Planning an experiment: identifying the apparatus

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This unit is the whole of the Unit 3 paper, WPH13, Practical Skills in Physics I. It is a written paper of 1 hour 20 minutes and 50 marks, with exactly four questions and no multiple choice, and you need a calculator and a ruler.

Every question is built on an experiment from Units 1 and 2, often a changed version of one of the eight core practicals (CP1 to CP8), so the physics comes from those units and the marks come from how you plan, measure, record and process.

This first section starts where every plan starts: deciding what apparatus the experiment needs.

The idea: an experiment is a question with instruments attached

Every Unit 3 experiment either asks how one quantity depends on another ("how does the terminal velocity of a ball depend on its radius?")

or uses a known relationship to find a constant ("find the viscosity of the oil").

Either way, the physics tells you which quantities appear, and each quantity needs a way of being measured.

Planning is turning an equation into a shopping list.

The most reliable way to build that list is to work back from the equation.

Write the relationship the experiment rests on, circle every quantity in it, and for each one decide: is it measured, calculated from other measurements, or already known?

Every measured quantity gets an instrument, and every instrument gets a resolution you can state.

The planning question is set by the examiners and you will not carry it out.

In practice WPH13 does not ask for one long plan: it asks for planning in short pieces of 2 to 4 marks, such as "describe how the student should measure ...", "include the use of any additional apparatus", or "identify a hazard".

Each piece rewards a named instrument used in a named way.

Working back from an equation: the falling-ball viscometer

Core Practical 2 finds the viscosity $\eta$ of a liquid from a ball falling at its terminal velocity.

At terminal velocity the forces balance, and with Stokes' law ( $F = 6\pi\eta rv$ , on the list) this gives

\eta = \frac{2r^2g(\rho_{\text{ball}} - \rho_{\text{liquid}})}{9v}

Each quantity points to apparatus:

Quantity

How it is found

Apparatus (typical resolution)

radius $r$

half the measured diameter

micrometer screw gauge (0.01 mm)

terminal velocity $v$

distance between two marks divided by the time

metre rule (1 mm), two rubber bands as markers, stopwatch (0.01 s)

$\rho_{\text{ball}}$

mass and volume of the ball

top-pan balance (0.01 g); volume from the diameter

$\rho_{\text{liquid}}$

mass and volume of a sample

balance and measuring cylinder

$g$

known

$9.81\ \text{m s}^{-2}$ , from the list

Two further items come from the method, not from the equation: a long, wide tube of liquid (so the ball reaches terminal velocity before the first mark and is not slowed by the walls) and a magnet to retrieve the steel balls.

Questions often say "include the use of any additional apparatus": that is an invitation to name exactly these extras.

Matching the instrument to the size of the quantity

An instrument is only right if its range covers the quantity and its resolution is small compared with it.

A metre rule is fine for 0.300 m between two markers, but useless for a 2 mm ball, where a micrometer is needed.

Timing is the same story: a stopwatch is fine for a 5 s fall through oil, but for a fall lasting a fraction of a second, human reaction time (typically about 0.2 s) is comparable with the time itself, so the plan needs light gates or a trapdoor and electromagnet connected to an electronic timer.

Connections

The apparatus choices here return in every later section: the micrometer and vernier calipers in the next section, technique in "Measuring techniques", and safety in its own section.

In the Unit 6 paper (WPH16), planning becomes a full 6-mark plan, so the habit of working back from an equation pays twice.

How WPH13 is marked

Every marking point is worth one mark, written "(1)", one fact or step per line. There are no letter codes.

Many second marks are dependent: "this reduces random error" scores only if the technique before it is correct.

When the scheme lists more points than marks, it caps them ("Max 3"). Wrong extra points can cancel right ones: a right answer and a wrong answer to the same point score zero.

Errors carry forward (ecf): a wrong mean, used correctly in a later percentage uncertainty, still earns the later marks.

Significant figures and units are marks of their own: means and processed values to 3 s.f., a constant from a graph to 2 or 3 s.f. with its unit.

A "show that" needs every step and a final value with more significant figures than the printed one; the printed value alone scores 0.

On the list and learn it (Unit 3)

On the list at the end of WPH13: the Unit 1 and Unit 2 equations (motion, forces, energy, power, density, Stokes' law, Hooke's law, Young modulus, waves, refraction, grating, photons, electricity) and seven constants, including $g = 9.81\ \text{m s}^{-2}$ and $9.81\ \text{N kg}^{-1}$ .

Learn it: not on the list: the mean; half the resolution; half the range; percentage uncertainty $= \dfrac{\text{uncertainty}}{\text{value}} \times 100\%$ ; percentage difference; the area of a circle $\pi d^2/4$ ; the volumes of a cylinder, a sphere ( $\tfrac{4}{3}\pi r^3$ ) and a triangular prism; Pythagoras and the cosine rule; $y = mx + c$ ; speed $=$ distance $\div$ time, doubled distance for an echo.

Key terms

Validity: A measurement is valid if it measures what it is supposed to be measuring – this depends both on the method and the instruments.

Resolution: The smallest measuring interval and the source of uncertainty in a single reading.

Worked example 1: apparatus from an equation

A student plans to find the refractive index $n$ of a glass block using $n = \dfrac{\sin i}{\sin r}$ , where $i$ and $r$ are the angles in air and in glass.

Describe the apparatus the student needs and what each item is for.

(3)

1. A ray box (or laser with a slit) to produce a narrow ray of light aimed at the block (1)

2. A protractor to measure $i$ and $r$ from a normal drawn at the point of incidence (1)

3. Paper, a sharp pencil and a ruler to trace the block's outline and the ray on both sides, so $r$ can be drawn in by joining the entry and exit points (1)

Answer: as above.

Each item is tied to the quantity it measures; a bare list ("ray box, protractor, block") earns less, because the scheme wants the purpose.

Worked example 2: is a stopwatch good enough?

A student wants to time a steel ball falling 0.50 m from rest.

Determine the time of fall and explain whether a hand-operated stopwatch is suitable.

(4)

1. $s = ut + \tfrac{1}{2}at^2$ with $u = 0$ , so $t = \sqrt{\dfrac{2s}{g}}$ (1) use of a suvat equation

2. $t = \sqrt{\dfrac{2 \times 0.50}{9.81}} = 0.32$ s (1)

3. A reaction time of about 0.2 s at each end is comparable with 0.32 s (1)

4. So the uncertainty would be a large fraction of the time: use a trapdoor and electromagnet with an electronic timer, or light gates (1)

Answer: about 0.32 s; a stopwatch is not suitable.

The calculation is what makes the judgement convincing: it shows the reaction time is more than half the quantity measured.

Worked example 3: the extra apparatus

For the falling-ball viscometer above, describe two items of additional apparatus, other than the instruments in the table, and explain why each is needed.

(2)

1. A tube long enough for the ball to reach terminal velocity above the first marker, with markers placed well below the surface (1)

2. A magnet to remove the steel balls from the bottom of the tube so the liquid need not be emptied, keeping its temperature and depth the same between runs (1)

Answer: as above.

A thermometer is also creditable: viscosity is temperature dependent, so the liquid's temperature must be checked to stay constant.

Exam tip

When a stem says "include the use of any additional apparatus", the marks are on the extra items and what each one does.

Name the instrument, say what it measures, and give a reason linked to this set-up (a set square to check the rule is vertical, a sand tray to mark where a ball lands).

Common mistakes

Listing apparatus with no purpose. "Ruler, stopwatch, ball" earns little. Pair each item with the quantity it measures and how.

Choosing a stopwatch for very short times. It is tempting because a stopwatch shows 0.01 s, but its display is not the limit: your reaction time is. For times under about a second, use light gates or an electronic timer.

Giving a generic plan. Examiners report that pre-learned answers which ignore the set-up in the question lose marks. Read the diagram first and plan for that apparatus.

Forgetting quantities that are "obviously" fixed. If a quantity appears in the equation (a density, a temperature), the plan must say how it is found or kept constant.

Check your understanding

1. A student uses a falling-ball viscometer with a glass tube of oil. State one reason why the tube should be wide compared with the ball. (1) Total [1]

2. A student plans to time a ball dropped from rest. The ball is released from the 1.450 m mark on a vertical metre rule and lands on a trapdoor level with the 0.250 m mark.
(a) Show that the time of fall is about 0.5 s. (4)
(b) Explain why an electromagnet and trapdoor connected to an electronic timer is more suitable than a stopwatch for this measurement. (2) Total [6]

3. A student says: "The more expensive the measuring instrument, the better the experiment." Explain whether the student is correct, using the measurement of the length of a 1.5 m pendulum as an example. (2) Total [2]

4. A student plans to determine the density of an irregularly shaped stone that will not fit into a measuring cylinder. Describe how the student could determine the density. You should include the use of any additional apparatus. (3) Total [3]

5. A student plans to find the spring constant of a spring by hanging masses from it. Describe the apparatus needed to measure the extension and the force, and how each item is used. (3) Total [3]

Answers

1. Near the walls the liquid is slowed, so a narrow tube increases the drag and the ball's speed is no longer given by Stokes' law for an unbounded liquid (or: the ball is less likely to touch the wall) (1).

2. (a) Distance fallen $s = 1.450 - 0.250 = 1.200$ m (1); $s = \tfrac{1}{2}gt^2$ , so $t = \sqrt{2s/g}$ (1); $t = \sqrt{2 \times 1.200 / 9.81}$ (1); $t = 0.495$ s (1), which is about 0.5 s. A final value of "0.5 s" alone does not earn the last mark. (b) Reaction time is about 0.2 s, a large fraction of 0.5 s (1); the electronic timer starts and stops automatically when the ball is released and hits the trapdoor, so there is no reaction time in the measurement (1).

3. Not correct (1 for a conclusion with a reason): the instrument must suit the quantity. A 1.5 m length needs a metre rule or tape measure (range); a micrometer is more expensive and has a finer resolution but cannot measure 1.5 m, and a resolution of 1 mm already gives a small percentage uncertainty in 1.5 m (1).

4. Measure the mass with a top-pan balance (1). Fill a displacement (eureka) can to the spout, lower the stone in on a thread, and collect the displaced water in a measuring cylinder: this is the stone's volume (1). Density $=$ mass $\div$ volume (1).

5. Clamp a metre rule vertically beside the spring, checked with a set square, and fix a pointer to the bottom of the spring; read the pointer position before and after each load, so extension $=$ new reading $-$ original reading (1); read the pointer at eye level, or with a set square against the rule, to avoid parallax (1); the force is the weight of the slotted masses, $W = mg$ , with each mass checked on a top-pan balance (1).

Planning an experiment: identifying the apparatus

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