I.1 Exploring and designing | IB DP Physics

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This is the half of an investigation that happens before any data exists — and it is the half that decides whether the data will be worth having. Most experiments that fail were doomed at the design stage, not the bench.

🎯What you need to be able to do

Turn a curiosity into a research question that can actually be answered by measurement.
State a hypothesis or prediction, and give the physics reason behind it.
Describe the three kinds of investigation: laboratory, database, and simulation or model.
Identify the independent, dependent and control variables for an investigation.
Choose a sensible range and number of values, and justify how many repeats you will take.
Explain the value of a pilot run.
Explain what calibration means and when an instrument needs it.
Describe how to reduce known problems in thermal, kinematics, circuit and radioactivity experiments.

🔍From curiosity to a question you can answer

Everything starts with noticing something. The job of this stage is to sharpen that into a research question narrow enough that measurement can settle it — which in practice means it must name what you will change, what you will measure, and over roughly what range.

Three cards describing kinds of investigation. A laboratory experiment, where you build a controlled set-up and manipulate the variables yourself, giving the most direct control and uncertainties you know, but limited to what the equipment can do. A database investigation, interrogating data somebody else has published, giving access to scales no school could reach, but requiring you to find out their uncertainties. And a simulation or model, where you vary parameters reality will not let you change, though it is only as good as the physics programmed in. Below, a contrast between a research question that is too vague, how does a pendulum work, and one that is answerable: how does the period of a simple pendulum depend on its length, for lengths from 0.20 to 1.00 metres. — A question that names both variables and the range has already written half the method. Add a prediction with a reason attached and you also know what to plot.

A hypothesis is a proposed explanation; a prediction is what that explanation says will happen. The prediction is the more useful of the two here, because it can be wrong in a way you would notice. “The period will increase with length” is a prediction. “The period will go as \( \sqrt{l} \), because \( T = 2\pi\sqrt{l/g} \)” is a better one — it is more specific, it carries its reason with it, and it tells you to plot \( T^{2} \) against \(l\).

✏️Worked example 1 — sharpening a question

A student writes: “I want to investigate solar panels.” Turn this into a usable research question, with a prediction.

What could be changed? The angle to the light, the distance from the lamp, the colour of the light, the area illuminated, the temperature of the panel. Pick one — say the distance.

What could be measured? The output potential difference, the short-circuit current, or the power delivered to a fixed load. Power is the most physically meaningful, so use it.

Over what range? Close enough that the panel is well lit, far enough that the power has fallen substantially — a pilot run will settle it, but 0.10 m to 1.00 m is a sensible first guess.

research questionHow does the power output of a solar panel depend on its distance from a lamp, between 0.10 and 1.00 m?

predictionPower should go as \( 1/d^{2} \), because the lamp radiates over a sphere of area \( 4\pi d^{2} \)

so plotpower against \( 1/d^{2} \), which should be a straight line through the origin

Sanity check. The question names one independent variable, one dependent variable and a range; the prediction gives a reason and implies what to plot. Notice that the prediction also tells you where the interesting data is: at large \(d\) the power falls off steeply, so readings should be closer together near the lamp than far from it.

📋The three kinds of variable

An experiment is a fair test only if one thing changes at a time. That gives three categories, and writing them out explicitly before you start is the single most useful habit in this whole topic.

Three cards defining the variables. The independent variable is the one you change, whose values and range you choose, and there must be only one or it is not a fair test. The dependent variable is the one you measure, which responds rather than being set, and it is what you plot. The control variables are everything else that could affect the dependent variable, held constant, and there should be as many as you can identify. Below, the three worked out for an investigation into how the resistance of a wire depends on its length: independent is the length at ten values from 0.10 to 1.00 metres; dependent is the resistance found from potential difference and current, repeated three times at each length; and the controls are the material, kept the same reel throughout, the diameter, measured at several points rather than assumed, and the temperature, kept down by using a low current and switching off between readings. — Every control variable listed here is a line you can return to in the evaluation. A control you did not think of is the usual reason two students doing “the same” experiment get different answers.

The trap: naming a control variable is not the same as controlling it. Writing “temperature was kept constant” asserts something you have not shown. If temperature matters, measure it — several times, during the experiment — and then you can say it was constant and prove it. And if it turns out to have drifted, you have discovered something genuinely worth writing about rather than an assumption that quietly failed.

📏Designing the method

Three decisions do most of the work: how far the independent variable will range, how many values you will take within that range, and how many times you will repeat each one.

On the left, five data points crowded into a narrow range, with three very different straight lines all passing plausibly through them, showing that the gradient is barely determined. On the right, the same five points spread across the whole graph, with a single line that is clearly pinned down. Below, the working minimums: at least five distinct values of the independent variable with eight or more better, at least three repeats at each value so that a mis-reading shows up, and so at least fifteen readings in total. Alongside, the case for a pilot run: set the apparatus up at the smallest and largest values you plan and take a reading at each, which tells you whether the dependent variable changes enough to measure, whether the apparatus works at all, and how long one reading takes. — Five points spread across the full range beat fifteen points bunched together. The gradient is what most experiments are really measuring, and a narrow range leaves it almost undetermined.

rangeas wide as the apparatus and the physics allow

valuesat least 5, and 8 or more if a reading is quick

repeatsat least 3 at each value, so an anomaly can be spotted

A pilot run costs one afternoon and routinely saves several. Set the apparatus up at the extremes of your intended range and take one reading at each. It answers three questions at once: does the dependent variable change enough over that range to be worth measuring, does the apparatus work at all, and how long does one reading take — which is what decides how many you can realistically collect.

🔧Controlling what you cannot eliminate

Some problems are inherent to the apparatus rather than to your technique. Each of the four below has a standard fix, and each fix is a design decision — made before any real data exists, so that the problem never has to be apologised for later.

Four standard fixes. For kinematics, a runway tilted so that it descends slightly, with a trolley running down it at constant velocity: the angle is adjusted until the component of weight down the slope exactly equals friction, so that from then on any acceleration measured is caused by the applied force alone. For thermal experiments, lag the container and use a lid, and start as far below room temperature as you finish above it so the heat gained early cancels the heat lost late. For circuits, remember that leads, contacts, the ammeter and the supply all have resistance, and that a current warms a wire which changes its resistance. For radioactivity, take a background count with the source removed and subtract it from every measurement. A fifth panel covers calibration: check an instrument if a reading looks wrong, if it has been dropped, repaired or moved, if a long time has passed, or if conditions have changed. — The tilted runway is the neatest of the four. Friction has not been removed — it has been exactly cancelled by a component of the trolley's own weight, so the apparatus behaves as if it were frictionless.

Calibration means checking an instrument against one whose reading is trusted. It is worth doing when a reading looks wrong, when the instrument has been dropped, repaired, modified or moved, when a long time has passed since the last check, or when conditions have changed. The quickest version in a school laboratory is simply to swap the instrument for an identical one and re-measure — if the two disagree, at least one of them needs attention.

✏️Worked example 2 — designing an investigation end to end

Design an investigation into how the resistance of a length of nichrome wire depends on its length. State the variables, the range and repeats, and two problems you would design out.

Variables.

independentlength of wire, from 0.10 m to 1.00 m in 0.10 m steps — ten values

dependentresistance, found from \( R = V/I \), three repeats at each length

controlthe material — use one reel throughout

controlthe diameter — measure with a micrometer at several points to confirm it

controlthe temperature — keep the current low, and switch off between readings

Why that range. Ten values across a factor of ten in length: wide enough that the resistance changes by a factor of ten too, so the gradient is well determined. A pilot at 0.10 m and 1.00 m confirms that both ends give a measurable current at the supply voltage available.

Two problems designed out.

Heating. A current warms the wire and warming changes its resistance, which would make the resistance depend on how long the current has been flowing rather than only on length. Fix: use the smallest current that still gives a readable meter deflection, and switch off between readings.

Lead and contact resistance. The leads and the crocodile clips have a resistance of their own, which adds to every reading equally — a systematic error. Fix: measure the resistance with the clips touching (zero length of wire) and subtract that from every result.

What this buys you. That second fix has a bonus: the lead resistance would otherwise appear as a non-zero intercept on a graph of \(R\) against \(l\). So if you plot the raw data and find an intercept you did not expect, you have just measured your own lead resistance — which is a far better thing to write in an evaluation than “there may have been systematic errors”.

The trap: designing an investigation whose answer you already know exactly. Measuring \(g\) with a pendulum is a fine exercise, but the interesting version asks something the textbook does not simply hand back — how the period depends on amplitude, say, where the small-angle approximation starts to fail. An investigation is judged partly on the thinking that went into the design, and a question with a known answer leaves nowhere for that to show.

📝Practise

Work through these, then reveal the answer. Each question targets a different objective from the list above.

1. Explain why “How does temperature affect a resistor?” is not yet a usable research question, and rewrite it.

It does not say what will be measured, over what range, or under what conditions — “affect” could mean resistance, power dissipated, physical size or lifetime, and no range is given, so there is no way to know when the investigation is finished.
A usable version: “How does the resistance of a thermistor depend on its temperature, between 20 °C and 80 °C?” That names the independent variable (temperature), the dependent variable (resistance) and the range, and so already implies the apparatus and the method.

2. Distinguish a hypothesis from a prediction, and give an example of each for a pendulum investigation.

A hypothesis is a proposed explanation for something; a prediction is what that explanation says will be observed, stated in a form that could turn out to be wrong.
Hypothesis: the period of a pendulum is set by the restoring force from gravity acting on the bob, and so should depend on the length of the string but not on the mass.
Prediction: a graph of \( T^{2} \) against \(l\) will be a straight line through the origin with gradient \( 4\pi^{2}/g \), and changing the mass of the bob will not change \(T\).
The prediction is the more useful, because it says exactly what to plot and what would count as disagreement.

3. For an investigation into how the current through a filament lamp depends on the potential difference across it, identify the independent, dependent and at least two control variables.

Independent: the potential difference across the lamp, varied with a variable resistor or a variable supply.
Dependent: the current through the lamp, read from an ammeter in series.
Control: the lamp itself — the same one throughout, since filaments differ; the ambient temperature and airflow, since cooling affects the filament's temperature and therefore its resistance; and the time the lamp is left on at each setting, since it takes a moment to reach a steady temperature.
That last one is easy to miss and matters here: this experiment is really about a resistance that changes with temperature, so anything affecting temperature is a control variable.

4. A student takes five readings, all between 4.0 cm and 4.4 cm of extension. Explain what is wrong with this design and what it does to the conclusion.

The range is far too narrow. All five points crowd into one small region of the graph, so many quite different straight lines pass plausibly through them — the gradient is barely determined at all, and the gradient is usually the quantity the experiment exists to find.
It also makes it impossible to tell whether the relationship is linear: over a short enough stretch, almost any smooth curve looks straight. The conclusion would therefore be unable to support either a value for the spring constant or a claim that Hooke's law holds.
The fix is to extend the range as far as the apparatus safely allows — here, up to just below the elastic limit — rather than to add more points inside the same narrow band.

5. State three things a pilot run tells you, and explain why each changes the design.

Whether the dependent variable changes measurably over your intended range. If it barely moves between the extremes, the range must be widened or the whole approach reconsidered before you waste an afternoon.
Whether the apparatus works as expected. Meters that will not read, a supply that cannot deliver enough current, a timer that will not trigger — all far cheaper to find at the start.
How long a single reading takes. That sets how many values and repeats are realistic. If one reading takes ten minutes, ten values with three repeats each is five hours of work, and the design has to be scaled to fit the time available.

6. Explain how tilting a runway lets you investigate the effect of a force on a trolley without friction spoiling the result.

Raise one end of the runway slightly and give the trolley a push. Adjust the angle until the trolley continues at constant velocity after the push — no acceleration and no slowing down.
At that angle, the component of the trolley's weight acting down the slope is exactly equal in magnitude to the frictional force opposing its motion, so the resultant force on the moving trolley is zero. Friction has not been removed; it has been precisely cancelled.
From then on, any acceleration you measure must be caused by whatever additional force you apply, which is what the experiment set out to investigate. If the trolley speeds up on its own the slope is too steep; if it slows down, too shallow.

7. In a thermal experiment, explain the advantage of starting as far below room temperature as you finish above it.

Energy always flows from hotter to colder, so while the apparatus is below room temperature it gains unwanted energy from the surroundings, and while it is above room temperature it loses energy to them. These are systematic errors that act in opposite directions.
By arranging the experiment to start as far below room temperature as it finishes above, the energy gained during the first half roughly cancels the energy lost during the second, so the two errors largely offset instead of accumulating.
It is a partial fix rather than a perfect one — the rate of transfer depends on the temperature difference and on how long each phase lasts — and it is used alongside insulation and a lid, not instead of them.

8. State when an instrument should be calibrated, and describe the quickest practical check available in a school laboratory.

Calibrate when: a reading looks wrong or disagrees with expectation; the instrument has been dropped, repaired, modified or moved; a long time has passed since the last calibration; or the conditions it is used in have changed.
The quickest practical check is to compare it against a second, identical instrument measuring the same thing, or against a known standard — a thermometer in melting ice should read 0 °C, a balance with a standard mass should read that mass, an ammeter in series with another ammeter should agree with it. Any disagreement tells you at least one of them needs attention, even if it does not immediately tell you which.

9. Explain why the resistance of the leads is a systematic error in a wire-resistance experiment, and how the design can remove it.

The leads and their contacts have a small resistance of their own, in series with the wire. Every measurement therefore includes that same extra amount, so all readings are shifted upward by a constant — the definition of a systematic error. Repeating and averaging cannot help, because every repeat contains it equally.
The fix is to measure it: connect the crocodile clips directly together, so the length of wire between them is zero, and record the resistance. That is the lead resistance, and subtracting it from every reading corrects the whole data set.
Equivalently, plot \(R\) against \(l\) and use the gradient rather than individual values — a constant offset shifts the intercept but leaves the gradient untouched, which is one of the reasons graphs are preferred to single readings.

10. A student proposes measuring background radiation once, at the start of a two-hour experiment. Explain why a longer background count is better, and where in the analysis it is used.

Radioactive decay is a random process, so a background count taken over a short interval is itself subject to large random fluctuation — counting for ten seconds might give 3 counts one time and 8 the next, and neither is a reliable estimate of the true rate. Counting for a long time, comparable with the duration of the real readings, averages that fluctuation down and gives a much better estimate of the background rate.
It is used at the very start of the analysis: the background rate is subtracted from every measured count rate before anything else is done with the numbers — before halving for half-lives, before plotting, before taking logs. Subtracting it later, or forgetting it, biases every result upward by the same amount, and it is a systematic error that no amount of repetition will reveal.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

The IB Physics guide internal assessment criteria — what the design work is actually marked against
Royal Society of Chemistry — risk assessment guidance, which transfers directly to physics practicals