Pearson Edexcel International A Level Physics: Unit 6: planning and evaluating experiments (YPH11)

This study guide is aligned to the Pearson Edexcel International Advanced Subsidiary/Advanced Level Physics specification (YPH11), Issue 3. It covers section 6.3 Planning and section 6.4 Implementation and Measurements, plus the unit description’s call for experience of log graphs. Unit 6 belongs to IA2, the second year. It assesses the experimental procedures and techniques you meet while doing the Unit 4 and Unit 5 experiments. Section 6.5 Analysis is outside this page.

The specification gives the paper as 1 hour 20 minutes and 50 marks, with at least 20 marks for mathematics at Level 2 or above. It says calculators may be used.

Links: course hub, printable checklist, revision notes, practice questions and the free diagnostics. For the experiments themselves see oscillations and thermodynamics.

What this unit covers

Section	What you must be able to do
6.3 Planning	Plan an experiment set by Pearson. You do not carry it out.
6.4 Implementation and Measurements	Judge a partly described experiment, which may include results.
Unit description	Use log graphs to find the relationship between two variables.

6.3 Planning

The experiment is set by Pearson, so it may be new to you. The specification lists seven things you are assessed on. Cover each one, in that order, and tie every point to the experiment in front of you.

Apparatus, range and resolution

Name the instrument and give its range and resolution. Give relevant dimensions too. Then show the choice is sensible.

Resolution is the smallest change an instrument can show. A metre rule reads to 1 mm. A micrometer reads to 0.01 mm. A digital stopwatch reads to 0.01 s, but your reaction time is about 0.2 s, and that is the real limit on a hand-timed reading.

Check by percentage: percentage uncertainty = (uncertainty / reading) × 100. A 1 mm uncertainty on a 0.250 m length is 0.4%. The same 1 mm on a 20 mm length is 5%, so a ruler is a poor choice there.

Calibration

Calibration means checking an instrument against a known value. The specification gives the example of whether a meter reads zero before measurements are made. A zero error is subtracted from every reading. Other checks:

• Close a micrometer fully and note the reading.
• Put a thermometer in melting ice and see whether it reads 0 °C.
• Check a balance reads zero with nothing on it.

Measuring the variables

Say what you measure, with which instrument, and how.

• Time many oscillations, not one. Twenty periods timed with a 0.2 s reaction error give about 1% uncertainty. One period of 1 s gives about 20%.
• Start and stop at the equilibrium position, where the object moves fastest. A fiducial marker, such as a pin or a taped card, makes the start point exact.
• Measure a length from the right place. A pendulum length runs from the pivot to the centre of the bob.
• Read scales at eye level. Use a set square or plumb line for vertical heights.

Controlling other variables

A fair test changes one variable and keeps the rest fixed. List them and say how each is held. For a pendulum these include the mass of the bob, the amplitude (kept under about 10°), the fixed pivot and the location. Say “same mass of 100 g bob”, not “keep the mass the same”.

Repeat readings

Repeats help when there is random scatter, such as hand timing. Repeat each setting, then average. Compare repeats to spot an outlier. Repeats do not remove a systematic error, such as a zero error.

Repeats are sometimes unnecessary. A reading from a calibrated digital meter that does not fluctuate may need no repeat. Say why.

Health and safety

Be specific to the apparatus. Name the hazard, the harm and the precaution.

• Hot water can scald. Use a lid, carry small volumes and clamp the beaker.
• A falling mass can hurt feet. Place a sand tray beneath it and keep your feet clear.
• A stretched wire can snap. Wear eye protection.
• A tall stand can topple. Clamp it to the bench.

Using the data

Say how the readings become a conclusion. Name the graph, the axes and the gradient or intercept you will use. Say what a straight line through the origin would show, and which constant you will calculate.

Worked example: planning a pendulum investigation

Task: investigate how the period T of a simple pendulum depends on its length L.

1. Apparatus. Use a metre rule (resolution 1 mm, range 1 m) and a stand, boss and clamp with two wooden blocks to hold the string. Use a 100 g brass bob on thin inextensible string. Use a digital stopwatch (0.01 s). Use lengths of 0.250 m to 1.000 m.
2. Calibration. Check the rule has an undamaged end. Measure from the pivot to the centre of the bob, not from the clamp top.
3. Measure. Pull the bob aside through an angle under 10°, release, and time 20 swings from the equilibrium position, using a marker. Divide by 20 to get T.
4. Control. Same bob, same pivot, same amplitude, same room.
5. Repeat. Time 20 swings twice per length. If the two times differ by more than about 0.3 s, take a third.
6. Safety. Clamp the stand to the bench. Keep the swing area clear.
7. Use the data. Plot T² against L. A straight line through the origin shows T² ∝ L. The gradient is 4π²/g, so g = 4π²/gradient.

6.4 Implementation and Measurements

Here you are given partial details of how an experiment was done, and sometimes results. Your job is to judge it.

Improving the experiment

Name a specific change and what error it cuts. The specification gives two examples: set squares to measure the diameter of a cylinder, and a marker for timing oscillations.

• Two set squares on a flat surface held against a cylinder make the ends of the diameter exact. A ruler held across the end does not.
• Use vernier callipers or a micrometer in place of a ruler for small diameters.
• Time more oscillations to reduce the reaction-time percentage.
• Use a data logger or light gate for fast events.
• Wait for thermal equilibrium before reading a temperature.

Number of readings

Too few readings hide scatter and make a line hard to judge. Aim for at least six well-spread points. Repeat each one, then average. A single reading at each setting cannot show whether a point is reliable.

Range of measurements

A narrow range makes the gradient poorly determined, and it cannot show whether a relationship holds outside that range. Lengths of 0.80 m to 0.90 m tell you little. Use as wide a range as the apparatus safely allows, with roughly even spacing. Compare 0.250 m to 1.000 m: a factor of four.

Significant figures

Rules to apply:

• Raw readings keep the resolution of the instrument. A 0.01 s stopwatch gives 20.06 s, never 20.1 s. Keep trailing zeros: a 1 mm rule gives 0.250 m, not 0.25 m.
• A calculated value has no more significant figures than the data it came from.
• Keep a consistent number of decimal places down a column of raw readings.

Units

Check each column heading, in the form quantity / unit, for dimensional sense. Length² is m², not m. Gradient units come from the axes. A spring constant is N m⁻¹. A heading of “k / N m” is wrong.

Inconsistent readings

A point off the line is not deleted. Check it: re-read the instrument, repeat the measurement, and compare it with the value the line predicts. If the repeat agrees with the line, the first reading was a mistake. If it still sits off the line, the relationship may really change there.

Worked example: correcting a table

A pendulum was timed with a 0.01 s stopwatch and a rule reading to 1 mm. The student’s table:

L / m	20T / s	T / s	T² / s²
0.25	20.06	1.003	1.006009
0.4	25.4	1.27	1.61
0.600	31.08	1.554	2.415
0.80	35.9	1.794	3.2184
1	40.12	2.006	4.024

The lab notes show the readings were 25.38 s and 35.88 s. Corrections:

• L: write 0.250, 0.400, 0.800 and 1.000, to the 1 mm resolution.
• 20T: restore 25.38 and 35.88.
• T: every time has 4 significant figures, so T has 4. The values are 1.003, 1.269, 1.554, 1.794 and 2.006.
• T²: 4 significant figures, so 1.006, 1.610, 2.415, 3.218 and 4.024. The trailing zero in 1.610 stays.

The gradient between the end points is (4.024 − 1.006)/(1.000 − 0.250) = 4.024 s² m⁻¹. So g = 4π²/4.024 = 9.81 m s⁻².

Log graphs

Straight-line graphs are easiest to judge. Taking logarithms turns a power law or an exponential into a straight line. The specification notes the graphs need not be for exponential relationships.

Relationship	Plot	Gradient	Intercept
y = kxⁿ	lg y against lg x	n	lg k
y = A e^(bx)	ln y against x	b	ln A

Derivation: lg y = lg k + n lg x. Compare with y = mx + c. Natural logs work equally well for the power law, and the gradient is still n. Only the intercept changes (ln k).

You cannot take a log of a quantity with a unit. Write the headings lg (V / cm³) and lg (p / kPa). The log columns have no units.

Worked example: pressure and volume of a gas

A fixed mass of air at constant temperature gives:

V / cm³	20.0	25.0	30.0	40.0	50.0	60.0
p / kPa	151	121	100.	76.0	60.5	50.4
lg (V / cm³)	1.30	1.40	1.48	1.60	1.70	1.78
lg (p / kPa)	2.18	2.08	2.00	1.88	1.78	1.70

Take two points far apart on the line: (1.30, 2.18) and (1.78, 1.70).

Gradient = (1.70 − 2.18)/(1.78 − 1.30) = −0.48/0.48 = −1.00.

So n = −1 and p ∝ V⁻¹, which is Boyle’s law. For the constant: lg k = 2.18 + 1.30 = 3.48, so k = 10^3.48 = 3.0 × 10³ kPa cm³. Check: 100 × 30.0 = 3000. The two methods agree.

Common errors

• Writing “use a ruler” with no range or resolution.
• Timing one oscillation instead of many.
• Saying “keep everything else constant” without naming the variables.
• Claiming repeats remove a zero error.
• Dropping a trailing zero, such as writing 1.61 for 1.610.
• Taking a log of a number with units attached.
• Throwing away an off-line point without checking it.

Official syllabus

Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (YPH11), Issue 3, Unit 6: Practical Skills in Physics II, sections 6.1 (log graphs), 6.3 and 6.4. Publisher: Pearson Education Limited.