Activity 1: Measurement of Length
SCORE
Date Performed
Activity No. 1
MEASUREMENT OF LENGTH
INTRODUCTION
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Activity 1: Measurement of Length
Measurement is the process of comparing an unknown quantity with a known quantity. Because
of human and mechanical limitations, every measurement is an approximation. Every
measurement has a limit of accuracy and precision beyond which certainty exists. Accuracy is a
way of describing how close a stated number to that of the actual quantity it represents.
A scientific measurement consists of a number and a dimensional unit. Since the metric system
is generally used in scientific word, all the instruments provided in these illustrations have a scale
graduated in metric units.
A. The Vernier Scale
The vernier scale is a movable auxiliary scale attached to a main scale that accurately determines
the fractional part of a division on the main scale as shown in see Figure 1.1. This auxiliary scale
has divisions that are slightly smaller than a division on the stationary main scale along which it
slides. When the zero mark of the vernier coincides on any main scale division, then the n
divisions of the vernier caliper will correspond to n-1 divisions on the main scale. If S is the length
of the smallest main scale division and D is the length of the smallest vernier scale division, then
nD = (n -1) S.
Figure 1.1: The vernier caliper
The least count LC of the instruments with the vernier scale is the term applied to the smallest
value that can be read directly from the vernier scale. It is equal to the difference between a main
scale division and the vernier scale division:
LC = S - [ (n-1) / n ] S = S / n
B. The Micrometer Caliper
A micrometer caliper is another precision instrument used to determine lengths. The value of the
measured quantity is accurately indicated by the use of a pitched screw as shown in Figure 1.2.
It measures length by translating distance into revolutions and fractions of a revolution of a
known pitch. One complete revolution of the pitched screw is equivalent to 0.5 mm, which is the
smallest division indicated on the graduated reference line found on the sleeve of the caliper.
Graduations touching the reference line are 1- mm apart.
Activity 1: Measurement of Length
Figure 1.2: The micrometer caliper
C. The Ruler
A rule (see Figure 1.3) is an instrument consisting of a smooth straight edge strip of material with
mark off units, used to measure the distance between two points.
Figure 1.3: The ruler
OBJECTIVE
To study the principles of vernier caliper scale and micrometer caliper and how to use
these precision instruments in the measurement of length.
APPARATUS
Vernier caliper, micrometer caliper, ruler, 4 different solids
PROCEDURE
A. The Vernier Scale
1. In making measurement with a vernier scale, the following procedure may be followed:
(a) Determine first the least count of the caliper by noting the number of vernier
divisions n, the length of the smallest main scale division S and the length of the
smallest vernier scale division D.
(b) Determine the zero reading of the caliper by closing the jaws and noting the vernier
division which coincides with a mark on the main scale division.
(c) Read the number of divisions on the main scale before the zero mark of the vernier
scale and then note which vernier division coincides with a mark on the main scale
Multiply the number of the coinciding vernier mark by the least count LC to obtain
the fractional part of the main scale division to be added to the main scale reading.
Activity 1: Measurement of Length
Final reading = Main scale reading + LC ( vernier reading) + LC (zero reading)
Example:
fixed scale
vernier scale
final reading
:
:
:
3.7 cm
.03 cm
3.73 cm
fixed scale
:
vernier scale :
final reading :
51.0 mm
.9 mm
51.9 mm
2. Use the vernier caliper to measure the dimension of all four objects provided in the
measurement set.
(a) Use the outside caliper to measure the length, width, and the height of the metal
block, and the diameter of the metal sphere.
(b) Use the inside caliper to measure the inner diameter of the hollow metal cylinder
and use the depth gauge to measure the inside depth of the hollow metal cylinder.
(c) Record all measurements for the metric scales in Table 1.1
B. The Micrometer Caliper
1. The micrometer caliper in the measurement set has a pitch of 0.5 mm. This means that
the screw advances 0.5mm when turned through one revolution. Fraction revolution of
the screw is indicated by the graduation on the circumference of the thimble. The scale
around the circumference of the thimble is divided into 50 parts. Each division
represents 1/50 of revolution. When the thimble is turned through one division, the
screw advances 1/50 of the pitch, i.e., 1.50 mm or 0.01 mm.
2. Use the micrometer caliper to measure the dimensions of the objects in Step 1.
(REMINDER: Micrometer measurement limit is 2.58 cm. Measurement beyond this limit
may damage the device. Just put N/A (not applicable) to any measurement beyond 2.58
cm). Record your measurements in Table 1.2. Compare your readings with the ones
obtained in Step 1. Measure the diameter of the sphere at several points. When
measuring the diameter of the sphere, only the center of the faces of both anvil and
spindle should touch the sphere.
3. In making measurements with the micrometer caliper:
(a) Determine the zero reading of the caliper by closing the jaws and noting what
graduation lines are after the thimble coincides with the reference line.
(b) Read and record the number of graduation lines before the thimble and determine
the line on the thimble that coincides with reference line. If the reference line does
not coincide with a line on the thimble but between two lines, do an interpolation.
Activity 1: Measurement of Length
Example:
Sleeve
:
Thimble
:
Interpolation :
Final reading :
8.00 mm
0.11 mm
0.005 mm
8.115 mm
C. The Ruler
1. Use the ruler to measure the dimensions of the objects specified in Table 1.3.
Make the following comparison for the thickness of the rectangular block:
a. Ruler vs. vernier caliper (1 pt.)
b. Ruler vs. micrometer caliper (1 pt.)
c. Vernier caliper vs. micrometer caliper (1 pt.)
Activity 1: Measurement of Length
TABLE 1.1 VERNIER CALIPER
S = _____ cm, n = _____, LC = _____ cm; S = _____ mm, n = _____, LC = _____ mm (2 pts)
Fixed Scale
Vernier Scale
Reading
mm
mm
mm
Object
Rectangular Block
Length
Height
Width
Inner diameter
of hollow
cylinder
Diameter of
metal ball
Activity 1: Measurement of Length
Sketch of Scale
Rectangular Block
Length
Height
width
Inner diameter
of hollow
cylinder
Diameter of
metal ball
Activity 1: Measurement of Length
TABLE 1.2 MICROMETER CALIPER
S = _____ mm, n = _____, LC = _____ mm (2 pts)
Object
Sleeve
Thimble
Reading
Thickness of
rectangular
block
Diameter of
solid cylinder
Diameter of
metal ball
There’s no Interpolation since there were no scale that goes in between two lines of the
Thimble.
Activity 1: Measurement of Length
Sketch of the Scale
Thickness of
rectangular
block
Diameter of
solid cylinder
Diameter of
metal ball
Activity 1: Measurement of Length
TABLE 1.3 RULE
Rectangular Block
Actual Reading (mm)
Length
Width
Thickness
Sketch of Scales