Welcome to Experimental Evaluation
Hello and welcome! In your CCEA AS Physics course, practical work isn't just about following instructions and getting a number at the end. An essential skill tested in AS 3: Practical Techniques and Data Analysis is Evaluation.
Evaluating an experiment means taking a step back and asking: "How trustworthy are my results? What went wrong? How could this experiment be redesigned to make the data more reliable and accurate?"
Don't worry if this sounds intimidating at first! Evaluation is a step-by-step skill that anyone can master with the right approach.
Quick Review: The Two Pillars of Good Data
• Accuracy: How close your measured/calculated value is to the true or accepted literature value.
• Precision: How close repeated measurements are to each other (the spread of your data), and the degree of detail given by your measuring instrument.
1. Comparing Experimental Values with Accepted Values
In many AS 3 experiments (such as finding the acceleration of free fall \(g\) or the Young modulus \(E\)), you will calculate an experimental value and compare it against an accepted reference value.
Calculating Percentage Difference
To quantify how far your result is from the true value, you calculate the percentage difference:
\(\text{Percentage Difference} = \frac{|\text{Experimental Value} - \text{Accepted Value}|}{\text{Accepted Value}} \times 100\%\)
Example:
Suppose you carry out a free-fall experiment and calculate \(g = 9.42\text{ m s}^{-2}\). The accepted value for the acceleration due to gravity is \(9.81\text{ m s}^{-2}\).
\(\text{Percentage Difference} = \frac{|9.42 - 9.81|}{9.81} \times 100\% = \frac{0.39}{9.81} \times 100\% = 3.98\%\)
Judging Consistency: The Golden Rule of Evaluation
How do you decide if an experiment was successful or if your discrepancies are just down to experimental uncertainties? You compare your percentage difference with your total percentage uncertainty:
• Case 1: \(\text{Percentage Difference} \le \text{Percentage Uncertainty}\)
If the percentage difference is smaller than (or equal to) your experimental percentage uncertainty, your result is consistent with the accepted value. This means experimental uncertainties (random variations) adequately explain the difference!
• Case 2: \(\text{Percentage Difference} > \text{Percentage Uncertainty}\)
If the percentage difference is greater than your percentage uncertainty, your result is not consistent with the accepted value. This suggests that significant systematic errors or flawed assumptions affected your experiment.
Key Takeaway: Never just say "my experiment went well because the numbers look close." Always support your judgment by numerically comparing the percentage difference to the percentage uncertainty.
2. Identifying Limitations and Sources of Error
When an examiner asks you to evaluate a practical procedure, they want you to pinpoint specific physical reasons why uncertainties exist.
Systematic Errors vs. Random Errors in Practical Setups
• Systematic Errors: Errors that cause readings to be consistently higher or consistently lower than the true value every single time. Examples include zero errors on meters or micrometers, calibration errors, and unmeasured resistive forces like air resistance or friction.
• Random Errors: Unpredictable fluctuations that cause readings to be scattered above and below the true value. Examples include human reaction time when pressing a stopwatch, parallax errors when viewing a scale from varying angles, and temperature fluctuations during a resistance test.
Did You Know?
Zero error is a classic systematic error. If your micrometer reads \(+0.02\text{ mm}\) when fully closed, every single wire diameter you measure will be \(0.02\text{ mm}\) too thick!
Common AS Practical Setups and Their Sources of Error
Let's look at standard practicals and the real-world limitations you should identify:
1. Simple Pendulum / Mass-Spring Oscillations:
• Limitation: Human reaction time at the start and stop of timing.
• Limitation: Difficulty in judging when an oscillation completes without a fixed reference mark.
• Limitation: Large amplitude oscillations causing non-simple harmonic motion.
2. Free-Fall Electromagnet Experiment (\(g\)):
• Limitation: Residual magnetism causing a slight delay when the ball is released from the electromagnet.
• Limitation: Parallax error when measuring the vertical drop height \(h\) with a metre rule.
3. Determining the Young Modulus of a Wire:
• Limitation: The wire may not be completely straight at the start (kinks in the wire).
• Limitation: Wire diameter varies along its length or is non-circular.
• Limitation: The support clamp might slip under heavy loads.
4. Internal Resistance and EMF of a Cell:
• Limitation: The cell warms up during current flow, which changes its internal resistance.
• Limitation: Resistance of the connecting leads is ignored.
Key Takeaway: Be specific to the apparatus in front of you. Generic answers like "human error" or "faulty equipment" will never gain marks in AS Level Physics!
3. Suggesting Realistic Modifications and Improvements
Evaluating an experiment always leads to the next step: How do we fix these problems?
Poor Answers vs. High-Scoring Answers
Examiners look for precise, practical engineering solutions rather than vague wishes.
• Weak: "Use a computer to make it better."
• Strong: "Use a light gate connected to a digital datalogger to record the time taken for the card to pass, eliminating human reaction time."
• Weak: "Measure the wire more carefully."
• Strong: "Measure the diameter of the wire at multiple points along its length and at different perpendicular orientations using a micrometer screw gauge, then calculate the average."
• Weak: "Time it more times."
• Strong: "Time \(20\) complete oscillations instead of \(1\), and divide the total time by \(20\) to find the period \(T\). This reduces the percentage uncertainty caused by reaction time."
Techniques for Reducing Experimental Uncertainties
Here is a toolkit of standard improvements you can apply across AS practicals:
• Use a Fiducial Marker: Place a pin or reference pointer at the equilibrium (centre) position of an oscillating system. The object moves fastest at the equilibrium point, making it the easiest position to judge accurately when timing swings.
• Reduce Percentage Uncertainty by Scaling Up: Instead of measuring very small quantities directly, measure a multiple (e.g., timing \(20\) swings instead of \(1\), or measuring the thickness of \(50\) sheets of paper together).
• Use Higher Precision Instruments: Replace a standard metre rule (precision \(\pm 1\text{ mm}\)) with Vernier callipers (precision \(\pm 0.1\text{ mm}\)) or a micrometer screw gauge (precision \(\pm 0.01\text{ mm}\)) when measuring small dimensions like diameters.
• Prevent Overheating in Circuits: Insert a switch and keep the circuit open between readings to prevent heating effects from changing component resistances.
• Avoid Parallax: Ensure your line of sight is perpendicular to the scale, use a set square against a vertical ruler, or use mirrors behind meter needles.
Memory Aid: The "PAR" Method for Timing Oscillations
Whenever an experiment involves timing repeated motion, remember PAR:
• P - Pointer: Use a fiducial marker at the equilibrium point.
• A - Average: Repeat readings at least 3 times to calculate a mean.
• R - Range/Repeats: Count a large number of cycles (e.g., \(N = 20\)) to spread reaction time error over a longer period.
Key Takeaway: When proposing an improvement, state what apparatus you would introduce, how you would use it, and which specific uncertainty it reduces.
4. Evaluating Graphs and Drawing Valid Conclusions
Graphs are the ultimate evaluation tool in physics. They allow you to see the big picture across your entire dataset.
Assessing Graph Quality and Trends
• Direct Proportionality: If a theory suggests \(y \propto x\), the graph of \(y\) against \(x\) must be a straight line passing directly through the origin \((0,0)\).
• Systematic Error Revealed by Intercept: If the graph is a straight line but has an unexpected non-zero intercept on the y-axis, this indicates an uncorrected systematic error (or an extra constant in your relationship, such as friction or mass of the holder).
Anomalous Points (Outliers)
• An anomalous point is a data point that lies visibly far from the line of best fit compared to the other points.
• When evaluating data, identify the anomaly and suggest a likely reason (e.g., misreading a scale by a factor of 10, or recording the time for 9 swings instead of 10).
• Anomalous points must be ignored when calculating the mean of repeated readings and when drawing the line of best fit.
Limits of Experimental Range
Be careful when extending conclusions beyond the range tested:
• Extrapolation Danger: Never assume a relationship continues indefinitely beyond your measured data points. For example, a spring obeys Hooke's law (\(F = k\Delta L\)) only up to its limit of proportionality. Extending the line beyond your highest load could be completely invalid!
Key Takeaway: A valid conclusion stays strictly within the boundaries of the data collected and acknowledges where the model or apparatus reaches its physical limits.
5. Common Mistakes to Avoid in Evaluation Questions
• Mistake 1: Blaming "human error" without explanation. Never write the words "human error". Always name the exact mechanism (e.g., "human reaction time in stopping the timer" or "parallax error when reading the meniscus").
• Mistake 2: Confusing resolution with accuracy. Just because a digital meter shows 4 decimal places does not mean it is accurate if it has not been calibrated!
• Mistake 3: Forgetting units in comparisons. Ensure both your experimental value and accepted value share identical units before calculating percentage difference.
• Mistake 4: Claiming an experiment is "wrong" simply because values do not match exactly. All physical measurements carry uncertainty. If the difference falls within your calculated uncertainty range, your result is valid and consistent!
Summary Checklist for AS 3 Evaluation
When tackling evaluation questions in your exam, run through this quick mental checklist:
1. Calculate: Find the percentage difference between your result and the true value.
2. Compare: Is \(\% \text{ difference} \le \% \text{ uncertainty}\)? Conclude whether your data is consistent.
3. Identify: Spot one major systematic error and one major random error specific to that setup.
4. Improve: Suggest realistic, specific changes to the method or apparatus that directly target those errors.
5. Validate: State clear conclusions without extrapolating beyond the experimental range.