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Measurement of Length and Distance
Length is a measure of how long an object is or the distance between two points in space. It is used for identifying the size of an object or distance from one point to another. The length of an object is its extended dimension, that is, its longest side. For example, the length of the ruler below is 15 cm.
The standard unit (SI) of length based on the metric system is a meter (m). According to the length that needs to be measured, we can convert a meter into various units like millimeters (mm), centimeter (cm), and kilometer (km).
Therefore:
- 1 km = 1000 m
- 1 Hm = 100 m
- 1 Dm= 10 m
- 1 mm = 0.001 m
Centimeters and millimeters help measure smaller lengths and meters and kilometers help measure larger lengths like distance.
The SI unit for length is the metre (m).
One hundred equal divisions of a meter give a centimeter. It is written as ‘cm’. That is,
1 m = 100 cm
One thousand equal divisions of kilometer give a meter. That is,
1 km = 1,000 m
According to the length conversion charts, the different units of lengths and their equivalents are given below:
A kilometer (km), meter (m), and centimeter (cm) are the commonly used units of length.
Conversion of these units is done using the given formula.
Length is measured using a metre rule (100 cm), tape measure (100 m, 300 m, 500 m),calipers. similarly, length can be measured using Vernier calipers and Micrometer screw gauge
- Meter Rule:
Meter rule is used to measure distance on paper. It is calibrated in millimeters, centimeters, . Some meter rules are calibrated in inch or feet. The accuracy of meter rule is 0.1 cm or 1.0 mm
With a meter rule ,distance is measured starting from the zero reference mark to any required length. The measured distance or length is read and recorded.
Callipers:
Callipers are not used to measure distance or length directly as the case is in meter rule. The claws of the callipers are adjusted to touch the edges of the object that is being measured. The span of the jaws of the callipers is then measured against a calibrated scale or meter rule to determine or estimate the size of the measured distance or length.
3.The Vernier Calipers
The vernier calipers may be used to measure outer dimensions of objects (using the main jaws), inside dimensions (using the smaller jaws at the top), and depths (using the stem).
A Vernier calliper has two scale : the main scale and the Vernier scale.
a. The main scale:
The calibrations or scales of the main scale of Vernier callipers vary depending on the range of measurement that the Vernier callipers are meant to measure. .
b. The vernier scale:
The vernier scale of a vernier calliper is obtained by dividing a 9mm length into 10 equal divisions or intervals such that each divisions is 0.9mm or 0.09cm.
The accuracy of a vernier caliper is 0.1mm or 0.01cm. This means the that the smallest distance that a vernier calliper can measure is 0.1mm or 0.01cm
How to use a vernier calliper:
Step I. Read and record the reading of the main scale
Step II. Read and record the reading of the vernier scale at the point where the main scale and the vernier scale coincide.
Step III. Multiply the reading of the vernier scale by the accuracy of the vernier scale which is 0.01cm.
Step IV. Add the result of step III to the main scale reading of step I to get the final answer which is the reading of the vernier calliper.
Example 1:
What is the reading of the vernier calliper as shown in the figures below?
Solution:
Reading of main scale. = 10.0 cm
Reading of vernier scale = 2
Reading of vernier scale x accuracy of vernier calliper
= 2 x 0.01 cm = 0.02 cm
Add the result of step III and step I to get the reading.
= 10.0 cm + 0.02 cm
Therefore, the reading of vernier calliper is 10.02cm
Example 2:
Estimate the reading of the vernier calliper as shown in the figure below:
Solution:
Reading of main scale. = 4.3 cm
Reading of vernier scale = 5
Reading of vernier scale x accuracy of vernier calliper
= 5 x 0.01 cm = 0.05 cm
Add the result of step III and step I to get the reading.
= 4.30 cm + 0.05 cm
Therefore, the reading of vernier calliper is 4.35 cm.
Micrometer Screw Gauge
The micrometer screw gauge is used to measure even smaller dimensions than the vernier callipers. The micrometer screw gauge also uses an auxiliary scale (measuring hundredths of a millimetre) which is marked on a rotary thimble. Basically it is a screw with an accurately constant pitch (the amount by which the thimble moves forward or backward for one complete revolution).
Just like a vernier calipers, a micrometer screw gauge has two scales : the main scale and the vernier scale.
a. The main scale:
The main scale of a micrometer is calibrated in mm. The calibrations of the main scale of micrometer screw gauge vary depending on the range of measurement that the micrometer screw gauges are meant to measure.
b.The thimble scale:
The thimble scale has 50 equal divisions. Each divisions is obtained by dividing 5 by 10. The thimble scale move a distance of 0.5mm along the main scale when it make 1 revolution by turning round once. One division on the thimble scale equal to 0.5/50 which equal to 0.01mm on the main scale.
The accuracy of a micrometer screw gauge is 0.01mm or 0.001cm. This means the that the smallest distance that a micrometer screw gauge can measure is 0.01mm or 0.001cm.
How to use a micrometer screw gauge :
Step I. Read and record the reading of the main scale
Step II. Read and record the reading of the thimble scale at the point where the main scale and the thimble scale coincide.
Step III. Multiply the reading of the thimble scale by the accuracy of the micrometer scale which is 0.01mm
Step IV. Add the result of step III to the main scale reading of step I to get the final answer which is the reading of the micrometer.
Example 1.:
What is the readings of the reading of the micrometer meter screw gauges as shown in the figures below?
Solution:
Reading of main scale. = 4.50 mm
Reading of thimble scale = 10
Reading of thimble scale x accuracy of micrometer
= 10 x 0.01 = 0.10 mm
Add the result of step III and step I to get the reading of the micrometer screw gauge.
= 4.50 + 0.10 = 4.60 mm
Reading of micrometer = 4.60 mm
Example2.:
What is the readings of the reading of the micrometer meter screw gauges as shown in the figures below?
Solution:
Reading of main scale. = 22.0 mm
Reading of thimble scale = 33
Reading of thimble scale x accuracy of micrometer
= 33 x 0.01 = 0.33 mm
Add the result of step III and step I to get the reading of the micrometer screw gauge.
= 22.0 + 0.33 = 22.33 mm
Reading of micrometer screw gauge = 22.33 mm
Example 3.:
What is the readings of the reading of the micrometer meter screw gauges as shown in the figures below?
Solution:
Reading of main scale. = 3.25 mm
Reading of thimble scale = 13
Reading of thimble scale x accuracy of micrometer
= 13 x 0.01 = 0.13 mm
Add the result of step III and step I to get the reading of the micrometer screw gauge.
= 3.25 + 0.13= 3.38 mm
Reading of the micrometer meter screw guage
= 3.38 mm