Group #: Three (3) Date Performed: 09-05-14Members: Arellano, Lory Mae Date Submitted: 09-12-14

Dagondon, Vanessa OlgaJomocan, Christine Anne

Class Schedule: TF 8:30 – 10:00

Experiment 1MEASUREMENT

I. OBJECTIVETo measure linear dimensions using different measuring devices, namely: the straight rule, the Vernier

caliper, and the micrometer caliper.II. APPARATUS

Vernier Caliper Micrometer Caliper Ruler Materials to be measured:

Hollow and solid cylinders Metal balls 5 – centavo coin Rectangular block

III. Method:Various instruments with Vernier scales and micrometer screws are examined. The least count is

determined and readings taken with each instrument. Vernier and micrometer calipers are used to measure certain lengths. The relative errors made in measuring a given length by various devices are estimated.

IV. PROCEDURE

1. Use the straight rule, the Vernier caliper, and the micrometer calliper to measure the linear dimensions of different geometric objects as specified below. Tabulate your data in the given tables.

A. STRAIGHT RULEa. length, width, thickness of the metal blockb. height and diameter of the solid cylinderc. outer height and outer diameter of the hollow cylinderd. Inner diameter of the hollow cylinder

B. VERNIER CALIPERa. length, width, thickness of the metal blockb. height and diameter of the solid cylinderc. outer height and outer diameter of the hollow cylinderd. inner height and inner diameter of the hollow cylinder

e. diameter of the metal sphere

C. MICROMETER CALIPERa. length, width, thickness of the metal blockb. height and diameter of the solid cylinderc. outer diameter of the hollow cylinderd. diameter of the metal sphere

2. Compute for the volume of each object using the measurements of each device. Show your computations below their respective tables

IV. DATA AND RESULTS

TABLE 1. METAL BLOCKINSTRUMENT LENGTH

(mm)

WIDTH

(mm)

THICKNESSS

(mm)

VOLUME

(mm3)

STRAIGHT RULE

48.0 24.9 12.8 15298.6

VERNIER CALIPER

48.00 25.00 12.70 15240

MICROMETER CALIPER

n/a 24.900 12.690 n/a

V = l w t where: l = length, w = width, t = thicknessCalculations:

VolumeV straight ruler = (48.0 mm) (24.9 mm) (12.8 mm) = 15298.6 mm3

V vernier caliper = (48.00 mm) (25.00 mm) (12.70 mm) = 15240 mm3

Statistical AnalysisMean = Standard Deviation =

mean Standard deviation Standard deviation of the mean (s/(n)1/2)

conclusion

width 24.93 0.15 ±0.03 No significant differences

thickness 0.05 0.06 ±0.04 No significant differences

TABLE 2. SOLID CYLINDERINSTRUMENT HEIGHT

(mm)

DIAMETER

(mm)

VOLUME

(mm3)

STRAIGHT RULE 22.0 16.0 1408 π

VERNIER CALIPER 22.30 15.90 1409.42 π

MICROMETER CALIPER

22.200 15.850 1394.285 π

V = π r2 h where: π = 3.1416 r = radius h = heightCalculations:

V straight ruler = (π) (16.02

mm) 2 (22.0 mm) = 1408 π mm3

V vernier caliper = (π) (15.902

mm) 2 (22.30 mm) = 1409.42 π mm3

V micrometer caliper = (π) (15.8502

mm) 2 (22.200 mm) = 1394.285 π mm3

Statistical AnalysisMean = Standard Deviation =

mean Standard deviation Standard deviation of the mean (s/(n)1/2)

conclusion

Height 22.17 0.15 ± 0.09 No significant difference

diameter 15.92 0.08 ± 0.05 No significant difference

TABLE 3. HOLLOW CYLINDERINSTRUMENT OUTER

HEGHT

(mm)

OUTER DIAMETER (mm)

OUTER VOLUME

(mm3)

INNER HEIGHT (mm)

INNER DIAMETER

(mm)

INNER VOLUME

(mm3)

STRAIGHT RULE

61.0 19.0 5505.3 π n/a 9.0

VERNIER CALIPER

61.0 19.10 5563.35 π

40.80 9.40 901.27 π

MICROMETER CALIPER

n/a 19.10 n/a n/a

Calculations:

Outer Volume

V straight ruler = (π) (19.02

mm) 2 (61.0 mm) = 5505.3 π mm3

V vernier caliper = (π) (19.102

mm) 2 (61.0 mm) = 5563.35 π mm3

Inner Volume

V vernier caliper = (π) (9.402

mm) 2 (40.80 mm) = 901.27 π mm3

Statistical AnalysisMean = Standard Deviation =

mean Standard deviation Standard deviation of the mean (s/(n)1/2)

conclusion

Outer diameter 19.07 0.06 ± 0.03 No significant difference

TABLE 4. METAL SPHEREINSTRUMENT DIAMETER VOLUME

(mm) (mm3)

VERNIER CALIPER 19.00 1143.17 π

MICROMETER CALIPER 19.000 1143.167 π

V = (4/3) π r3 where: π = 3.1416 r = radiusCalculations:

V straight ruler = (43

) (π) (19.002

mm) 3 = 1143.17 π mm3

V vernier caliper = (43

) (π) (19.0002

mm) 3 = 1143.167 π mm3

Statistical AnalysisMean = Standard Deviation =

Mean Standard Deviation Standard deviation of the mean (s/(n)1/2)

Conclusion

diameter 19.0 0 0 No significant difference

QUESTIONS:1) A scale whose smallest division is 1 cm is to be provided with a vernier scale that will enable fifths

of centimetre divisions to be accurately estimated. How many vernier divisions should be used, and how long will each one be? Based on the problem, there will be 5 divisions in the vernier scale.

Let n be the number of divisions in the vernier scale V be the length of one division on the vernier scale S be the length of the smallest scale division

Given: S = 1 cm or 10 mm; n = 5Find: Least count = S – V = 1/n S

= (1/5) (10mm) = 2 mm or 0.02cm

Each division will be 2mm long.

2) A micrometer caliper has a zero error such that as the jaws are closed the zero mark on the sleeve turns 0.05 mm past the zero on the main scale. The reading of the instrument is 7.82 mm. What is the correct reading? The uncertainty in the original reading is 0.05mm. Therefore, we can say that the correct reading is 7.87 mm or 7.77 mm.

V. OBSERVATION AND DISCUSSION

A certain object has no exact measurement. However, this measurement can still be identified if not exactly but accurately with the use of devices or instruments that can measure objects yielding only a small value for its uncertainty (e. g. straight rule, vernier caliper, micrometer caliper).

The task in the experiment was to measure four (4) objects (metal bock, solid cylinder, hollow cylinder, and metal sphere) using three (3) different measuring devices already mentioned above.

The first instrument used was a straight rule. The straight rule was 10 decimeters long with 10 divisions measuring 1 centimetre each. The second instrument was the vernier caliper. Values reported in the data were in tenths place. A vernier caliper is a slide type measuring instrument that can measure the inside, outside and depth of a certain object. Compared to that of the straight rule, it is much more flexible in measuring other complex objects (e. g. hollow cylinder in the experiment). It is observed in the tables above that there are “boxes” labelled as “n/a”. This is due to the limitations of the measuring device used. As seen, there is no “n/a” under vernier caliper. This proves its reliability in terms of measuring difficult objects than the other two measuring devices. Values reported are in hundredths place. This makes this more accurate than that of the straight rule. The third device used was the micrometer caliper. As the name suggests, it can be deduced that it widely used to measure smaller objects, thus putting a limitation on the objects it can measure. However, the measurement being reported using this device is in the thousands decimal place and therefore, compared to the other instruments, it is the most accurate.

Vernier caliper and micrometer caliper are examples of calipers. A caliper is an instrument with two jaws, widely used to determine the dimensions of linear dimensions. Both of these instruments uses two scales, one main scale and the vernier scale. These two scales are related to each other and therefore would increase the reliability of the estimate of the measurement. Usually, a vernier scale has ten divisions and nine divisions on the main scale. To sum up, the vernier scale makes the reading of the measurement accurate than common devices such as the straight rule that will give us only the rough estimate.

Over the previous paragraphs, the differences between the three instruments were being tackled. In the experiment however, the values being reported does not have a significant difference. The standard deviation computed in every table yielded a value close to zero thus proving that the instruments used in doesn’t have that much difference. Thus, the measurements tabulated are precise.

VI. CONCLUSION:

Accuracy in a measurement is very crucial in our daily life. Living in the world without proper measurement is unbearable not to mention unimaginable. This is why scientists keep creating instruments and devices that can measure an object accurately and precisely. In the experiment, three instruments for measurements were introduced - the straight rule, the vernier caliper, and the micrometer caliper. All of these instruments are good estimate in determining the measurement of an object. However, it should always be noted that these devices have their own limitations. For example, the micrometer cannot measure the depth of hollow cylinder. In this dilemma, we should always put into consideration the type of object measured and the kind of device used.

Sources: http://physics.bk.psu.edu/teaching/LabManuals/Physics211/Measurement%20Instructions.pdf

https://www.physics.upenn.edu/uglabs/lab_manual/Error_Analysis.pdf