Before you start
This is the first practical in the IGCSE course. It builds the measuring skills you will use in every other experiment.
Key words
- Estimate: use the information you have to decide on a sensible, approximate value before you measure.
- Diameter: the length of a straight line from one side of a circle to the other, through its centre.
- Circumference: the distance around the outside of a circle.
- Precision: the smallest scale division on an instrument. A ruler marked in millimetres has a precision of 1 mm.
- Average (mean): add the readings together and divide by how many there are.
- Parallax error: a wrong reading caused by looking at a scale from an angle instead of straight on.
- Zero error: an instrument that does not read zero when it should, so every reading is wrong by the same amount.
Getting started: which instrument?
Fill in this table in your head before you begin (it is the first task in your practical book):
| Measurement | Equipment | Precision |
|---|---|---|
| length | metre ruler, 30 cm ruler, tape measure | 1 mm |
| volume | measuring cylinder | 1 cm³ (often) |
| mass | top-pan balance | 1 g or 0.1 g |
| time | stopwatch (digital) | 0.01 s |
| weight (a force) | newton scale (newton meter) | 0.1 N (often) |
Why estimate?
Physicists estimate all the time. An estimate tells you roughly what answer to expect, so you notice at once when a measurement is wrong: if your ruler says a student is 17 cm tall, or the stopwatch says ten star jumps took 1 s, something has gone wrong.
Use things you already know: a door is about 2 m high, your little finger is about 1 cm wide, 1 litre of water has a mass of 1 kg.
Skills you need
- Reading a scale to the nearest division, with your eye straight in line with it.
- Recording every reading of a quantity to the same number of decimal places, with the unit in the table heading.
- Calculating a mean of three readings.
- Converting units: 10 mm = 1 cm, 1000 g = 1 kg.
Aim and apparatus
Aim
To estimate, and then take accurate measurements of, length, mass and time using appropriate equipment, and to calculate average values.
Syllabus link: Cambridge IGCSE Physics 0625 / 0972, 1.1 Physical quantities and measurement techniques: describe the use of rulers and measuring cylinders to find a length or a volume; describe how to measure a variety of time intervals using clocks and digital timers; determine an average value for a small distance and for a short interval of time by measuring multiples (including the period of oscillation of a pendulum).
Practical book: Practical investigation 1.1, Estimating measurements.
Apparatus
- Metre ruler (two, fixed to the wall one above the other, 0 cm at the floor) and a set square
- Stopwatch
- Top-pan balance and a bag of sugar
- Newton scale
- 30 cm ruler, a glass block, a length of thin wire and a pencil
- For More to explore: a ream of 500 sheets of paper
Theory
Why take three readings?
No measurement is perfect. A student stands slightly differently each time; you start and stop a stopwatch a little late; a glass block is not exactly the same length everywhere. These random errors make repeated readings differ slightly.
Taking several readings and calculating the mean reduces the effect of random errors, and lets you spot a reading that does not fit (an anomaly).
Measuring something very small: multiples
A thin wire is about 0.5 mm thick, smaller than the 1 mm divisions of a ruler. So wind it tightly round a pencil, measure the length of the coil, and divide by the number of turns:
The ruler is still only read to ±1 mm, but that uncertainty is shared between all the turns: with 20 turns it becomes ±0.05 mm. The same trick gives the thickness of one sheet of paper: measure a stack of 500 and divide by 500.
Measuring a short time: multiples again
A digital stopwatch reads to 0.01 s, but your reaction time (about 0.2 s) when you start and stop it is far bigger than that. For one star jump lasting about 1 s, a 0.2 s error is 20%. For ten star jumps lasting about 10 s, the same error is only 2%.
So time many repeats and divide: ten star jumps, or twenty swings of a pendulum.
Reading scales correctly
- Parallax: look at the scale straight on, with your eye in line with the mark you are reading.
- Zero: line up the object with the zero mark of the ruler, not with its worn end (unless the zero is at the very end).
- Zero error: check that a balance reads zero with the pan empty; press Zero (tare) if it does not.
- Nearest division: read to the nearest millimetre on a ruler. If the edge is between two marks, record the nearer one.
Planning the investigation
What you will measure
| Quantity | Instrument | Technique |
|---|---|---|
| Height of a student | Metre rulers on the wall | Shoes off, back to the wall, set square flat on the head |
| Time for ten star jumps | Stopwatch | Start on “Go!”, stop as the tenth jump lands |
| Length, width, thickness of a glass block | 30 cm ruler | Zero at one edge; measure in three different places |
| Diameter of a wire | 30 cm ruler and a pencil | 20 turns round the pencil; coil length ÷ 20 |
| Mass of a bag of sugar | Top-pan balance | Zero with the pan empty, then weigh |
Recording data
Use a table like the one in your practical book, with the unit in each row heading:
Measurement type | Estimated value | Measured value 1, 2, 3 | Average measurement
Tip: record all measurements of a quantity to the same number of decimal places (or significant figures). A ruler that reads to 0.1 cm gives readings like 10.0 cm, not 10 cm.
Method in a real lab
- Look at everything you are going to measure. Estimate each value and record your estimates in the table before you measure anything.
- Height: the student takes off their shoes and stands with heels, back and head against the wall, looking straight ahead. Hold a set square flat on their head and against the wall, and read the metre rulers at its bottom edge, in cm to the nearest 0.1 cm. Ask them to step away and stand again for each reading.
- Ten star jumps: clear the area and check the jumper is wearing suitable shoes. Start the stopwatch as you say “Go!” and stop it as the tenth jump lands.
- Glass block: measure its length, width and thickness with a 30 cm ruler, each in three different places.
- Wire: wind the wire tightly round a pencil to make 20 turns with no gaps. Measure the length of the coil and divide by 20.
- Bag of sugar: zero the top-pan balance with the pan empty, then place the bag in the centre of the pan and read the mass in g.
- Take each measurement three times. Record everything in the table, with units.
- Calculate the average of each measurement, and the volume of the glass block.
How to use this virtual lab
- Choose what to measure at the top of the panel: Height, Star jumps, Glass block, Wire or Sugar. The view moves to it.
- Step 1, Estimate: type your estimate. There is a hint, but no answer: estimates are locked once you start measuring.
- Step 2, Choose: pick the instrument. You get feedback on every choice, and its precision.
- Step 3, Measure: set up the measurement with the buttons, read the scale in the magnifier and type the reading (to 0.1 cm for rulers). Keep your eye in line; Help me read it marks where to read. For the star jumps, press Start and Stop yourself: your own reaction time is part of the experiment!
- Step 4, Average: calculate the mean of your three readings yourself and press Check. You then see how close your estimate was. For the glass block, calculate its volume too.
- Table & graph: the full results table, as in your practical book, and a graph of how good each estimate was.
- More to explore: wind 10, 20 or 40 turns of wire and plot coil length against turns (the gradient is the diameter); measure a sheet of paper; time a single star jump; and see a zero error on the balance.
Results
Sample results
| Measurement | Estimate | 1 | 2 | 3 | Average |
|---|---|---|---|---|---|
| Height of a person / cm | 160 | 165.3 | 165.6 | 165.2 | 165.4 |
| Time for 10 star jumps / s | 8 | 9.62 | 9.41 | 9.55 | 9.53 |
| Glass block: length / cm | 12 | 10.0 | 10.1 | 10.0 | 10.0 |
| Glass block: width / cm | 6 | 6.5 | 6.5 | 6.4 | 6.5 |
| Glass block: thickness / cm | 2 | 1.8 | 1.9 | 1.8 | 1.8 |
| Diameter of the wire / mm | 1 | 0.60 | 0.55 | 0.60 | 0.58 |
| Mass of the bag of sugar / g | 1000 | 1006 | 1007 | 1006 | 1006 |
The wire readings come from coils of 1.2, 1.1 and 1.2 cm for 20 turns.
Volume of the glass block
For a cuboid, multiply the three averages:
The thickness is only known to 2 significant figures, so the volume should not be given to more than 2 or 3 significant figures: about 120 cm³ (or 117 cm³).
Analysis and conclusion
Comparing estimates with measurements
“My estimate of the student's height (160 cm) was within 4% of the measured value (165.4 cm), and the bag of sugar (1000 g) was within 1%: I knew these because they are familiar. My estimate of the wire diameter (1 mm) was nearly twice the measured value (0.58 mm): very small lengths are much harder to estimate.”
Use numbers from your own table, and say whether each estimate was too high or too low.
What the averages show
Repeated readings of the same quantity were close together (for example, 165.2 to 165.6 cm), so the measurements are reliable. The small spread comes from random errors: the student's posture, the stopwatch timing, the block not being perfectly rectangular, the gaps between the turns of wire.
Evaluation
| Measurement | Was the instrument suitable? | Precision | Improvement |
|---|---|---|---|
| Height | Yes: metre rulers are long enough and read to 1 mm | 1 mm | A height gauge with a sliding head piece, or a tape measure |
| Star jumps | Yes, but the reaction time (≈0.2 s) is much bigger than the precision | 0.01 s | Time more jumps; use the same person to start and stop the watch |
| Glass block | Yes for length and width; the thickness (about 2 cm) has only 2 significant figures | 1 mm | Vernier callipers (0.1 mm) for the thickness |
| Wire | Only with the coil method: the wire is thinner than one division | 1 mm ÷ 20 turns = 0.05 mm | More turns; a micrometer screw gauge (0.01 mm) |
| Sugar | Yes: the balance reads to 1 g, after zeroing | 1 g | A newton scale would be less precise (0.1 N ≈ 10 g) |
Remember: the precision of an instrument is its smallest scale division. A reading cannot be more precise than the instrument, so a ruler reading is written as 10.0 cm, never 10.03 cm.
Safety
- Before timing the star jumps, check that the surrounding area is clear of objects.
- Make sure the person doing the star jumps is wearing suitable footwear.
- Handle the glass block carefully; report any chipped edges.
- Do not overload the top-pan balance (check its maximum, here 2000 g).
Exam practice
Practical-style questions like those in Paper 5 (Practical Test) and Paper 6 (Alternative to Practical), and questions from your coursebook and practical book. Try each one before opening the answer.
1. A student measures the time for ten star jumps three times: 9.62 s, 9.41 s and 9.55 s. Calculate the average time for one star jump.
Mean time for ten = (9.62 + 9.41 + 9.55) ÷ 3 = 28.58 ÷ 3 = 9.53 s. Time for one = 9.53 ÷ 10 = 0.953 s (≈ 0.95 s).
2. Suggest how you would work out the thickness of a single sheet of paper if the only measuring device available was a ruler whose smallest division was 1 mm.
Measure the thickness of a large stack, for example 500 sheets, with the ruler, then divide by the number of sheets (500).
3. A stack of 500 sheets of paper measures 0.297 m × 21.0 cm × 50.0 mm. (a) What is the thickness of one sheet? (b) What is the volume of the stack in cm³?
(a) 50.0 mm ÷ 500 = 0.100 mm. (b) 29.7 cm × 21.0 cm × 5.00 cm = 3120 cm³ (3.12 × 10³ cm³).
4. A student winds 25 turns of wire round a pencil. The coil is 1.4 cm long. Calculate the diameter of the wire in mm.
d = 1.4 cm ÷ 25 = 0.056 cm = 0.56 mm.
5. Why is it better to wind 40 turns than 10 turns when measuring the diameter of a wire with a ruler?
The coil length can only be read to about ±1 mm, whatever its length. With more turns the coil is longer, so this uncertainty is a smaller fraction of the measurement; dividing by 40 instead of 10 makes the uncertainty in one diameter four times smaller.
6. Why should you time ten star jumps (or twenty swings of a pendulum) rather than one?
Your reaction time when starting and stopping the stopwatch (about 0.2 s) is the same however long the timing is. Over a longer time it is a much smaller percentage error. Dividing by ten gives a more accurate time for one.
7. A top-pan balance reads 4 g with nothing on it. A student weighs a bag of sugar without zeroing and records 1010 g. What is the mass of the bag, and what is this kind of error called?
Mass = 1010 − 4 = 1006 g. This is a zero error: the instrument reads 4 g too much every time. It is avoided by pressing Zero (tare) with the pan empty.
8. A glass block measures 10.0 cm × 6.5 cm × 1.8 cm. Calculate its volume and give the answer to a suitable number of significant figures.
V = 10.0 × 6.5 × 1.8 = 117 cm³. Two of the measurements have only 2 significant figures, so write 120 cm³ (2 s.f.); 117 cm³ is also usually accepted.
9. State the precision of: (a) a metre ruler marked in mm, (b) a digital stopwatch reading to 0.01 s, (c) a balance that reads to the nearest gram.
(a) 1 mm (0.1 cm); (b) 0.01 s; (c) 1 g. The precision is the smallest scale division.
10. Describe how to measure the height of a student accurately using a metre ruler.
The student removes their shoes and stands straight against a wall, heels and back touching it. Place a set square (or a flat book) on the head, held against the wall, and mark or read the height at its lower edge, with the eye level with it to avoid parallax. Use metre rulers fixed vertically to the wall with zero at the floor. Repeat with the student stepping away and back again, and take the average.
11. A student records the length of a block as 10 cm, 10.1 cm and 10.05 cm. What is wrong with these results?
They are not recorded to the same number of decimal places. A ruler with mm divisions reads to 0.1 cm, so they should be written to one decimal place, e.g. 10.0 cm and 10.1 cm. The value 10.05 cm claims more precision than the ruler has.