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The Excellence discussion: critical issues

What Excellence asks you to discuss

Excellence requires a discussion addressing issues critical to the investigation — around two substantial points. The standard names three kinds, and each has a required structure.

For every point: name the issue → explain the mechanism → state the direction and size of its effect on the measured variable or the gradient → state the effect on the validity of the conclusion.

1. Other variables that could have changed, and how they would have changed the results

Not the variables you controlled successfully — the ones that could have varied and would have mattered.
The word "how" is doing work in the criterion: you must say which way the result would move.
- "The temperature of the wire rises as current flows. Resistivity increases with temperature, so the resistance of the longer wires — which were measured last, after the current had been flowing longest — would read high. That would steepen the graph of $R$ against $l$ and overestimate the resistance per unit length."

2. Limitations to the theory's applicability

This is the discussion point most specific to Level 3, and it comes in two forms.

In the practical situation: the theory assumes something your apparatus does not provide.
- "The theory $T = 2\pi\sqrt{L/g}$ assumes a point mass on a light, inextensible string. My bob had a radius of $1.5$ cm and the string stretched slightly under load, so the effective length was not exactly the length I measured."
At extreme values of the independent variable: the theory holds in the middle of the range but breaks down at one end.
- "At the shortest lengths the amplitude was a larger fraction of the length, so the small-angle approximation behind the theory became less valid, and the true period would be slightly longer than the theory predicts — which is consistent with my shortest-length points sitting above the line."

3. Unexpected outcomes of the processing

Not just an odd raw reading — something that emerged when you processed the data: an intercept that should not be there, a gradient consistently off, curvature in a graph that should have been straight, error bars that do not overlap the line.
Say what could have caused it, and what it does to the validity of the conclusion.
- "My linearised graph curved slightly upward at the high-current end. Above $2$ A the filament was visibly glowing, so its temperature — and therefore its resistance — was rising with current, which is a departure from the constant-resistance assumption rather than a measurement error. The conclusion is therefore valid only below about $2$ A, and I have restricted my stated range accordingly."

What does not count

"Human error" — names nothing.
"The equipment was old" — no mechanism, no direction.
A list of five issues, each in one sentence — the criterion asks for issues to be addressed, and two developed points beat five named ones.
Improvements with no reasoning: "I would use better equipment next time."

A template for one full discussion point

The issue: state it specifically, with a number if you have one.
The mechanism: the physics by which it affects the measurement.
The direction: does it make readings too high or too low, and is the effect constant (systematic) or scattered (random)?
The consequence: what it does to the gradient, the intercept or the derived quantity.
The verdict: does the conclusion survive, and over what range?

Worked ExampleBuilding one substantial discussion point

A student tests $v^2 = 2gh$ by rolling a ball off a bench from various heights and timing its fall. Their measured $g$ came out at $9.2 \pm 0.2$ m s⁻², below the accepted $9.81$ m s⁻². Write a full discussion point about a limitation of the theory in their practical situation.

Step 1 — Name the issue specifically

The theory $v^2 = 2gh$ assumes the ball is in free fall, with gravity as the only force acting. In practice the ball also experiences air resistance, and it was rolling before it left the bench rather than sliding.

Step 2 — Explain the mechanism

Air resistance acts opposite to the motion and grows with speed, so it reduces the acceleration below $g$ . Rolling matters for a different reason: a rolling ball stores some of the energy released as rotational kinetic energy, so less of the potential energy is available as translational kinetic energy — the ball arrives moving more slowly than the theory predicts.

Step 3 — State the direction and where it is worst

Both effects make the measured speed too low for a given height, so the measured $g$ comes out too small — which is exactly what was observed. Air resistance grows with speed, so its effect is largest at the greatest heights, where the ball is fastest. That means the effect is not a constant offset but a progressive one that flattens the graph at the high end, reducing the gradient.

Step 4 — Estimate the size

For a solid sphere, rotational energy accounts for about $\tfrac{2}{7}$ of the total kinetic energy, which alone would reduce the measured $g$ by around $30\%$ if the ball rolled the whole way. The measured value is only $6\%$ low, which suggests the ball was mostly in free fall after leaving the bench and that rolling affected only its initial speed — so air resistance is the more plausible dominant cause of the remaining discrepancy at this scale.

Step 5 — State the effect on the validity of the conclusion

The shape of the relationship, $v^2 \propto h$ , is still supported — the graph is straight. What is affected is the gradient, so the derived value of $g$ is a systematic underestimate rather than a random one. The conclusion should therefore state that the data supports the form of the theory but that the value of $g$ obtained is a lower bound, and that the discrepancy has an identified physical cause rather than being unexplained scatter.