📚 Experimental Investigation in OxfordAQA PH01: Jan 22 Report Insights | 牛津AQA PH01实验探究：2022年1月报告启示
The January 2022 examiner report for OxfordAQA International AS Physics Unit 1 (PH01) provides valuable feedback on students’ performance in experimental investigation questions. Such questions assess practical skills including planning, data analysis, and evaluation of errors. This article draws on the key observations from that report to help you master experimental techniques and avoid common pitfalls.
2022年1月牛津AQA国际AS物理单元1(PH01)的考官报告为学生实验探究题的表现提供了宝贵的反馈。这类题目考查包括规划、数据分析和误差评估在内的实验技能。本文借鉴该报告中的关键观察，帮助你掌握实验技术并避免常见错误。
1. The Context of the Investigation | 实验探究的背景
In the PH01 paper, one investigation required determination of the acceleration of free fall, g, using a trapdoor-and-electromagnet arrangement. A steel ball is held at a measured height above a trapdoor switch; when released, the timer starts, and the ball’s impact stops the timer. From the height h and fall time t, the equation h = ½ g t² allows g to be found.
在PH01试卷中，有一项探究要求学生利用捕集开关与电磁铁装置测定自由落体加速度g。钢球被固定在距捕集开关一测量高度处；释放时计时器启动，撞击使计时停止。由下落高度h和时间t，方程h = ½ g t²可求出g。
2. Key Apparatus and Setup | 关键装置与设置
The apparatus includes a rigid stand, an electromagnet connected to a dc supply, a steel sphere, a trapdoor switch (or impact plate) placed directly underneath, and an electronic millisecond timer. The circuit is designed so that breaking the magnet supply starts the timer, and closing the trapdoor contact stops it. A metre rule measures vertical distance from the bottom of the ball to the trapdoor surface.
装置包括坚固支架、连接直流电源的电磁铁、钢球、正下方放置的捕集开关（或撞击板），以及电子毫秒计时器。电路设计确保切断电磁铁电源时启动计时，捕集开关触点闭合时停止计时。用米尺测量从球底到捕集开关表面的垂直距离。
Careful alignment is essential: the ball must fall along the vertical axis to avoid dragging on guides and to ensure the impact triggers the trapdoor centrally. Report comments emphasised that many candidates neglected to check that the electromagnet switched off cleanly, leading to timing errors.
仔细的校准至关重要：球必须沿垂直轴下落，避免与引导装置摩擦，并确保撞击中心触发捕集开关。报告评论强调，许多考生忽视检查电磁铁是否干净利落地断电，导致计时误差。
3. Minimising Systematic Errors | 最小化系统误差
Systematic errors affect all readings and cannot be reduced by repetition. In this experiment, a dominant systematic error is the residual magnetism of the electromagnet, which delays release after the circuit is broken. Consequently, the measured fall time is slightly too long, and g is underestimated.
系统误差影响所有读数且无法通过重复减小。本实验中，主要的系统误差是电磁铁的剩磁，它使断电后释放延迟。因此，测得的下降时间稍长，导致g被低估。
To reduce this, a thin piece of paper can be placed between the ball and the magnet core to eliminate direct contact. Parallax error when measuring h can be minimised by ensuring the eye is level with the ball’s bottom and the trapdoor surface. The report also noted that some students used a ruler with worn ends, introducing zero error.
为减小此误差，可在球与磁铁芯之间垫一张薄纸以消除直接接触。测量h时的视差可通过确保眼睛与球的底部和捕集开关表面齐平来最小化。报告还指出，一些学生使用端部磨损的尺子，引入了零位误差。
4. Reducing Random Errors through Repeated Trials | 通过重复试验减少随机误差
Random errors arise from unpredictable variations such as reaction time in manual release circuits, small air currents, or electronic noise. The examiner report stressed that repeating measurements at each height substantially reduces the impact of such errors on the final g value.
随机误差由不可预测的变化引起，例如手动释放电路中的反应时间、微小气流或电子噪声。考官报告强调，在每一高度进行重复测量可显著降低此类误差对最终g值的影响。
For each h, at least three timing trials should be taken, and the mean time t̅ calculated. If a timing anomaly occurs (e.g. due to ball missing the trapdoor), that reading should be discarded and the trial repeated. Students who took only one reading per height struggled to justify the precision of their results.
对于每个h，应至少进行三次计时，并计算平均时间t̅。若出现计时异常（如球未击中捕集开关），则应舍弃该读数并重做。仅对每个高度取一次读数的考生难以证明其结果的精度。
5. Recording Data with Appropriate Precision | 以适当的精度记录数据
The metre rule can typically be read to ±1 mm, while the electronic timer may offer a resolution of 0.01 s or better. The report highlighted that many candidates failed to match significant figures of derived quantities to the measurement precision. For instance, t² values must be given with the same number of significant figures as the underlying t, or one more during calculation.
米尺通常可读至±1 mm，而电子计时器可提供0.01 s或更高的分辨率。报告强调，许多考生未能使导出量的有效数字与测量精度相匹配。例如，t²值必须与原始t具有相同的有效数字位数，或在计算中间保留多一位。
A properly drawn data table should include columns for h / cm, time trials t₁, t₂, t₃ / s, mean t / s, and t² / s². Units must be stated in column headings, and all raw data recorded immediately in ink. Completing such a table systematically earns marks for presentation and helps identify anomalous points.
正确的数据表应包括列：h/cm、计时 t₁, t₂, t₃/s、平均t/s、以及t²/s²。单位必须注明在列标题中，所有原始数据用墨水即时记录。系统地完成这样的表格可赢得表述分数，并有助于识别异常点。
6. Linearising the Equation and Plotting Graphs | 线性化方程与绘制图形
The relationship h = ½ g t² suggests that h is directly proportional to t². Therefore, plotting a graph of h (y-axis) against t² (x-axis) should yield a straight line through the origin. The gradient m of this line equals ½ g, so g = 2m. This linearisation method is strongly favoured over calculating individual g values from single pairs of h and t.
关系式 h = ½ g t² 表明h与t²成正比。因此，绘制h（纵轴）对t²（横轴）的图应得到一条过原点的直线。该直线的斜率m等于½ g，因此g = 2m。相对于用单组h和t计算各个g值，这种线性化方法更受青睐。
The report pointed out that many students plotted h against t, obtaining a curve that makes gradient analysis unreliable. They then incorrectly attempted to draw a tangent to find g. Always check the linearised form before plotting.
报告指出，许多学生绘制h对t的图，得到使斜率分析不可靠的曲线。随后他们错误地尝试画切线来求g。绘图前务必先检查线性化形式。
h = ½ g t² → graph of h vs t²
7. Determining g from the Graph’s Slope | 从斜率确定g
To calculate the gradient m, choose two well-separated points on the best-fit line (not necessarily data points) and use m = (h₂ – h₁) / (t₂² – t₁²). Then determine g = 2m. If the best-fit line passes through the origin within experimental uncertainty, the gradient from the origin to a far data point can be used, but it is safer to show the calculation with two labelled points on the line.
要计算斜率m，在最佳拟合线上选择两个间距大的点（不一定是数据点），使用 m = (h₂ – h₁) / (t₂² – t₁²)。然后求出 g = 2m。如果最佳拟合线在实验不确定度范围内通过原点，可以使用从原点到远端数据点的斜率，但更安全的做法是用线上两个标记点进行计算。
Candidates often lost marks by omitting units for the gradient and final g, or by quoting g to an unrealistic number of significant figures (e.g. 9.814 m s⁻² when the uncertainty is ±0.1 m s⁻²). The reported g should be given to the same decimal place as the uncertainty, e.g. 9.81 ± 0.05 m s⁻².
考生常因省略斜率和最终g的单位，或将g报至不合理的有效数字（例如不确定度为±0.1 m s⁻²却报出9.814 m s⁻²）而失分。报告的g值应与不确定度取相同小数位，如9.81 ± 0.05 m s⁻²。
8. Uncertainty in the Gradient | 斜率的不确定度
The examiner report emphasised that a simple estimate of uncertainty in g comes from drawing the worst acceptable line or calculating the maximum and minimum gradients from the extremes of the error bars. If error bars are not plotted, a range of gradients by eye can be used.
考官报告强调，g的不确定度简单估计来自画出最差可接受线，或根据误差棒的极端值计算最大和最小斜率。若未画误差棒，可采用目视的一组斜率范围。
Let m_max be the steepest plausible gradient and m_min the shallowest. Then the uncertainty Δm = (m_max – m_min) / 2. Consequently, Δg = 2 Δm. Expressing the final result as g ± Δg is expected for higher marks.
设m_max为可能的最陡斜率，m_min为最浅斜率。那么不确定度Δm = (m_max – m_min) / 2，从而Δg = 2Δm。最终结果表示为 g ± Δg 能获得更高分数。
The report noted that some students simply quoted the percentage uncertainty from the raw timing and height measurements without linking it to the slope. Direct propagation using the slope range is more robust and creditworthy.
报告指出，一些学生仅引用原始计时和高度测量的百分比不确定度，而未将其与斜率关联。利用斜率范围进行直接传递更为可靠且值得给分。
9. Common Errors Identified in the Jan 22 Report | 2022年1月报告中发现的常见错误
One major mistake was using the simple equation g = 2h / t² on a single pair of values without any linearisation. This approach cannot reveal systematic errors or demonstrate the quality of fit. The examiners expected a graph and slope analysis.
一个主要错误是，对单组数值直接使用公式 g = 2h / t² 而不进行任何线性化。这种方法无法揭示系统误差，也无法证明拟合优度。考官期望的是图形与斜率分析。
Many candidates overlooked the initial velocity condition: they assumed u = 0 but did not verify that the ball was truly at rest when the timer started. A slight initial downward push, or an electromagnetic delay, gave u > 0, causing the h vs t² graph to possess a positive intercept on the h-axis. Such a feature should be commented upon.
许多考生忽视了初速度条件：他们假设u=0，但未验证计时开始时球确实静止。微小的向下推动或电磁延迟导致u>0，使h vs t²图在h轴上存在正截距。应对此特征加以评述。
Poor graph plotting also cost marks: using unsuitable scales, not labelling axes with quantity and unit, and data points drawn as large blobs rather than small crosses. The report reminded that a sharp HB pencil and a clear 30 cm ruler are essential.
绘图不佳也导致失分：使用不合适的比例尺、轴未标注物理量与单位、数据点画成大圆点而非小十字。报告提醒，一支削尖的HB铅笔和一把清晰的30厘米尺子是必不可少的。
10. Final Exam Tips for Experimental Questions | 实验题考试技巧
Before starting calculations, always identify the independent and dependent variables, and express the expected relationship in a linear form y = mx + c. In this case, y = h, x = t², m = ½ g, c = 0.
计算前，务必确定自变量和因变量，并将预期关系表达为线性形式 y = mx + c。本例中，y = h, x = t², m = ½ g, c = 0。
When planning an investigation, list the key measurements, the instruments, and how you will minimise both systematic and random errors. For instance, mention taking repeated timings, checking zero errors, and using large enough heights to make timing uncertainty negligible.
规划探究时，列出关键测量量、仪器以及如何最小化系统误差和随机误差。例如，说明要重复计时、检查零误差，并采用足够大的高度使计时不确定度可忽略。
Lastly, evaluate your result against the accepted value of g (≈9.81 m s⁻²). If the discrepancy is larger than your estimated uncertainty, suggest a specific systematic error as a cause, not just ‘human error’. The report demonstrated that high-scoring candidates could propose logical improvements such as a vacuum chamber to eliminate air resistance or a more precise release mechanism.
最后，将结果与公认的g值（约9.81 m s⁻²）进行比较。若差异大于估计的不确定度，应提出具体的系统误差作为原因，而非仅仅“人为误差”。报告表明，高分考生能提出合理的改进，例如使用真空室消除空气阻力，或采用更精确的释放机制。
Published by TutorHao | Physics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导Cancel reply