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1.4 Measurement

Introduction

The characteristics which are emphasized in the selection  of a measuring instrument  include precision , accuracy and sensitivity.

The meaning of  Precision, Accuracy and Sensitivity.

Precision is the degree of uniformity or reproducibility of the measurements.

OR

Precision is the degree of a measuring instrument  to record consistent reading for each measurement by the same way.

When we say the measurements are consistent, we mean that all the values of the measurements are close together.

Accuracy is the degree of closeness of the measurements to the actual  or accepted value.

When we say the measurements are accurate, we are actually saying that the values of the measurements are close to the true or accepted value.

The diagram shows the result  for four shooters A, B , C and D  in a tournament. Every shooters shot  five times .

idea of precision,consistency and accuracy
idea of precision,consistency and accuracy

The table shows the conclusion .

Shooter

Precision

Accuracy

A

High

Low

B

Low

High

C

High

High

D

Low

Low

Sensitivity of a measuring instrument is defined as the capability of that instrument to respond to physical stimuli or to register small physical amount or differences.

OR

Sensitivity is the degree of a measuring instrument to record small change in its reading.

The smallest scale division on the measuring instruments shows the  sensitivity of the instruments. Thus the more sensitive the measuring instruments the finer  the scale divisions.

A vernier callipers is more sensitive than a ruler or a miliammeter is more sensitive than an ammeter.

A  sensitive instrument is not always an accurate instrument.

Errors

Any measurement  of a physical quantity has errors or uncertainty.

There are two types of errors.

(a)       Systematic errors

(b)       Random errors

Systematic errors

Systematic errors are errors in the measurement of a physical quantity  due to instruments, the effects of surrounding conditions and physical constraints of the observer.

The main characteristic of systematic error is that its magnitude is almost constant or appears in one direction only. The value of the measurement is always greater or is always less than the actual value.

Sources of systematic errors are:

(i)   Zero errors or end errors

Zero errors occurs when the instrument gives a non- zero reading when in fact  the actual reading is zero.

Example :

(a) Positive zero error and negative of vernier callipers

clip_image002

(b) negative zero error of micrometer screw gauge

clip_image002[5]

(c) Positive zero error of micrometer screw gauge

clip_image004

(ii)    Personal error of the observer.

Physical constraints or limitations of the observer  can cause systematic errors.

An example is the reaction time.

(iii)    Errors due to instruments

The examples are;

A  stopwatch which is faster than normal would give readings which are always larger than the actual time.

A thermometer which is used under different conditions from which it was calibrated.

A voltmeter manufactured in Germany had been calibrated under different temperature and earth’s magnetic field from Malaysia where the voltmeter is used.

(iv)   Errors due to wrong assumption.

For example, we assumed  that the value of the acceleration due to gravity g is 9.81 ms-2, but the actual value may 9.79 ms-2. Hence there is a positive error of 0.02 ms-2.

Systematic errors cannot be reduced or eliminated by taking repeated readings using the same method, the same instrument or by the same observer.

Systematic errors can be eliminated or reduced by improving the procedure of taking the measurements , using a different instrument or getting somebody else to make the the measurements.

For example for the zero errors can be eliminated by subtracting the zero reading from the obtained readings.

Random errors

The main source of random  error is the observer or has non -constant  size of error and is unpredictable.

The characteristics of random errors are:

(i)    it can be positive or negative. The obtained readings may be greater or less than the actual value.

(ii)  its magnitude is not constant.

Examples of random errors are:

(i)      Parallax errors – occur when the position of the eye is not perpendicular to the scale.

(ii)     Different  pressures are applied when closing the gap of the micrometer screw gauge when it is used to measure the diameter  of a wire.

(iii)    Changes in the temperature during an experiment.

(iv)    Recording the wrong reading.

(v)     Mistake in counting

To eliminate or reduce random errors , repeated reading are taken.

 

Length Measurement

We normally use ruler, measuring tape , vernier callipers or micrometer screw gauge to measure length.

Measuring instrument

Smallest scale division

Ruler

0.1 cm or 1 mm

Vernier callipers

0.01cm

Mikrometer screw gauge

0.01 mm

Vernier callipers

vernier calipher
vernier calliper
sensitivity : 0.01 cm

A pair of vernier callipers can be used to measure  thickness of a wire , internal and external diameter of a  beaker, depths of a test tube ,etc.

The inside jaws are used to measure  internal diameters and the outside jaws are used to measure external diameters and thickness.

The tail is used to measure depths.

The main scale is marked in divisions of 0.1 cm , while the vernier scale is marked in divisions of  0.01 cm.

The following steps shows how to read the vernier callipers.

Step 1. Read the main scale marking just before the zero marking on the vernier scale.

Step 2. Find the vernier scale marking which joins the main scale marking.

Step 3. The reading for a vernier scale is always recorded in cm with two decimal places (The accuracy is 0.01 cm)

Micrometer screw gauge

screwmeter gauge
screwmeter gauge

Sensitivity : 0.01 mm

The micrometer screw gauge is used to measure thickness and diameters of  very small objects.

The main scale is marked in divisions of 0.5 mm , while the vernier scale is marked in divisions of  0.01 mm.

The jaws tigh the object that is to be measured.

The thimble is turned until its jaw touches the object.

The ratchet knob prevents overtightening by making a click sound when the micrometer is ready to be read.

The following steps shows how to read the micrometer screw gauge.

Read the main scale marking just before the zero marking on the vernier scale.

Step 1. Read the main scale marking just before the zero marking before the thimble.

Step 2. Find the vernier scale marking which joins the main scale.

Step 3. The reading for a micrometer screw gauge  is always recorded in mm with two decimal places (The accuracy is 0.01 cm)

In physic there are other instrument that used to measure time,mass,temperature and electric current.

Measuring Time

analogue stopwatch
analogue stopwatch
Sensitivity: 0.1 s

The most importance is every student have to know how to read the scale on the surface of the stopwatch.

Digital stopwatch
Digital stopwatch
sensitivity : 0.01s

Measuring Mass

Compression Balance
Compression Balance
sensitivity : 0.01 kg

usually used in market, to weight vegetables etc.

Lever Balance
Lever Balance
sensitivity: 0.001 Kg

usually used in laboratory for the scientific used.

Triple Balance Beam
Triple Balance Beam

Sensitivity : 0.0001 kg

triple balance beam is used in laboratory.

Measuring Temperature

Termometer
Thermometer
Sensitivity :  1° C

Measuring Electric Current

Double Scale Ammeter
Double Scale Ammeter

Max 5A ,sensitivity : 0.1 A

Max 1 A, sensitivity : 0.02

Always being ask to choose which one is suitable to use according the limit of the current.

image
Single Scale Ammeter
sensitivity : 5A

Conclusion

There are a few apparatus that is used to measure certain quantity , of course the reading is depend on the scale of the apparatus. For that reason we have the uncertainty.

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One Response

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