Unit 6: Practical Skills in Physics A2 II

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.

Evaluate an experimental method by linking a specific weakness to a practical modification and then explaining how the change improves the measurement. The causal link matters more than naming sophisticated apparatus.

Discuss limitations as well as benefits. A light gate removes human reaction time, for example, but its trigger position or the part of an object that breaks the beam may still create uncertainty. A video helps only if its frame rate and scale suit the event.

Quantify the advantage when possible: a finer resolution, faster sampling, simultaneous readings or a longer timing interval should reduce a named uncertainty or prevent a named bias.

Judge the number of readings from the intended conclusion. There must be enough independent-variable settings to reveal the shape or key feature of the relationship, and enough repeated readings where random scatter affects each setting.

If a resonance curve has only one or two readings between $1.4$ and $1.6\,\mathrm{Hz}$, the peak frequency is poorly located even if many points exist far from the peak. More readings should be concentrated around the maximum.

Use the actual table or graph: count the distinct values, inspect their spacing and note whether repeats are shown. Explain what additional readings would make the conclusion more secure.

The range is the interval from the smallest to the largest value of the independent variable. Evaluate whether it is wide enough to expose the predicted change while remaining within safe, measurable and physically valid conditions.

A spring investigation using extensions only from $1.0$ to $1.5\,\mathrm{cm}$ may show too little force change to judge proportionality. Extending the interval can clarify the trend, but only while the spring remains below its elastic limit.

State a justified new minimum or maximum when the context permits, not merely 'use a wider range'. The proposed extension should target the weak evidence without changing the physical question.

A results table must not imply more precision than the apparatus and input data support. Check raw readings by instrument resolution and calculated values by the precision of the measurements used.

If measured values $3.4$ and $1.26$ are multiplied, the calculator gives $4.284$, but $3.4$ has only two significant figures, so reporting $4.3$ is appropriate. Writing $4.28400$ would invent precision.

Scan each column for one entry with extra or missing digits, then use the heading, instrument detail and neighbouring entries to decide the correction. Keep leading zeros non-significant: $0.00450$ has three significant figures.

Identify a unit by tracing what quantity was measured or calculated. A table heading should normally separate the quantity symbol from its unit, and every derived or transformed column needs the corresponding derived unit.

Convert prefixes consistently before calculation: $1\,\mathrm{mm}=10^{-3}\,\mathrm{m}$, so $1\,\mathrm{mm^2}=10^{-6}\,\mathrm{m^2}$. Squaring a value also squares its conversion factor.

To amend an incorrect heading, first identify the underlying quantity and transformation, derive the unit algebraically, then rewrite the unit without changing the numerical data unless a unit conversion is also required.

An inconsistent reading is one that does not follow the pattern of the other results beyond their normal scatter. Locate it in the table or as a point displaced from the graph trend, then investigate before deciding how it should be treated.

If a repeat under controlled conditions agrees with the surrounding trend and not the original value, record the original as anomalous and justify excluding it from a mean or fit. If the unusual value repeats, retain it and reconsider the assumed relationship or method.

Judge inconsistency relative to scatter and measurement precision. A point slightly off a best-fit line is not automatically anomalous; experimental data are not expected to lie exactly on a mathematical line.

Report a calculated result only to the precision justified by the measured inputs. Keep extra calculator digits during the working, then round once at the end so intermediate rounding does not distort the final value.

For $v=1.25\,\mathrm{m}/0.42\,\mathrm{s}$, the calculator gives $2.976\ldots\,\mathrm{m\,s^{-1}}$. The time has two significant figures, so report $v=3.0\,\mathrm{m\,s^{-1}}$, not every displayed digit.

Leading zeros are placeholders, while trailing zeros after a decimal can show precision: $0.00450$ has three significant figures. Scientific notation makes the intended precision unambiguous.

Choose axes that test the intended relationship, label each quantity and unit, and use a simple scale that spreads the data across most of the available grid. Plot points accurately before drawing a best-fit line or curve.

For a power law $y=kx^n$, form dimensionless processed variables $Y=\log(y/y_0)$ and $X=\log(x/x_0)$ using stated reference units. Then $Y=nX+C$, where $C$ depends on $k$ and the chosen reference units. Plotting $Y$ against $X$ on linear graph paper can reveal a straight line.

A log-log graph labelled $\log(T/\mathrm{s})$ vertically and $\log(M/\mathrm{kg})$ horizontally has dimensionless plotted values. Use consistent decimal places for the processed logarithms.

Carry units through substitutions, transformations, graph labels, gradients and final constants. Unit algebra is an independent check that the calculation and chosen relationship are physically consistent.

Convert prefixes before combining quantities. If $d=2.4\,\mathrm{mm}=2.4\times10^{-3}\,\mathrm{m}$, then $d^2=5.76\times10^{-6}\,\mathrm{m^2}$; both the number and the unit conversion are squared.

When a gradient represents a physical constant, derive its unit from the plotted axes and compare it with the unit expected from the model. A mismatch often exposes a reversed axis, missed power or unconverted prefix.

A trend comment states what the data show: direction, form, important region and scatter. Separate this observation from a physical explanation or causal claim unless the evidence and controlled design support that conclusion.

Transform the proposed relationship when useful. To test $T\propto\sqrt D$, check whether $T/\sqrt D$ is approximately constant or whether $T^2$ plotted against $D$ is linear through the origin.

Use data to support the comment: quote a range, ratio or change and acknowledge scatter. 'Increases' is weaker than 'approximately linear with a small positive intercept'.

Rearrange the proposed model into $Y=mX+c$, choose plotted quantities $Y$ and $X$, then interpret the gradient $m$ and intercept $c$ in terms of the required relationship or constant.

Choose two well-separated points on the best-fit line, not necessarily measured data points. Draw a large triangle spanning at least about half the plotted line, read coordinates carefully and keep the subtraction signs. A large triangle reduces the percentage effect of coordinate-reading uncertainty.

Give the gradient an appropriate sign, significant figures and unit derived from vertical-axis unit divided by horizontal-axis unit. A log-log gradient is dimensionless.

Two sets can have the same mean but different ranges: the set with the smaller range is more precise. Without an accepted value, their accuracy cannot be decided from agreement alone.

Greater sensitivity can make small input changes easier to distinguish, but sensitivity is not the same as resolution, precision or accuracy. An instrument can respond strongly yet retain a calibration offset.

Use uncertainty when judging accuracy: if $g=10.0\pm0.6\,\mathrm{m\,s^{-2}}$, the accepted $9.81\,\mathrm{m\,s^{-2}}$ lies in the interval, so the result is consistent with it.

A realistic error-reduction proposal names the error source, changes one practical feature and explains which uncertainty or bias becomes smaller. Match the modification to random or systematic behaviour.

Prefer a change whose effect can be predicted. Timing ten cycles makes the measured interval about ten times larger while similar start-stop uncertainty remains, so percentage uncertainty in the period decreases.

The proposal must suit the existing experiment, available range and safety constraints. Explain any new limitation introduced by additional apparatus, such as sensor alignment or sampling rate.

An experiment is improved when its method can support the intended conclusion more securely. Diagnose the weakest link—validity, data coverage, control, measurement quality or reproducibility—then propose a feasible change and explain the evidential gain.

State how the modification changes the decision made from the data. If it adds time, complexity or a new uncertainty, weigh that cost against the expected improvement.

Use details from the actual setup and results. A good proposal names the variable, apparatus setting or data region to change rather than giving a generic list of laboratory virtues.

Measurement uncertainty expresses a justified interval around a reported value. Write $x\pm\Delta x$, where $\Delta x$ is the absolute uncertainty in the same unit as $x$; it reflects resolution, scatter and method limitations rather than a known error from the true value.

Discuss the dominant source and direction when relevant: limited resolution creates a reading interval, repeats reveal random spread, and an uncorrected zero error could shift all values. State whether a proposed change reduces the absolute or percentage contribution.

Compare an accepted value or another result with the uncertainty interval. If $E=14.3\pm0.7\,\mathrm{GPa}$, values from $13.6$ to $15.0\,\mathrm{GPa}$ are consistent with the measurement; a candidate value outside that interval is not.

Propagate uncertainties by following how measured quantities are combined. The standard school-level rules give a maximum estimated uncertainty for independent contributions.

For $R=V/I$, if $V$ has $2.0\%$ uncertainty and $I$ has $3.0\%$, then $R$ has approximately $5.0\%$ uncertainty. If $A=\pi d^2/4$ and $d$ has $1.5\%$, then $A$ has $3.0\%$ uncertainty.

After finding the combined percentage uncertainty, convert to an absolute uncertainty when an interval is needed: $\Delta Q=(\%U_Q/100)Q$. Round the uncertainty sensibly and match the value's decimal place.

For one reading, use half the instrument resolution as the absolute uncertainty. If a scale's smallest division is $1\,\mathrm{mm}$, a single length reading has $\Delta x=0.5\,\mathrm{mm}$ under this syllabus convention.

For repeated readings, calculate the mean and use half the range as the absolute uncertainty. The range is maximum minus minimum.

Repeated times for five cycles are $4.84$, $4.92$, $4.88$ and $4.96\,\mathrm{s}$. Their mean is $4.90\,\mathrm{s}$ and half range is $(4.96-4.84)/2=0.06\,\mathrm{s}$. For one period, divide both by five: $T=0.980\pm0.012\,\mathrm{s}$, with the same percentage uncertainty, about $1.2\%$.