motion 4 introduction to measurement (shared)

Making measurements

A-level Physics

Unit G481: Mechanics

Practical skills in physics

Width of bench

width

How wide is the bench? LOs

Learning objectivesAt 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.

Lesson focus• Making and recording measurements

Motion


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.

How to make a measurement LOs


The vernier caliper LOs


The micrometer LOs


web siteweb site

The micrometer LOs

http://www.stefanelli.eng.br/webpage/en-aka-micrometer-caliper-outside-millimetre-hundredth.html


The micrometer 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).

Significant figures 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.

Making measurements LOs


Using significant figures in calculations

1. When multiplying or dividing numbersThe 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 numbersThe 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



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.



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 error

measurement error

+ + ...measurement uncertainty

Measurement uncertainty: what is it? 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?

Measurement errors LOs


Decide which type of error (random or systematic) is present in

each of these sets of data.

current

volta

gea

b

++++

++++ +

+++

++++

++++

a. Voltage vs current for a fixed resistor.

b. The variation of a with b.

++++ +

+++ +

+++ +

+++ +

+++

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.

Why? Because there is an uncertainty of ± 0.5 at each end of the rule making

± 1 division in total.

0 5 10 15 20 25 30 35

5 ± 0.5 29 ± 0.5

measured length = 24 ± 1

Estimating 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

Likely measurement errors LOs


If two measured values are multiplied or divided, the overall percentage uncertainty is the sum of the two percentage uncertainties.

So, fory = 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

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

Combining uncertainties LOs

motion 4 introduction to measurement (shared)

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