Design and conduct a student-directed practical investigation related to fields, motion or light, including formulating a research question, identifying independent, dependent and controlled variables, collecting and analysing data with explicit uncertainty estimates, and communicating findings

What this dot point is asking

VCAA wants you to design, conduct and communicate a student-directed practical investigation in fields, motion or light. The investigation is the entire Unit 4 AoS 3 (sometimes 2 depending on the version of the study design), assessed as a SAC and presented as a scientific poster of around 600 to 1000 words. The dot point covers research question, variable identification, design, data handling, uncertainty propagation and analysis.

Choosing a research question

The starting point is a specific, testable question of the form:

How does (independent variable) affect (dependent variable) for (system), with (controlled variables) held constant?

Good research questions:

• "How does the angle of release affect the period of a simple pendulum?"
• "How does the slit separation affect the fringe spacing in a Young's double-slit setup?"
• "How does the inclination of an inclined plane affect the acceleration of a cart down the plane?"
• "How does the resistance of a circuit affect the time constant of an RC charging curve?"

Avoid:

• Yes / no questions ("Does light reflect off a mirror?").
• Questions without a measurable dependent variable ("Why is the sky blue?").
• Questions with too many uncontrolled variables ("How does air affect a falling object?").

The question should fit the time and equipment available, typically 4 to 6 hours of practical work over 2 to 3 weeks.

Identifying variables

Three variable categories:

Independent variable (IV)

The variable you deliberately change. Choose a range of at least 5 values, with sensible spacing.

Dependent variable (DV)

The variable you measure in response. The DV depends on the IV.

Controlled variables

Variables that could affect the DV but which you hold constant. List them explicitly.

Each variable has a measurement method, range, precision and a unit. For example:

• IV: angle of release, range 5 to 45 degrees in 5-degree steps, measured with a protractor (precision 0.5 degrees).
• DV: pendulum period, measured by averaging the time for 10 oscillations, divided by 10. Stopwatch precision 0.01 s.
• Controlled: pendulum length (1.00 m, measured with a metre rule, precision 1 mm), bob mass (50 g), air resistance (assumed negligible at small amplitudes).

Designing the procedure

Schematic / labelled diagram. A clear diagram of the setup is essential. Label all equipment, distances, and measurement points.

Step-by-step procedure. Sufficient detail that another student could replicate the investigation. Include:

• Setup steps (assembly, alignment, calibration).
• Measurement steps (how each measurement is made, how the IV is changed).
• Repetition (how many trials per IV value; typically 3 to 5).

Risk assessment. Identify hazards (heat, sharp edges, electrical, optical) and the mitigation for each (safety glasses, low-voltage supply, no looking at laser beam).

Justification. For each design choice, justify why. Why this range? Why this number of repeats? Why this measurement device?

Recording data

Use two tables: a raw data table and a processed data table.

Raw data table records the direct measurements (e.g. time for 10 oscillations) with units and the instrument precision.

Processed data table records derived quantities (e.g. period = time / 10, with propagated uncertainty), with units and uncertainty.

Tables should include columns for the IV, DV, and any computed quantities. Include trial numbers and the mean of trials per IV value.

Uncertainty: types and estimation

Random uncertainty arises from measurement-to-measurement variability. Estimated by:

• The half-range of repeated measurements: $\Delta = (x_{\max} - x_{\min}) / 2$.
• Or the standard deviation of the mean (more rigorous, requires statistics).

Systematic uncertainty arises from a consistent bias in the measurement (e.g. zero offset on a balance, parallax in a metre rule reading). Estimated from instrument calibration or known biases.

Instrumental uncertainty is the half-precision of the instrument (typically). A stopwatch with 0.01 s resolution has instrument precision $\pm 0.005$ s.

The reported uncertainty is typically the larger of random and instrumental.

Uncertainty propagation

When derived quantities are computed, uncertainties propagate.

Addition / subtraction. Add absolute uncertainties.

(Strictly, $\Delta z = \sqrt{(\Delta x)^2 + (\Delta y)^2}$ for independent uncertainties; VCAA accepts the simpler additive rule.)

Multiplication / division. Add fractional (or percentage) uncertainties.

Powers. Multiply fractional uncertainty by the power.

So for $T^2$ (used in linearising a pendulum experiment), the fractional uncertainty doubles compared to $T$ alone.

Constants. Constants do not contribute uncertainty. $z = k x$ has $\Delta z / z = \Delta x / x$.

Plotting graphs

Plot the processed data with uncertainty bars on both axes (or at least on the more uncertain axis).

Linearisation. If the predicted relationship is non-linear, transform the data to produce a linear plot.

• $y = k x$: linear. Plot $y$ vs $x$, gradient $k$, intercept 0.
• $y = k x^2$: parabolic. Plot $y$ vs $x^2$, gradient $k$, intercept 0.
• $y = k / x$: inverse. Plot $y$ vs $1/x$, gradient $k$, intercept 0.
• $T = 2 \pi \sqrt{L/g}$: rearrange to $T^2 = 4 \pi^2 L / g$. Plot $T^2$ vs $L$, gradient $4 \pi^2 / g$.
• $y = a x + b$: linear with non-zero intercept. Both gradient and intercept extracted from plot.

Best-fit line. Draw a line through the data using a line of best fit. The gradient and intercept (with uncertainties) come from the slope and y-intercept of this line.

Maximum and minimum gradient lines. To estimate the uncertainty in the gradient, draw two further lines: one with the maximum reasonable slope through the data with uncertainty bars, and one with the minimum reasonable slope. The half-range of these slopes is the uncertainty in the gradient.

Analysis

Compare to theory. State the theoretical prediction (e.g. $g = 4 \pi^2 / \text{gradient}$ from a pendulum). Calculate the experimental value from the measured gradient. Compare to the accepted value within uncertainty.

Result statement. "From the gradient of the linearised graph, $g_{\text{exp}} = (9.6 \pm 0.4)$ m s$^{-2}$. The accepted value at this latitude is $9.80$ m s$^{-2}$. The experimental result agrees with the accepted value within uncertainty."

Discussion

Uncertainty sources

Name the major contributions to uncertainty and which step they enter. Distinguish random and systematic sources.

Limitations

What the investigation cannot conclude. (Are the controlled variables truly held constant? Are the measurements limited by instrument precision? Is the range of the IV sufficient?)

Improvements

Concrete changes that would reduce uncertainty or extend the result. (Use a longer pendulum to reduce relative uncertainty; use a photogate instead of a stopwatch.)

Broader physics

Connect the result to wider physics. (A pendulum experiment links to the universal $g$ and to the period formula derived from torque equations.)

Conclusion

A direct answer to the research question, in one or two sentences, citing the experimental value and uncertainty. Avoid restating the discussion.

Example: "The period of a simple pendulum was found to increase as the square root of the length, with the gradient of $T^2$ vs $L$ giving $g = (9.6 \pm 0.4)$ m s$^{-2}$. The result supports the theoretical relationship $T = 2 \pi \sqrt{L/g}$ within experimental uncertainty."

Scientific poster structure

VCAA's Unit 4 AoS 3 SAC asks for a scientific poster (typically A1 size, 600-1000 words plus graphs and diagrams). Standard section order:

1. Title (specific, descriptive).
2. Research question.
3. Hypothesis.
4. Methodology (with diagram).
5. Variables and risk assessment.
6. Results (data tables and graphs).
7. Analysis (gradient, comparison to theory).
8. Discussion (uncertainty, limitations, improvements).
9. Conclusion.
10. References (any sources consulted).

Examples in context

Example 1. Pendulum-period investigation at a Melbourne secondary school. A Year 12 student investigates the period $T$ of a simple pendulum as a function of length $L$, predicting $T = 2\pi \sqrt{L/g}$. The student varies $L$ from $0.20$ to $1.00$ m in $0.10$ m steps (independent variable), times $20$ oscillations with a digital stopwatch (dependent variable, division by $20$ reduces reaction-time uncertainty to $\pm 0.005$ s per period), and controls amplitude $< 10^\circ$ and bob mass. Plotting $T^2$ versus $L$ should give a straight line of gradient $4\pi^2/g$, giving $g = 9.78 \pm 0.05$ m s$^{-2}$, comparable to the accepted Melbourne value of $9.80$ m s$^{-2}$.

Example 2. Boyle's-law investigation with a Synchrotron-grade pressure sensor. A student uses a digital pressure sensor ($\pm 0.5\%$ accuracy) and a graduated syringe ($\pm 0.5$ mL) to investigate $PV =$ constant for a fixed mass of air at constant temperature. Volume varied from $20$ to $60$ mL; pressure measured at each. Fractional uncertainty in $P$ is $0.5\%$, in $V$ is $0.5/20 = 2.5\%$ at smallest volume, so total uncertainty in $PV$ product is dominated by volume and reaches $\pm 3\%$. Plotting $P$ versus $1/V$ should give a straight line through origin; experimentally a slope of $1015 \pm 30$ kPa mL was measured, consistent with the $1013$ kPa $\times$ initial-volume prediction.

Try this

Q1. Define independent, dependent and controlled variables, with one example each from a physics investigation. [3 marks]

• Cue. Independent: variable changed by experimenter (e.g. mass on spring). Dependent: variable measured (e.g. period). Controlled: held constant (e.g. spring constant, amplitude).

Q2. A student measures the diameter of a wire as $0.42 \pm 0.01$ mm and its length as $2.000 \pm 0.005$ m. Calculate (a) the cross-sectional area and its absolute uncertainty, and (b) the fractional uncertainty in resistance if $R \propto L/A$. [4 marks]

• Cue. (a) $A = \pi d^2/4 = 0.1385$ mm$^2$; fractional uncertainty $= 2 \times 0.01/0.42 = 4.8\%$; absolute $\approx 0.007$ mm$^2$. (b) $0.25\% + 4.8\% = 5.0\%$.

Q3. Refer to the pendulum investigation. (a) Identify the independent and dependent variables. (b) Calculate the percentage uncertainty in $T$ for $20$ oscillations timed to $\pm 0.1$ s with $T_{20} = 38.0$ s. (c) Explain why plotting $T^2$ versus $L$ is preferable to $T$ versus $L$. [2+2+3 marks]

• Cue. (a) IV: length $L$. DV: period $T$. (b) $\Delta T/T = 0.1/38 = 0.26\%$. (c) Theoretical relationship is linearised; gradient gives $g$ directly with linear regression.