Understanding lab

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Experiment 1

Mass, volume and density

Purpose 1. Familiarize with basic measurement tools such as vernier caliper, micrometer, and laboratory balance.

2. Learn how to use the concepts of significant figures, experimental uncertainty (error) and some

methods of error and data analysis in your experimental measurements.

Equipment A steel ball, a rectangular aluminum block, a brass cylinder, an aluminum annular cylinder, vernier

caliper, micrometer, laboratory balance.

Basic measurement tools 1. Least Count of an Instrument Scale

Least Count of an instrument is the smallest subdivision marked on its scale. This is the unit of the

smallest reading that can be made without estimating.

Figure 1 Least count

Meterstick is commonly calibrated in centimeter

(numbered major division) with a least count, or

smallest marked subdivision, of millimeter.

2. Vernier Caliper

The vernier caliper in Fig. 2 consists of a rule with two main engraved scales (in inch and cm

respectively) and movable jaws with engraved vernier scales (i.e., small movable graduated scales for

obtaining fractional parts of subdivisions on a fixed main scale of a measuring instrument). The span of

the lower external measuring jaw is used to measure length and is particularly convenient for measuring

the diameter of a cylindrical object. The span of the upper internal measuring jaw is used to measure

distances between two surfaces (e.g. the inside diameter of a hollow cylindrical object).

In this experiment we only use the cm main scale which is calibrated in cm with a mm least count,

and the movable vernier scale has 10 divisions that cover 9 divisions on the main scale. Figure 3 shows an

example of reading the vernier scale on a caliper.

Figure 2 Vernier Caliper

Internal measuring jaws Locking screw Main scale (inch)

Depth probe Fine adjustment

Vernier scale (cm) Main scale (cm)

External measuring jaws

Vernier scale (inch)

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The first two significant figures are read directly from the main scale. The vernier zero mark is past

the 2-mm line after the 1-cm major division mark, so we have 1.2 cm. The next significant figure is the

fractional part of the smallest subdivision on the main scale. This is obtained by referring to the vernier

scale markings.

If a vernier mark coincides with a mark on the main scale, then the mark number is the fractional part

of the main-scale division. In Fig. 3a, this is the third mark to the right of the vernier zero, so the third

significant figure for a reading is 3 (0.03 cm). Finally, since the 0.03-cm reading is known exactly, a zero

is added as the doubtful figure for a reading of 1.230 cm or 12.30 mm. Note how the vernier scale gives

more significant figures or extends the precision.

However, a mark on the vernier scale may not always line up exactly with one on the main scale (Fig.

3b). In this case, there is more uncertainty in the 0.001-cm or 0.01-mm figure. In Fig. 3b, the second

vernier mark after the zero is to the right of the closest main-scale mark and the third vernier mark is to

the left of the closest main-scale mark. Hence, the marks change phase between 1.22 cm and 1.23 cm.

Most vernier scales are not fine enough to make an estimate of the doubtful figure, so a suggested method

is to take the middle of the digit for a reading of 1.225 cm.

Before making a measurement, the zero of the vernier caliper should be checked with the jaws

completely closed. It is possible that through misuse the caliper is no longer zeroed. And thus gives

erroneous readings (systematic error). If this is the case, a zero correction must be made for each reading.

In Fig. 4 (b), the “zero” reading is +0.05 cm and this amount must be subtracted from each measurement

reading. Similarly, if the “zero” reading is negative, or the vernier zero lies to the left of the main-scale

zero, the measurements will be too small and the zero correction must be added to the measurement

readings.

(a)

1 cm + 0.2 cm + 0.03 cm + 0.000 cm = 1.230 cm

(major division) (aligned mark) (estimated of doubt) (minor division)

Vernier zero mark

Main scale

Figure 3 Vernier scale. Examples of reading the vernier scale on a caliper.

1 cm + 0.2 cm + 0.025 cm = 1.225 cm

(b)

(major division) (phase change for 2 and 3 marks) (minor division)

Vernier zero mark

Main scale

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3. Micrometer Caliper

Figure 5 shows a micrometer and an example of a micrometer reading.

The micrometer provides for accurate measurements of small lengths and is particularly convenient in

measuring the diameters of thin wires and the thickness of thin sheet. It consists of a movable spindle

(jaw) that is advanced toward another, parallel-faced jaw (called an anvil) by rotating the thimble. The

thimble rotates over an engraved sleeve (or “barrel”) mounted on a solid frame.

Most micrometers are equipped with a ratchet (ratchet handle to far right in Fig. 5) which allows

slippage of the screw mechanism when a small and constant force is exerted on the jaw. This permits the

jaw to be tightened on an object with the same amount of force each time. Care should be taken not to

force the screw, so as not to damage the measured object and/or the micrometer.

The axial main scale on the sleeve is calibrated in millimeters, and the thimble scale is calibrated 0.01

mm. The movement mechanism of the micrometer is a carefully machined screw with a pitch of 0.5 mm.

The axial line on the sleeve main scale serves as a reading line. Since the pitch of the screw is 0.5 mm

and there are 50 divisions on the thimble, when the thimble is turned through one of its divisions, the

thimble moves 1

50 of 0.5 mm or 0.01 mm (

1

50 * 0.5 mm = 0.01 mm).

One complete rotation of the thimble (50 divisions) moves it through 0.5 mm, and second rotation

moves it through another 0.5 mm.

Figure 4 Zeroing and systematic error (zeroing the vernier caliper with the jaws closed)

Vernier zero mark

Main scale

0.00

(a) Properly zeroed

(b) Positive error + 0.05 cm (subtracted from measurement reading)

Vernier zero mark

Main scale

0.05

c

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4. Laboratory Balance

Laboratory balance is used to balance the weight of an unknown mass m against that a known mass m1,

i.e. mg = m1g or m = m1.

Mass, volume and density of an object

The density  of a substance is defined as the mass m per volume V, i.e.  = m

V . This may be

determined experimentally by measuring the mass and volume of a sample of a substance and calculating

the ratio m

V . The volume of a regular shaped object can be calculated from length measurements; for

example:

Sphere 3 / 6V D= D, diameter

Rectangular block 1 2 3

V L L L=   L1, length; L2, width; L3, thickness

Cylinder 2 / 4V D L= D, diameter; L, height

Annular Cylinder ( )2 2

1 2 / 4V D D L= − D1, outer diameter; D2 inner diameter; L, height

(b)

Figure 5 Micrometer

(a) This particular micrometer has the

1.0 mm and 0.5 mm scale divisions

below the reading line.

(b) In this diagram, as on some

micrometer, the 1.0 mm divisions are

above the reading line and the 0.5 mm

divisions are below it.

The thimble in the diagram is in the

second rotation of a mm movement, as

indicated by its being past the 0.5 mm

mark.

The reading is 5.500 + 0.285 or 5.785

mm, where the last 5 is the estimated

figure.

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Procedure Use appropriate measurement tools to do following measurements on 4 objects.

1. For each object take five measurements to determine the average dimensions. Notice the significant

figures of the reading. Remember to make a zero correction for each reading if it is necessary.

2. Calculate the volume of each object (V  dV ), where V is the mean of volume and dV is the

mean deviation of volume.

3. Using laboratory balance to determine the mass (m) of each object.

4. Calculate the density (   d ) of the material of each object, where  is the mean of density and

d is the mean deviation of density.

5. Compare the measured  with accepted  of each object and calculate the percent %.

Table 1 Steel ball

Compare the measured  with accepted Fe (7.8x103 kg/m3) and calculate the percent % error.

Table 2 Aluminum block

Compare the measured  with accepted Al (2.7x103 kg/m3) and calculate the percent % error.

1 2 3 4 5 average

D (mm) 3

/ 6V D=

Vi i d V V= −

m (g)

 (g/mm3)

i i d 

 = −

1 2 3 4 5 average

L1 (cm)

L2 (cm)

L3 (cm)

1 2 3 V L L L=  

Vi i d V V= −

m (g)

 (g/cm3)

i i d 

 = −

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Table 3 Brass cylinder

Compare the measured  with accepted brass (8.9x103 kg/m3) and calculate the percent % error.

Table 4 Aluminum annular cylinder

Compare the measured  with accepted Al (2.7x103 kg/m3) and calculate the percent % error.

Work to be done: 1. Put measurement tools and objects in proper places.

2. Let your TA check your data Tables. If they are OK, your TA will sign them.

3. Clean up your bench.

Lab report on Experiment 1

1. Your lab report should be in the required format described in the “Introduction” of the lab manual.

2. Tables 1 to 4 should be included in your lab report.

3. It is required that the answers to the following questions should be included in your lab report.

4. You can tear those pages out of the lab manual as a part of your lab report, which contain measured

(raw) data and analyzed data, answers to questions. The data sheets must be checked and signed by

your lab TA.

1 2 3 4 5 average

D (mm)

L (cm) 2

/ 4V D L=

Vi i d V V= −

m (g)

 (g/mm3)

i i d 

 = −

1 2 3 4 5 average

L (cm)

D1 (cm)

D2 (cm)

( )2 2

1 2 4

L V D D

 = −

VVd iVi −=

m (g)

 (g/cm3)

 −= iid

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Question and exercises 1. Write down the readings on the side of Figs. 6 (a), (b) and (c) respectively. What is the least count of

instrument scale for each of the three measurement tools?

2. What is the difference between the measured values 1.05 m and 1.050 m? What factor of a

measurement tool determines the significant figures of a measured value?

Fig. 6 (a) Meterstick (cm)

10 20

Fig. 6 (b) Vernier Caliper (cm)

1 2

Fig. 6 (c) Micrometer (mm)

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