Understanding Measurements

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Malaysia SPM Form 4, Chapter 1: Introduction to Physics
Back to F4 Physics content page.

[edit] Measuring Instrument

[edit] Ruler

A metre rule has sensitivity or accuracy accuracy of 1mm.

Precaution to be taken when using ruler

Make sure that the object is in contact with the ruler.
Avoid parallax error.
Avoid zero error and end error.

[edit] Vernier Caliper

[edit] How to Read

[edit] Micrometer Screw Gauge

Range and Accuracy The range of a micrometer is 0-25mm. The accuracy of a micrometer is up to 0.01mm.

How to Use a Micrometer?

Turn the thimble until the object is gripped gently between the anvil and spindle.
Turn the ratchet knob until a "click" sound is heard. This is to prevent exerting too much pressure on the object measured.
Take the reading.

How to Read the Reading?

Reading = Reading of main scale + Reading of thimble scale.

Reading of main scale = 0 - 25 mm
Reading of thimble scale = 0 - 0.49mm

Example 1

Find the reading of the Vernier Caliper below

Reading of main scale = 5.5mm
Reading of thimble scale = 0.27mm

Actual Reading = 5.5mm + 0.27mm = 5.77mm

[edit] Precaution Steps

The spindle and anvil are cleaned with a tissue or cloth, so that any dirt present will not be measured.
The thimble must be tightened until the first click is heard.
The zero error is recorded.

[edit] Stopwatch

There are 2 types of stopwatches

analogue stopwatches of sensitivity 0.1s or 0.2s
digital stopwatches of sensitivity 0.01s.

The sensitivity of a stopwatch depends on the reaction time of the user.

[edit] Thermometer

There are 2 types of mercury thermometer

Thermometers of range -10oC - 110oC with accuracy 1oC.
Thermometers of range 0oC - 360oC with accuracy 2oC.

Precaution to be taken when using thermometer

Make sure that the temperature measured does not exceed the measuring range.
When measuring temperature of liquid
1. immerse the bulb fully in the liquid
2. stir the liquid so that the temperature in the liquid is uniform
3. do not stir the liquid vigorously to avoid breaking the thermometer

[edit] Ammeter and Voltmeter

Ammeters are measuring instrument used to measure electric current. An Ammeter is always connected in series with the load (resistor) in a circuit.

Voltmeters are measuring instrument used to measure potential difference (voltage). A voltmeter is always connected parallel to the load (resistor) in a circuit.

[edit] Error Analysis

Error is the difference between the actual value of a quantity and the value obtained in measurement. There are 2 main types of error

Systematic Error
Random Error

[edit] Precision

Precision is the ability of an instrument in measuring a quantity in a consistent manner with only a small relative deviation between readings.
The precision of a reading can be indicated by its relative deviation.
The relative deviation is the percentage of mean deviation for a set of measurements and it is defined by the following formula:

[edit] Accuracy

The accuracy of a measurement is the approximation of the measurement to the actual value for a certain quantity of Physics.
The measurement is more accurate if its number of significant figures increases.
Table above shows that the micrometer screw gauge is more accurate than the other measuring instruments.
The accuracy of a measurement can be increased by

taking a number of repeat readings to calculate the mean value of the reading.
avoiding the end errors or zero errors.
taking into account the zero and parallax errors.
using more sensitive equipment such as a vernier caliper to replace a ruler.

The difference between precision and accuracy can be shown by the spread of shooting of a tar-get (as shown in Diagram below).

[edit] Sensitivity

The sensitivity of an instrument is its ability to detect small changes in the quantity that is being measured.
Thus, a sensitive instrument can quickly detect a small change in measurement.
Measuring instruments that have smaller scale parts are more sensitive.
Sensitive instruments need not necessarily be accurate.

[edit] Systematic Error

Systematic Error Systematic errors are errors which tend to shift all measurements in a systematic way so their mean value is displaced. Systematic errors can be compensated if the errors are known.

Examples of systematic errors are

zero error, which cause by an incorrect position of the zero point,
an incorrect calibration of the measuring instrument.
consistently improper use of equipment.

Systematic error can be reduced by

Conducting the experiment with care.
Repeating the experiment by using different instruments.

[edit] Zero Error

A zero error arises when the measuring instrument does not start from exactly zero.
Zero errors are consistently present in every reading of a measurement.
The zero error can be positive or negative.

NO ZERO ERROR: The pointer of the ammeter place on zero when no current flow through it.

NEGATIVE ZERO ERROR: The pointer of the ammeter does not place on zero but a negative value when no current flow through it.

POSITIVE ZERO ERROR: The pointer of the ammeter does not place on zero but a negative value when no current flow through it.

[edit] Random Error

Random errors arise from unknown and unpredictable variations in condition.
It fluctuates from one measurement to the next.
Random errors are caused by factors that are beyond the control of the observers.
Random error can cause by

personal errors such as human limitations of sight and touch.
lack of sensitivity of the instrument: the instrument fail to respond to the small change.
natural errors such as changes in temperature or wind, while the experiment is in progress.
wrong technique of measurement.

One example of random error is the parallax error. Random error can be reduced by

taking repeat readings
find the average value of the reading.

[edit] Parallax Error

A parallax error is an error in reading an instrument due to the eye of the observer and pointer are not in a line perpendicular to the plane of the scale.