6.3 - Planning

Choose apparatus by working backwards from the variable, its expected size and the precision needed to test the proposed relationship. A named instrument is incomplete unless its usable range and resolution fit the measurement.

For a diameter near $20\,\mathrm{mm}$, vernier calipers with $0.1\,\mathrm{mm}$ resolution give an uncertainty small compared with the diameter and are more suitable than a millimetre ruler. A micrometer may be preferable for a thickness near $1\,\mathrm{mm}$.

Calibration checks whether an instrument's indication corresponds to known input values. Before measurements, check the zero where appropriate; a non-zero reading with zero input reveals a zero error.

If an instrument reads $+0.04\,\mathrm{mm}$ when it should read zero and cannot be reset, subtract $0.04\,\mathrm{mm}$ from every raw reading. Record both the check and the correction in the plan.

Calibration chiefly addresses systematic error: an offset can shift all readings in the same direction, so taking a mean of repeated uncorrected readings does not remove it.

For every measured variable, state the instrument, the exact technique and how its reading becomes the required quantity. The description should let another person reproduce the measurement without guessing reference points, timing events or conversions.

State how the independent variable will be changed and measured for at least a useful spread of values. Define the dependent-variable reading at each setting and include any necessary derived quantity.

Use techniques that reduce avoidable reading error: fixed fiducial markers for timing, perpendicular viewing to limit parallax, and unambiguous centre-to-centre or end-point definitions for distance.

A fair test changes the independent variable, measures the dependent variable and holds other variables that could affect the result constant. For every control variable, state both how it is controlled and why its variation would matter.

Choose controls from the physics of the system rather than listing generic conditions. Temperature, alignment, initial displacement, source-detector distance or component values matter only when they can change the dependent variable in that experiment.

A useful sentence pattern is: 'Keep ___ constant by ___ because ___ would otherwise change ___.'. This makes the variable, method and causal reason explicit.

Repeat a reading under the same stated conditions when random variation is plausible and the measurement can be reproduced. Repeats reveal scatter, help identify an anomalous result and allow a representative mean.

A planning answer should say whether repeats are appropriate, how many or at which settings, what will be averaged, and how an anomalous value will be checked. The choice should match the source of variation.

Identify each hazard created by the proposed apparatus or procedure, state the harm it could cause, then specify a control that reduces likelihood or exposure without preventing the measurement.

Prefer removing or enclosing the hazard and limiting exposure before relying on personal protection. Include only controls relevant to the actual setup and explain what each control manages.

Safety is part of the executable method: specify when equipment is isolated, discharged, cooled, shielded or repositioned. If a hazard remains significant, change the apparatus or method.

State how the measurements will test the proposed relationship. This determines which raw quantities, repeats, range and derived columns must be collected; analysis is therefore part of planning, not an afterthought.

Derive the graph from the proposed model. For constant acceleration from rest, $x= frac12at^2$, so plotting $t^2$ against $x$ should give a straight line through the origin with gradient $2/a$. For $T^2=C(2l-h)$, plotting $T^2$ against $h$ should be linear with the predicted sign and intercept relationship.

Plan enough well-spaced values to reveal the trend rather than merely comparing two endpoints. State how the best-fit line or curve will be used; do not promise a conclusion unsupported by the chosen plot.