# What we need to do in this experiment

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```					                     Practice on Measuring Length and
Processing Experiment Data

What we need to do in this experiment?
To obtain the volume of a hollow cylinder and a sphere

What measuring tools we can use in this experiment?
A metal ruler, a vernier caliper & a micrometer

Why we need to do such an experiment?
From this experiment, 1. we can know the correct use of the vernier caliper & the micrometer
2. we can do some exercises for processing experiment data

Operating guideline for the three measuring tools:

1. Metal ruler:

1) The scale should close to the object to be measured as much as possible

√

×

2) The middle section of the ruler should be used, because there might be abrasion at the
start and the end of the ruler

Parameters for a ruler:
1) Graduation value (i), for a ruler, which is defined as the value between two closed
graduation marks, for example the graduation value of the metal ruler we used in this

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experiment is 1mm.

2)    Instrument error (  I ), for a ruler, which is defined as half of the graduation value.

2. Vernier caliper:
Attention please: There is a button used as a lock below the vernier arm. When you need to
move the arm, please press the button at the same time.

Structure of a vernier caliper:

Parameters for a vernier caliper:
1) Graduation value, for a vernier caliper, which is defined as i=a/n. where a means the
graduation value of the major gauge; n means the number of the graduation on the
vernier arm. For the vernier caliper we used in this experiment, a=1mm & n=20
2) Instrument error, for a vernier caliper, which has same value as the graduation value.

L=L0+ki

Where, L means the final result; L0 means the result obtained from the major gauge; k means the
k-th line on the vernier arm is aligned or most closed to a line on the major gauge; i means the
graduation value of the vernier caliper.

For example:

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Here L0=0mm; k=8; i=a/n=1mm/20=0.05mm, so L=L0+ki=0+80.05=0.40mm

3. micrometer:
Attention please: 1. There is a handle used as a lock on the front of the bracket. When you
need to rotate the vernier tube, please rotate the handle rightward at first.
2. When an object to be measured is placed between the two measuring
faces, the fixation ring can be used to fix the object.

Structure of a micrometer:

Parameters for a micrometer:
1) Graduation value, for a micrometer, which also can be defined as i=a/n, where a means
the graduation value of the major gauge; n means the number of the graduation on the
vernier tube. For the vernier caliper we used in this experiment, a=0.5mm & n=50
2) Instrument error, for a micrometer, which has half of the graduation value.
3) Original reading, which is defined as the difference between the expected zero mark and
the actual one and can be obtained when the length to be measured is zero i.e. the two
measuring faces are contacted with each other.
The ideal case for the zero mark when the length to be measured is zero:

There are two actual cases for the original reading:

(1)                                                            (2)

In case (1), the zero mark on the vernier tube is above the horizontal line on the major gauge. In
this case, the reading is defined as a negative value. For the Fig.(1), the original reading should be
-0.010mm.

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In case (2), the zero mark on the vernier tube is below the horizontal line on the major gauge. In
this case, the reading is defined as a positive value. For the Fig.(2), the original reading should be
-0.018mm.

When we get the reading, we should pay more attention that the reading could confuse us
sometime owing to the existence of the original reading. For example:

Fig.1                                                  Fig.2
Similar state of the major gauge in Fig.1 & Fig.2, but the zero mark is above and below the
horizontal line in Fig.1 & Fig.2, respectively, so there is a difference between the two measuring
results.
The result showed in Fig.1 should be 4.0mm+0.435mm=4.435mm
The result showed in Fig.2 should be 4.5mm+0.035mm=4.535mm

Experiment report guideline:
Experiment report should include the following items:
1. name of the experiment
2. purpose of the experiment
3. devices used in the experiment
4. necessary explanation for the experiment
5. processing the experiment data
6. conclusion (Do you think your experiment successful or not? What makes your experiment
successful or not?)

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How to process the experiment data
1) Datasheet

a. Height of the hollow cylinder (measured by the metal ruler)
mm
Times                               h

1

2

3

4

5

Mean value

b. Outside & inside diameter of the hollow cylinder (measured by the vernier caliper)
mm
Times                       Do                 Di
1
2
3
4
5
Mean value
c.   Diameter of the sphere (measured by the micrometer)
mm
Times              original
1

2

3

4

5

Mean value

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2) Complete experiment result

a.    Volume of the hollow cylinder
V

Do  S 2   I  ? 2  ? 2 
2

Di  S 2   I 
2

h  S 2  2   I 
*                         2

V      lnV 2                 lnV 2                 lnV 2
 (       )  ( Do )2  (       )  ( Di )2  (       )  ( h )2 
V       Do                    Di                     h
V
V  V     
V
 V  V  V =

b. Volume of the sphere
V

D  S 2  2   I 
*                             2

V      ln V 2
 (       )  ( D ) 2 
V       D
V
V  V  
V
 V  V  V =

Where S 
(x  i    x)2
n 1

*
It should be noted that when we use micrometer to measure a length, actually, we need two
readings for one final result, so twice instrument error would be introduced. For a ruler, the case is
similar to that of micrometer.

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