Planning: choosing the apparatus, its range and its resolution

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This unit is A Level (IA2) content, and it assumes everything from the AS practical unit (WPH13): resolution, half range, percentage uncertainty, plotting a straight line and finding its gradient.

It is the whole of the Unit 6 paper, WPH16, Practical Skills in Physics II: 1 hour 20 minutes, 50 marks, exactly four questions, no multiple choice, with a calculator and a ruler.

Each question follows one experiment from start to finish.

About two thirds of the marks in recent papers used Unit 4 and Unit 5 physics (capacitors, gases, oscillations, absorption) and one third used Unit 1 and Unit 2 physics (density, viscosity, springs, circuits), so you need the techniques of all sixteen core practicals.

This first section starts where every plan starts: choosing the apparatus.

How WPH16 marks work

Each marking point is one mark, written "(1)" on its own line. Schemes call them MP1, MP2 and so on; there are no M1, A1 or B1 codes, no asterisked question and no levels.

Many marks are dependent: "MP2 dependent on MP1" means a reason scores only if the technique or expansion before it is right.

Errors carry forward (ecf): a wrong mean used correctly later still earns the later marks, so always finish.

The scheme states the figures it wants, item by item: a mean to the same decimal places as the data ("only"), a percentage uncertainty to 1 or 2 s.f. with a % sign, processed log values to 3 d.p., a gradient or constant to 2 or 3 s.f., a show-that to at least one more s.f. than printed.

Answer lines print the quantity without its unit ("Mean value of d = ....."): the unit is yours to write, and a missing unit loses the final mark.

Where two reasons are asked for, a wrong extra answer can cancel a right one.

On the list and learn it (Unit 6)

On the list at the back of WPH16: the full list of data, formulae and relationships for Units 1, 2, 4 and 5 (for example $\tfrac{1}{2}CV^2$ , $pV = NkT$ , $P = IV$ , $T = 2\pi\sqrt{m/k}$ , $V = V_0e^{-t/RC}$ ) with constants such as $g = 9.81\ \text{m s}^{-2}$ , $k$ and $e$ .

Printed in the question: any unfamiliar working formula (a flow formula, a rolling-sphere formula), the model to be linearised, and every measurement with its uncertainty.

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 three compounding rules; the log laws $\log(ab) = \log a + \log b$ , $\log a^n = n\log a$ , $\ln e^x = x$ ; volume of a sphere $\tfrac{4}{3}\pi r^3$ (radius, not diameter); areas of a circle, semicircle and rectangle; $0\ ^\circ\text{C} = 273\ \text{K}$ ; $\tau = RC$ ; resolutions of a metre rule (1 mm), vernier calipers (0.1 mm) and a micrometer (0.01 mm).

The idea: apparatus is chosen by the quantity, not by habit

A planning question gives you a goal ("determine the spring constant", "test whether $T = am^b$ ") and asks what you would use.

The quickest route is to work back from the equation: list every quantity in it, and for each decide how it is measured.

Each measured quantity needs an instrument, and each instrument needs two numbers you can state: its range (the largest value it can read) and its resolution (the smallest step it shows).

The skill is to identify the most appropriate apparatus, giving details.

These may include the range and resolution of instruments and/or relevant dimensions of apparatus (e.g. the length of string used for a pendulum).

"Giving details" is where the marks are: "a ruler" earns little, "a metre rule with a resolution of 1 mm, clamped vertically" earns a mark.

Range and resolution together

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

A useful test is the percentage uncertainty from half the resolution: if it is around 1% or less, the instrument is suitable.

Instrument

Resolution

Half resolution (single reading)

Suits

metre rule or half-metre rule

1 mm

0.5 mm

lengths from about 10 cm to 1 m

vernier calipers

0.1 mm

0.05 mm

external and internal diameters, 5 mm to 150 mm

micrometer screw gauge

0.01 mm

0.005 mm

wire diameters and sheet thicknesses up to 25 mm

top-pan balance

0.01 g or 0.1 g

0.005 g or 0.05 g

masses from a few grams

digital stopwatch

0.01 s

(reaction time dominates)

times of several seconds

light gate with timer or data logger

0.001 s or better

0.0005 s

short times and speeds

digital thermometer

0.1 °C

0.05 °C

temperatures of liquids

protractor

1°

0.5°

angles above about 20°

Some vernier calipers read to 0.05 mm or 0.02 mm, and digital calipers to 0.01 mm: quote the resolution of the instrument you name.

A multimeter's resolution depends on its range: on the 2 A range it may read to 0.001 A, on the 20 A range only to 0.01 A. Choose the lowest range that still covers the largest value you expect.

Relevant dimensions

Some details are not instruments at all but sizes of apparatus.

A pendulum string should be long enough to give a period of a second or more, so a hand timing is not swamped by reaction time.

A falling-ball tube must be long enough for the ball to reach terminal velocity before the first marker.

A capacitor and resistor must give a time constant long enough to read a voltmeter by hand, or the plan needs a data logger.

Giving the size, with a reason, is a creditable detail.

Connections

This builds on WPH13, where the same instruments were met in short items.

At A Level the same choices reappear inside 6-mark plans (see "Using the data: the six-point plan") and in "explain why the micrometer is suitable" items with a calculation.

The instrument table returns in the uncertainty sections, where half the resolution becomes a number you compound.

The examiners' general advice on all three recent papers was the same: learn the guidance on uncertainties and the command words, revise WPH13, and handle vernier calipers and micrometers until reading them is routine.

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: is the micrometer suitable?

A student measures the thickness of a sheet of card, which is about 0.42 mm.

Explain why a micrometer screw gauge is suitable for this measurement.

Your answer should include a calculation.

(2)

1. The resolution of a micrometer is 0.01 mm, so the uncertainty in one reading is 0.005 mm (1) resolution with its unit, or half of it as the uncertainty

2. Percentage uncertainty $= \dfrac{0.005}{0.42} \times 100\% = 1.2\%$ , which is small (1) calculation and conclusion

Answer: 1.2%, so the micrometer is suitable.

For contrast, a metre rule's 0.5 mm would be more than the thickness itself.

The word is resolution: "precision" or "accuracy" in its place does not score.

Worked example 2: a relevant dimension

A student plans to use a simple pendulum whose period is about 2.0 s, so that timing by hand is reliable.

The equation $T = 2\pi\sqrt{l/g}$ is on the list.

Determine the length of string needed and identify the instrument to measure it.

(3)

1. $l = \dfrac{gT^2}{4\pi^2}$ (1) rearrangement

2. $l = \dfrac{9.81 \times 2.0^2}{4\pi^2} = 0.994\ \text{m}$ (1) answer with unit

3. A metre rule (resolution 1 mm), measuring from the point of suspension to the centre of the bob, with the bob's diameter found with vernier calipers and halved (1)

Answer: about 0.99 m.

The length of a pendulum is to the centre of mass of the bob, so the bob's radius is part of the measurement.

Worked example 3: choosing a meter range

A student expects a current of about 0.35 A. A digital ammeter has a 2 A range reading to 0.01 A and a 20 A range reading to 0.1 A. Explain which range the student should use.

(2)

1. On the 2 A range the uncertainty is 0.005 A, so $\dfrac{0.005}{0.35} \times 100\% = 1.4\%$ ; on the 20 A range it is 0.05 A, so 14% (1) both percentages

2. Use the 2 A range: it covers 0.35 A and gives the smaller percentage uncertainty (1) conclusion

Answer: the 2 A range.

Always choose the most sensitive range that still covers the largest value expected.

A mass hanger on a vertical spring hanging from a clamp stand, with a pin clamped beside it at the rest position as a timing marker and a stopwatch on the bench

Worked example 4: the six-point plan for Core Practical 16

The photograph above shows apparatus for CP16, which determines an unknown mass from the period of a mass on a spring, $T = 2\pi\sqrt{m/k}$ (on the list).

The spring constant is about 25 N m⁻¹.

Devise a method to determine the mass of an unlabelled object.

Your method should include the use of a suitable graph.

(6)

1. Add known slotted masses $m$ from 0.100 kg to 0.600 kg, checking each total on a top-pan balance (resolution 0.01 g) (1) independent variable with a named instrument

2. Displace the mass slightly and release; use a fixed pin at the rest position as a marker and time 20 oscillations with a stopwatch, then divide by 20 (1) dependent variable with a named technique

3. Use the same spring throughout and keep the displacement small, so the motion stays simple harmonic (1) control variable

4. Record $T$ for each value of $m$ (1)

5. Use at least 5 different masses (here six, in 0.100 kg steps) (1) number of values

6. Plot $T^2$ against $m$ : a straight line through the origin; time the unknown object in the same way and read its mass from its $T^2$ on the graph (1) graph and how the answer is read from it

Answer: as above, six independent marks.

With $k = 25\ \text{N m}^{-1}$ the periods run from 0.40 s to 0.97 s, so timing 20 oscillations gives totals of 8 s to 19 s, long enough to time by hand.

Exam tip

When an item asks for "details", attach a number or a property to every instrument you name: its resolution, its range, or the size that matters ("a pendulum about 1 m long").

In a suitability item, write the resolution with its unit, halve it, calculate the percentage and call it small or large: that is both marks.

Common mistakes

"Precision" or "accuracy" for resolution. Examiners refuse both. Resolution is the smallest interval the instrument shows; learn the word.

No unit on the resolution. "The resolution is 0.01" is incomplete: write 0.01 mm.

A micrometer for an internal diameter. Its jaws only close on the outside of an object. An internal diameter needs vernier calipers (the inside jaws), and the plan should say "internal".

A stopwatch for a fraction of a second. The display reads 0.01 s, but your reaction time (about 0.2 s) is the real limit. Time many oscillations, or use a light gate with a timer.

Generic lists. "Ruler, stopwatch, masses" ignores the set-up in the question. Name the instrument for each quantity in this experiment.

Check your understanding

1. A student needs the internal diameter of a glass tube, which is about 18 mm. Explain why vernier calipers are more suitable than a micrometer screw gauge for this measurement. (2) Total [2]

2. The diameter of a copper wire is about 0.38 mm.
(a) Show that the percentage uncertainty in a single micrometer reading of this diameter is about 1.3%. (2)
(b) Explain whether vernier calipers with a resolution of 0.1 mm would be suitable for this measurement. Your answer should include a calculation. (2) Total [4]

3. A student times one swing of a pendulum with a stopwatch that reads to 0.01 s and says that the uncertainty in the time is therefore 0.005 s. Explain why the student is wrong. (2) Total [2]

4. A student investigates ripples on shallow water in a tray. For shallow water the speed $v$ of the ripples is given by $v = \sqrt{gd}$ , where $d$ is the depth of the water, which is about 12.0 mm.
(a) Determine the speed of the ripples. (2)
(b) The student measures $d$ with the depth rod of a pair of vernier calipers of resolution 0.1 mm. Determine the percentage uncertainty in $d$ . (2) Total [4]

5. A student wants to determine the resistivity of a metal wire. Devise a method to determine the resistivity. Your method should include the use of a suitable graph. (6) Total [6]

Answers

1. The micrometer's jaws only measure an external size, so it cannot reach across the inside of the tube (1); vernier calipers have internal jaws, and 18 mm is within their range with a resolution of 0.1 mm (1).

2. (a) Uncertainty $=$ half of 0.01 mm $= 0.005$ mm (1); $\dfrac{0.005}{0.38} \times 100\% = 1.32\%$ (1), which is about 1.3%. (b) Uncertainty 0.05 mm, so $\dfrac{0.05}{0.38} \times 100\% = 13\%$ (1); this is large, so vernier calipers are not suitable (1).

3. The uncertainty in a hand timing comes from the reaction time at the start and the stop, about 0.2 s or more, not from the display's resolution (1); this is a large fraction of one swing, so the student should time many swings and divide (1).

4. (a) $v = \sqrt{9.81 \times 0.0120}$ (1) $= 0.343\ \text{m s}^{-1}$ (1). (b) Uncertainty $= 0.05$ mm (1); $\dfrac{0.05}{12.0} \times 100\% = 0.42\%$ (1).

5. Any six, one mark each: measure the diameter with a micrometer at several places along the wire and in two perpendicular directions, and find the mean (1); measure the length between two crocodile clips with a metre rule (1); keep the temperature constant by using a small current and switching off between readings (1); measure the resistance for each length with an ammeter in series and a voltmeter across the wire, $R = V/I$ (1); use at least 5 different lengths, for example 0.200 m to 0.900 m (1); plot $R$ against $l$ : the gradient is $\rho/A$ , so $\rho = \text{gradient} \times A$ with $A = \pi d^2/4$ (1).

Planning: choosing the apparatus, its range and its resolution

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