This document discusses making measurements in physics. It covers using tools like rulers, vernier calipers, and micrometers to make measurements. It explains key concepts like significant figures, measurement uncertainty, and types of measurement errors. It provides examples of estimating uncertainties and combining uncertainties from multiple measurements. The goal is for students to learn to make accurate measurements and account for measurement errors and uncertainties.

1. A-level Physics
Unit G481:
Mechanics
Making
measurements

2. How wide is the bench? LOs
Width of bench
width
Practical skills in physics

3. Lesson focus
• Making and recording measurements
Learning objectives
At the end of the lesson you will be able to:
• make measurements using a metre rule, vernier caliper and micrometer;
• record measurements to an appropriate level of precision;
• explain the meaning of measurement uncertainty;
• describe some origins of measurement errors;
• estimate uncertainty when using simple instruments;
• combine uncertainties.
Motion

4. How to make a measurement LOs
When using a metre rule, vernier caliper or micrometer, measure to the closest
scale division . Do not estimate parts of a division.
To do
• Use a vernier caliper and micrometer to measure the diameter of a piece
of copper pipe.
• Record your measurements to an appropriate number of decimal places.
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5. The vernier caliper LOs
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6. The vernier caliper LOs
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7. The micrometer LOs
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8. The micrometer LOs
web site
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9. The micrometer LOs
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10. The micrometer LOs
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11. Significant figures LOs
A reliably known number in a measurement is called a significant
figure (s.f. or ‘sig fig’).
Examples: 2.50 (3 s.f.); 2.503 (4 s.f.); 0.025 (2 s.f. – the second ‘0’ is
used as a spacer between the number and the decimal point).
The number of s.f. tells us something about the precision of a
measurement (the smallest interval of measurement that is used).
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12. Making measurements LOs
a) Write down a measurement that can legitimately be made with this ruler.
Examples are: 1.1 cm, 0.058 m and 84 mm.
b) Write down a measurement (of between 0 and 10 cm) that cannot be
made with this ruler.
Examples are: 2.35 cm and 73.8 mm
c) How many significant figures are there in your answer to a)?
All of the measurements have 2 significant figures.
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13. Significant figures LOs
Using significant figures in calculations
1. When multiplying or dividing numbers
The answer should have no more s.f. than the least number of s.f. in any
of the factors.
E.g. 2.7 (2 s.f.) x 3.142 (4 s.f.) = 8.5 (2 s.f.)
2. When adding or subtracting numbers
The answer should have no more s.f. beyond the last decimal place in
which each number had a s.f..
E.g. 1.040 + 0.21342 = 1.253
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14. Significant figures LOs
1. How many significant figures are there in each of the following numbers?
a) 3.47 b) 2.30 c) 0.3774 d) 1.056 e) 256 f) 0.003774
2. Round each of the following numbers to two significant figures.
a) 3.406 b) 3.478 c) 3.99 x 105
3. Calculate the following, giving your answers to an appropriate number of
significant figures.
a) 1.58 x 0.03 b) 1.4 + 2.53 c) 2.34 x 102 + 4.93
4. How many s.f. are there in the number 5000 ?
5. Express the following:
a) 500 to 1 s.f. b) 3000 to 3 s.f. c) 1 550 000 to 4 s.f.
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15. Measurement uncertainty: what is it? LOs
In a perfect world….
• perfect measuring instruments
• no human error.
In reality, all measurements are approximately correct. How correct
depends on things such as
• how careful we have been
• how accurate the instrument is.
error = measured value - ‘true’ value
The effect of errors is to make a measurement uncertain.
measurement measurement measurement
+ + ...
error error uncertainty
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16. Measurement errors LOs
There are two main types of measurement error:
1. Random error  a reading is just as likely to be too high as too low
 caused by human error, or small, uncontrolled
changes in the environment or the thing you are
measuring (e.g. due to temperature changes,
mechanical vibration or electrical interference).
2. Systematic error  the same error affects all measurements (e.g.
a ‘zero error’ of a meter).
Questions
1. Which type of error is more difficult to detect?
2. What can be done to reduce random errors?
3. What can be done to reduce systematic errors?
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17. Measurement errors LOs
a
+
+
+
+ +
voltage
+
+ +
+ +
+ +
+ +
+
+
current b
a. Voltage vs current for a fixed b. The variation of a with b.
resistor.
Decide which type of error (random or systematic) is present in
each of these sets of data.
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18. Estimating measurement errors LOs
You need to be able to estimate the maximum likely uncertainty for
measurements.
For a metre rule, vernier or micrometer, the uncertainty is given as ± 1 division.
5 0.5 29 0.5
0 5 10 15 20 25 30 35
measured length = 24 1
Why? Because there is an uncertainty of ± 0.5 at each end of the rule making
± 1 division in total.
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19. Likely measurement errors LOs
1. Write down the absolute error implied by each of the following
measurements.
a) 2.1 cm b) 2.15 m c) 2.162 m
2. What possible error is implied in each of the following standard form
numbers?
a) 2.54 x 103 b) 3.5 x 104 c) 3.444 x 103 d) 2.4 x 106
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20. Combining uncertainties LOs
If two measured values are multiplied or divided, the overall percentage
uncertainty is the sum of the two percentage uncertainties.
So, for
y = ab or y = a/b
% uncertainty in y = %uncertainty in a + %uncertainty in b
y = a2
% uncertainty in y = %uncertainty in a + %uncertainty in a
= 2 x %uncertainty in a
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21. Combining uncertainties LOs
This ruler is used to determine the area of a piece of paper. The length and
width are 9.7 cm and 4.5 cm respectively.
Use this data to calculate the area of the paper in cm2 and give an uncertainty
for this value.
length = (9.7 ± 0.1) cm % uncertainty = (0.1 / 9.7) x 100 % = 1%
width = (4.5 ± 0.1) cm % uncertainty = (0.1 / 4.5) x 100 % = 2%
area = length x width
= ( 9.7 x 4.5 ) ± (1 + 2)% cm2
= 44 ± 3 % cm2
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