Topic 2Measurement Technique

Vernier Caliper

Example 1Answer: mm37.00+ 0.46= 37.46

Example 2Answer: mm34.00+ 0.60= 34.60

Exercise 1

Exercise 2

Micrometer

Example 1Answer: mm3.00+ 0.09= 3.09

Example 2Answer: mm5.50+ 0.30= 5.80

Exercise 1

Exercise 2

Cathode-ray OscilloscopeOne of the application of CRO is to measure the frequency of a periodic signal (e.g. sine wave output of a signal generator)

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ExampleSettings:Voltage axis (Y) = 50 mV / divTime axis (X) = 50 s / divPeriod of the outputT = 4 x 50 s = 200 s

Frequency f = 1 / T = 5.0 kHz

Voltage V = 3 x 50 mV = 150 mV

ExerciseSettings:Voltage axis (Y) = 5 V / divTime axis (X) = 50 ms / divPeriod of the outputT =

Frequency f =

Voltage V =

Errors and UncertaintiesErrorsSystematic errorsRandom errors

Systematic ErrorsSystematic errors are constant deviations of the readings in one direction from the true value.always greateralways less than

Systematic Errors

(1) Zero ErrorOccur when the instrument shows a non-zero reading when in fact the reading is zero.

Correct a zero errorCheck instrument before experimentTwo ways:Manually adjust the instrumentMinus zero error in calculation

Manually adjust the instrument

Minus the zero error in calculationExample:Mass of a beaker = 50.32gZero error = 0.02 gActual mass of beaker = 50.32 0.02 = 50.30g

(2) Instrument Error A stopwatch which is faster than normal would give readings which are always larger than the actual time.An ammeter manufactured in Germany which is calibrated under different temperature from Malaysia.

e.g. wrong assumptiong = 9.79 ??g = 9.81 ??Certain Human Errors

Correcting systematic errorsby calibrating equipment, comparing two or more identical pieces of apparatus. Good research experiments are marked by thoroughness and skill in removing the effects of systematic errors. The ultimate safeguard is agreement in results from various independent measurements, made by different people with different equipment and methods.

Random ErrorsRandom errors refer to the scatter of readings about the accepted value. can be more than or less than

Example 1: Parallax Error

However, if a scale reading is always from the same non-normal angleParallax error = Systematic ErrorParallax error = Random Error

4 X

Example 2: Human Error in starting and stopping the stopwatch

Other examplesWhen a micrometer screw gauge is used to measure the diameter of a wire, random errors occur when different pressures are applied when closing the gap of the micrometer.Changes in the temperature during an experiment can result in the measurements being bigger or smaller than the actual value.Mistake in counting the oscillation of a simple pendulum.

Differences of Systematic Error and Random ErrorSystematic ErrorOnly in one direction and constant Cannot be reduced by repeated readingsCan be avoided/eliminated by using different instruments or using the right experimental technique

Random ErrorCan be positive or negative and keep changingCan be reduced by repeated readings and take the average valueCannot be eliminated

Precision and AccuracyPrecise measurement = small random errors

Precision indicates the agreement among several measurements that are made in the same way.Accurate measurement = small systematic errors

Accuracy refers to the degree of closeness to the true value

High Precision

Low AccuracyLow Precision

High AccuracyHigh Precision

High Accuracy

Graphs of Precision and AccuracyLow PrecisionLow AccuracyLow PrecisionHigh AccuracyHigh PrecisionLow AccuracyHigh PrecisionHigh Accuracy