将是：“2h 与 t² 的图像是一条经过原点的直线，证实了 h ∝ t²，与方程 h = ½ g t² 一致。该直线的斜率给出 g。”如果某个数据点明显偏离，把它圈出来作为异常值，不要将其纳入最佳拟合直线。仔细标注图像可以赢得加分。

4. Determining Gradient and Intercept | 求斜率和截距

To find the gradient, select two points far apart on the line of best fit – do not use data points from the table. The points should be at least half the line’s length apart. Read coordinates (x₁, y₁) and (x₂, y₂), then calculate:

要求斜率，应在最佳拟合直线上选取相距较远的两个点——不要使用表格中的数据点。两点间距至少为线长的一半。读取坐标 (x₁, y₁) 和 (x₂, y₂)，然后计算：

gradient = (y₂ – y₁) / (x₂ – x₁)

Show the working clearly using the triangle method on the graph itself. Give the unit of the gradient – in this case, m s⁻². If the line does not pass through the origin, also read the y-intercept and comment on whether it matches the expected zero value. In an evaluation, a non-zero intercept might indicate a systematic error, such as a delay in the timing mechanism.

在图上用三角形法清晰展示计算过程。给出斜率的单位——此处为 m s⁻²。如果直线不经过原点，还要读取 y 截距，并评论它是否符合预期的零值。在评估中，非零截距可能表明存在系统误差，例如计时机构的延迟。

For the sample data, choosing (x₁ = 0.040 s², y₁ = 0.410 m) and (x₂ = 0.200 s², y₂ = 1.960 m) gives:

对于示例数据，选取 (x₁ = 0.040 s², y₁ = 0.410 m) 和 (x₂ = 0.200 s², y₂ = 1.960 m) 得到：

gradient g = (1.960 – 0.410) / (0.200 – 0.040) = 1.550 / 0.160 = 9.69 m s⁻²

This experimental value is close to the accepted 9.81 m s⁻². In your answer, state the gradient as your measured value of g.

这个实验值接近公认的 9.81 m s⁻²。在你的答案中，把斜率表述为你测得的 g 值。

5. Calculating and Propagating Uncertainties | 计算和传递不确定度

Uncertainty is a key part of Unit 3. You must find the absolute uncertainty in each raw measurement. For a metre ruler, the resolution is 1 mm, so the absolute uncertainty in h might be ± 0.001 m (although a more realistic estimate is ± 0.002 m due to parallax). For the timer, the resolution might be 0.01 s, giving an uncertainty of ± 0.005 s if a single reading, but because you take repeat times, you should calculate the mean and the half‑range of the repeats. The uncertainty in the mean time is the larger of the instrumental resolution and the half‑range (or standard deviation for advanced courses). For example, if times for one height are 0.19 s, 0.20 s, 0.20 s, the range is 0.01 s, so half‑range = 0.005 s. The timer resolution is ±0.01 s, so the instrumental uncertainty is ±0.005 s. Both give ±0.005 s, so the uncertainty in mean t is ± 0.005 s.

不确定度是单元3的关键部分。你必须找到每个原始测量量的绝对不确定度。对于米尺，分辨率为 1 mm，因此 h 的绝对不确定度可能是 ± 0.001 m（但由于视差，更现实的估算为 ± 0.002 m）。对于秒表，分辨率可能为 0.01 s，如果单次读数不确定度为 ± 0.005 s，但由于你进行重复计时，应计算平均值的半区间和平均值。平均时间的不确定度取仪器分辨率的绝对不确定度和重复读数的半区间（或标准偏差）中的较大值。例如，若某高度下的时间为 0.19 s、0.20 s、0.20 s，极差为 0.01 s，半区间 = 0.005 s。计时器分辨率 ±0.01 s 意味着仪器不确定度 ±0.005 s，两者均为 ±0.005 s，所以平均 t 的不确定度是 ± 0.005 s。

Then propagate uncertainties to t². The percentage uncertainty in t is (0.005 / 0.197) × 100% ≈ 2.54%. Since t² = t × t, the percentage uncertainty doubles to ≈ 5.08%. Similarly, the percentage uncertainty in h for the smallest height, say ± 0.002 m out of 0.200 m, is 1%. When plotting, the uncertainty in 2h is the same absolute uncertainty as h but doubled, so the points should have vertical error bars showing ± 0.004 m and horizontal error bars showing the absolute uncertainty in t², which you calculate from the percentage uncertainty. For the first data point, t² = 0.0388 s², 5.08% gives an absolute uncertainty of 0.0020 s². Draw these bars on the graph.

然后将不确定度传递到 t²。t 的百分比不确定度为 (0.005 / 0.197) × 100% ≈ 2.54%。由于 t² = t × t，百分比不确定度翻倍为 ≈ 5.08%。类似地，最小高度 0.200 m 时 h 的百分比不确定度为 ± 0.002 m / 0.200 m = 1%。在绘图时，2h 的不确定度与 h 的绝对不确定度相同但数值加倍，因此数据点应显示 ± 0.004 m 的纵向误差限和由百分比不确定度计算出的 t² 绝对不确定度所决定的横向误差限。对于第一个数据点，t² = 0.0388 s²，5.08% 给出绝对不确定度 0.0020 s²。在图上画出这些误差限。

To find the uncertainty in the gradient, draw the steepest and shallowest lines that still pass through the error bars. The difference between the gradient of the best-fit line and the extreme lines gives the absolute uncertainty in g. For example, if best gradient = 9.69 m s⁻², max gradient = 9.89 m s⁻² and min gradient = 9.51 m s⁻², then uncertainty = (9.89 – 9.51) / 2 = 0.19 m s⁻². So the final answer is g = 9.69 ± 0.19 m s⁻². Always quote the result to the decimal place consistent with the uncertainty.

要求出斜率的不确定度，画出仍能穿过所有误差限的最陡和最缓的两条直线。最佳拟合直线的斜率与这两条极端直线斜率之差，给出 g 的绝对不确定度。例如，若最佳斜率为 9.69 m s⁻²，最大斜率为 9.89 m s⁻²，最小斜率为 9.51 m s⁻²，则不确定度 = (9.89 – 9.51) / 2 = 0.19 m s⁻²。因此最终答案是 g = 9.69 ± 0.19 m s⁻²。始终将结果保留到与不确定度小数位一致。

6. Percentage Difference and Accuracy | 百分差与准确性

Calculate the percentage difference between your experimental value and the accepted value (9.81 m s⁻²). Use:

计算你的实验值与公认值 (9.81 m s⁻²) 之间的百分差。使用公式：

% difference = |(experimental value – accepted value)| / accepted value × 100%

With g = 9.69 m s⁻², the difference is |9.69 – 9.81| / 9.81 × 100% ≈ 1.22%. This is less than the typical target of 5%, indicating good accuracy. If the percentage difference is larger than the percentage uncertainty (or if the accepted value lies outside the range of your uncertainty), a systematic error is likely present. Discuss this in your evaluation.

对于 g = 9.69 m s⁻²，差值为 |9.69 – 9.81| / 9.81 ×100% ≈ 1.22%。该值小于通常 5% 的目标，表明准确性良好。如果百分差大于百分比不确定度（或公认值落在你测得值的不确定度范围之外），则很可能存在系统误差。在你的评估中讨论这一点。

A common mistake is to confuse percentage difference with percentage uncertainty. The former compares your result to the true value; the latter reflects the precision of your measurements. An accurate result can have a large uncertainty if the experiment is imprecise, and vice versa. Examiners want to see this distinction made clearly.

一个常见错误是混淆百分差和百分比不确定度。前者比较你的结果与真实值；后者反映测量的精密度。如果实验不精密，一个准确的结果也可能有很大的不确定度，反之亦然。考官希望看到你清晰地区分二者。

7. Identifying and Minimising Sources of Error | 识别并减小误差来源

List at least two significant systematic errors and two random errors with realistic mitigation strategies. For the free-fall experiment:

至少列出两项重要的系统误差和两项随机误差，并给出切实可行的减小策略。对于自由落体实验：

Systematic error: Reaction time delay when using a stopwatch manually. This can make the measured time larger than the true time. Use an electronic timer triggered by the electromagnet release and a trapdoor switch at the bottom to eliminate human reaction time.
系统误差：手动使用秒表时的反应时间延迟。 这会使测得的时间大于真实时间。使用由电磁铁释放触发、底部活板门开关终止的电子计时器，以消除人的反应时间。

Systematic error: Air resistance and the ball not falling perfectly freely. This reduces the acceleration, especially for a light ball. Use a small, dense metal sphere (e.g., steel) and keep heights moderate to minimise air drag. Dropping in a partial vacuum would be ideal but is impractical in a school lab.
系统误差：空气阻力及球未做到完全自由下落。 这会减小加速度，尤其对于轻球。使用小而高密度的金属球（如钢球），并保持高度适中以减少空气阻力。在部分真空中进行是理想做法，但在校内实验室不现实。

Random error: Parallax error when reading the metre rule or marking the release point. This leads to scatter in height values. Use a set square to align the rule vertically, and position your eye level with the measurement point. Use a pointer or a thin light beam to fix the exact release height.
随机误差：读取米尺或标记释放点时的视差。 这会导致高度值的分散。使用直角尺确保尺子竖直，并将眼睛平视测量点。使用指针或细光束来固定准确的释放高度。

Random error: Variation in release – the ball might be given a small initial velocity. Take great care to release from rest, possibly using an electromagnet that cuts the current instantly. Repeating and using the mean time reduces the effect of occasional poor releases.
随机误差：释放的不一致性——球可能获得微小的初速度。 务必从静止释放，可使用能瞬间断流的电磁铁。重复试验并取平均时间可减小偶尔释放不良的影响。

8. Plotting a Log Graph for Verification | 绘制对数图像加以验证

An alternative way to verify the relationship h ∝ t² is to plot a log-log graph. Take logarithms of h and t. If h = k tⁿ, then log h = log k + n log t. The slope of a graph of log h against log t should be n = 2, and the intercept gives k = ½ g. While not always required, knowing how to do this sets apart a top-grade response. You should be able to present a table with columns for log h and log t and explain that a straight line with slope of about 2.0 confirms the quadratic relationship.

验证 h ∝ t² 关系的另一种方法是绘制双对数图像。对 h 和 t 取对数。如果 h = k tⁿ，则 log h = log k + n log t。以 log h 对 log t 作图，斜率应为 n = 2，截距给出 k = ½ g。虽然不常考，但掌握这种方法能让你在回答中脱颖而出。你应该能给出包含 log h 和 log t 列的表格，并解释斜率约为 2.0 的直线证实了二次关系。

For high marks, mention that this method also allows you to determine n without assuming the exponent is exactly 2, adding robustness to your investigation. The associated uncertainty in n can be found from extreme lines on the log-log graph, and you can comment on whether 2.0 lies within the experimental range.

想要得高分，要提及这种方法还能在不假设指数恰好为 2 的情况下求出 n，增强探究的可靠性。从双对数图上的极端直线可求出 n 的不确定度，你还可以评论 2.0 是否落在实验范围之内。

9. Safe and Ethical Conduct of the Experiment | 实验的安全与规范操作

Unit 3 often asks how you carried out the investigation safely and with attention to fair testing. In your write-up, note that the heavy metal ball could cause injury if dropped from height; perform the experiment in a clear space, and wear closed-toe shoes. Ensure the clamp stand is stable and the release mechanism is securely attached. If using an electromagnet, avoid overheating by switching off when not in use. These simple safety precautions show a mature practical awareness.

单元3经常问你是如何安全地进行实验并注意公平测试的。在报告中，要指出重的金属球若从高处落下可能造成伤害；在空旷处实验，并穿包脚鞋。确保铁架台稳固，释放装置固定牢靠。如果使用电磁铁，不使用时关闭电源以防过热。这些简单的安全预防措施体现了成熟的实验意识。

Fair testing involves keeping all variables that might affect the outcome constant. In the free-fall experiment, ensure the same ball is used throughout, the release mechanism is identical each time, and the laboratory conditions (temperature, air currents) do not change significantly. State how you monitored these controls.

公平测试要求使所有可能影响结果的变量保持不变。在自由落体实验中，确保全程使用同一个球，每次释放机构相同，实验室条件（温度、气流）没有显著变化。说明你是如何监控这些控制的。

10. Evaluating Limitations and Suggesting Improvements | 评估局限性并提出改进

A top-level response critiques the method honestly. State that the largest source of uncertainty was likely the timing method; even with electronic timing, the sensitivity of the trapdoor may introduce a small delay. To improve, a light-gate positioned at the top and bottom would record the time interval with far greater precision (down to microseconds). Another limitation: measuring the height from the bottom of the ball to the trapdoor can be tricky; a travelling microscope or a laser distance meter could enhance accuracy. Mention that increasing the number of data points and the range of heights would improve the reliability of the gradient.

一份高水平的回答会诚实地评价方法。要指出最大的不确定度来源很可能是计时方法；即使使用电子计时，活板门的灵敏度也可能引入微小延迟。改进方法：在顶部和底部各放一个光电门，能精确得多地记录时间间隔（可达微秒级）。另一个局限：从球底到活板门测量高度可能不易操作；使用读数显微镜或激光测距仪能

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International A-Level Physics Example Responses: PH03 Unit 3 Practical Investigation | 国际A-Level物理示例答案：PH03单元3实验探究