physicsexp#1
TRANSCRIPT
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PAMANTASAN NG LUNGSOD NG MAYNILAIntramuros, Manila
COLLEGE OF SCIENCEDepartment of Physical Science
General Physics I
Experiment No.1UNCERTAINTY OF MEASUREMENT
Blasco, Julien Marise
Dizon, Jesiree Mae
Herrera, Khristine Marie
Juaban, Kim Alexie
Nualla, Allen Pierre
Quilantang, Leonard
Sibug, Alma Melissa
INTRODUCTION
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Measurement is the process of observing, recording and collecting of quantitative data. A measurement is made by comparing a quantity with a standard unit. Since this comparison cannot be perfect, measurements inherently include error.
In ancient times, the body ruled when it came to measuring. The length of a foot, the width of a finger, and the distance of a step were all accepted measurements. A well documented example (the first) is the Egyptian cubit which was derived from the length of the arm from the elbow to the outstretched finger tips. In England units of measurement were not properly standardized until the 13th century, though variations (and abuses) continued until long after that. In the U S A the system of weights and measured first adopted was that of the English, though a few differences came in when decisions were made at the time of standardization in 1836. In France the metric system officially started in June 1799 with the declared intent of being 'For all people, for all time'.
Measurement is important because it has been part of our daily lives. For an instance, food and raw materials are bought by weight or size and our environment is constantly monitored from air quality to weather conditions. Indeed, it is almost impossible to describe anything accurately or conduct our day without the use of measurement.
LIST OF MATERIALS/EQUIPMENTS:
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Steel ballWooden blockHollow cylindrical objectBook (Physics I Lab)Two coins (25¢ & 10¢)
Vernier CaliperMicrometer CaliperMeter StickGraduated Cylinder
PROCEDURE:
A. METER STICK1. Using the metric side of the meter stick, determine the length,
width and thickness of the book (Do not include the covers).2. Repeat step 1 using the English side of the meter stick (inches)3. Make five trials for each measurement.4. Determine the total number of pages of the book. Be sure to include
those pages marked I, ii and the like and find the thickness (by computation) of a single sheet of the book you used in the experiment using:
a. English systemb. Metric system
5. Compute for the area of the surface of a page of the book ina. English systemb. Metric system
DO NOT CONVERT.
6. Calculate the volume of the book in English and Metric system.7. Determine the experimental value for the relationship between:
a. A centimeter and an inch (use data on the length, width and depth)
b. A square centimeter and a square inch (Use computed value area)
c. A cubic centimeter and a cubic inch (use the computed value of volume)
8. Determine the % error by using the formula
True value- experimental value _________________________% error = True value X 100%
Where the true value in each case are:a. Length = 2.54b. Area = 6.45c. Volume = 16.39
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B. VERNIER CALIPER1. Measure in both English and the metric system the ff. dimensions of
a hollow cylindrical object.a. Outside diameterb. Depthc. Inside diameter
2. Make five trials for each measurement.3. Immerse the material you used in step 1 into a graduated cylinder
that is partially filled with water. Its displacement will give you the true volume of the object.
Determine the experimental volume of the hollow cylindrical object using the
data you gathered. Use the formula V= π4
(d2outside−d2inside )h
Compare it with the true volume by using the formula for the % error. NOTE: 1mL = 1cm 3
C. MICROMETER CALIPER Note: In opening or closing the cap between the anvil and the screw, do not rotate the thimble. Instead, use or rotate the milled head. Once a clicking sound is heard, it is an indication that a reading can be made. Do not force it further by rotating the thimble. Over-tightening will damage the caliper.
1. Close the cap between the anvil screw to get 0-reading. 2. Determine the diameter of a metal sphere. 3. Measure also the diameter and thickness of two different coins. 4. Make five trials for each measurement. 5. Determine the volume of each of the material used.
a. For the coins use the formula V=π r2h∨V=14π d2h
b. For the metal sphere use the formula V=16π d3
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DATA AND RESULTS:
Table 1. Meter Stick
No. of pages: 102 pages / 51 leaves
Thickness of one page: 0.7 mm
Table 2. Vernier Caliper
English Scale Metric Scale
Length
Trial
Length
Trial 1 10.8 1 27.52 10.8 2 27.53 10.8 3 27.54 10.8 4 27.55 10.8 5 27.5
Average 10.8 Average 27.5
Width
1 8.5
Width
1 21.52 8.4 2 21.53 8.5 3 21.54 8.4 4 21.55 8.5 5 21.5
Average 8.46 Average 21.5
Depth
1 0.4
Depth
1 12 0.4 2 0.93 0.3 3 14 0.3 4 15 0.3 5 1
Average 0.34 Average 0.98Average Area (in2) 91.37 in2 Average Area (cm2) 591.25 cm2
Average Volume (in3)
31.07 in3 Average Volume (cm3)
579.43 cm3
Outside Diameter (cm)
Trial 1 2.1 cm2 2.1 cm3 2.1 cm4 2.1 cm5 2.1 cm
Average (cm) 2.1 cm
Inside Diameter (cm)
1 1.6 cm2 1.6 cm3 1.6 cm4 1.6 cm5 1.6 cm
Average (cm) 1.6 cm
Depth
1 4.8 cm2 4.8 cm3 4.8 cm4 4.8 cm5 4.8 cm
Average (cm) 4.8 cm
Experimental Volume (cm3) 105.43cm3
True Volume (cm3) 100cm3
Percentage error 5.43%
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Table 3. Micrometer Caliper
Object Used Diameter Thickness
Coin 1
Trial Trial 1 11.39mm 1 0.19mm2 11.39mm 2 0.19mm3 11.39mm 3 0.19mm4 11.39mm 4 0.19mm
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5 11.39mm 5 0.19mmAverage (mm) 11.39mm 0.19mmVolume (mm3) 19.38mm3
Coin 2
1 20.39mm 1 0.30mm2 20.39mm 2 0.30mm3 20.39mm 3 0.30mm4 20.39mm 4 0.30mm5 20.39mm 5 0.30mm
Average (mm) 20.39mm 0.30mmVolume (mm3) 98.01mm3
Metal Sphere
1 5.41mm2 5.41mm3 5.41mm4 5.41mm5 5.41mm
Volume (mm3) 82.86mm3
ANALYSIS OF DATA:
The data that we have gathered from the three experiments were analyzed and we have finally arrived to these interpretations:
1. In experiment number 1, we could see that the measurements that we have gathered using the meter stick, both in English and Metric Scales in five different trials, are closely related to each other. Some measurements from different trials were the same as the ones gathered from a different trial. It only shows that the data we have gathered were of high precision. Due to the absence of the true
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measurement of the book we took our data from, we were not able to get the accuracy of our gathered data.
2. In experiment number 2, each datum that we have gathered using the Vernier Caliper was the same as the rest of the different trials. It shows that the precision of our gathered data was excellent. The experimental volume that we came up with was 105.43 cm3 and the true volume of the tube was 100 cm3. By computing for the percentage error, we arrived having 5.43% as our error. This means that the accuracy of our gathered data was still high.
3. In accordance to the data gathered in experiment number 2, we could say that our gathered data in experiment number 3 was also of excellent precision. This is due to the equality of the data for every trial, just like in experiment number 2. The true measurements of the diameter and thickness of the metal sphere and the two coins were also not given, causing us not to be able to compute for the percentage error of our work, which would determine the accuracy of the gathered data.
GUIDE QUESTIONS:
1. If several persons measured the thickness of the same coin with the same micrometer, there would still be a small spread in values measured. Give two reasons why this would be so.
A: The results may still vary because there may be a difference in the way each person uses the micrometer. Another reason is that there may also be differences in the way they read the micrometer.
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2. Define: a) precision b) accuracy
a) Precision - The degree to which repeated measurements under unchanged conditions show the same results.b) Accuracy - The degree of closeness of measurements of a quantity to that quantity's actual (true) value.
3. Does percent error pertain to accuracy or precision? Explain.
A: The percent error pertains to accuracy. We can determine the accuracy of the data gathered by getting the percent error because its purpose is to show the difference between the experimental value and the true value.
4. How could the error be improved in this experiment?
A: The results in the experiment can be improved by making several trials with several people observing. Taking enough time to take the measurements can also be helpful in getting more accurate results.
5. Why are several observations better than one experiment?
A: Several observations are better than one because many observers offer different varieties of results. Comparison between answers can be executed to determine which answer is the most accurate.
CONCLUSION & RECOMMENDATIONS:
There are many devices we can use to measure different objects. Such devices can give us different results depending upon the way we use each device. Several observers show a variety of results for every trial. Some of the trials gave us different numbers even though we were measuring the same object. From that experiment we have accomplished, we could finally say that precision is indeed the closeness of the measurement from one trial
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to the other. We could now also say that accuracy is the closeness of the experimental value to the true value.
This experiment and its results would be a lot better if there is a uniform object to be used for each group to be measured, whose true measurements are given in the book so that there would be a clear reference for us to depend on. These true measurements are also needed to compute for the accuracy of our data, which evidently shows how important it is to have these true measurements printed on the book as given data.
COMPUTATION SHEET:
TABLE 1. Meter Stick
English scale:Average: L: 10.8+10.8+10.8+10.8+10.8 = 54
54/5 = 10.8W:8.5+8.4+8.5+8.4+8.5 = 42.3 42.3/5 = 8.46D: 0.4+0.4+0.3+0.3+0.3 = 1.7
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1.7/5 = 0.34
Average Area:10.8 x 8.46 = 91.37 in2
Average Volume: 10.8 x 8.46 x 0.34 = 31.07in3
Metric Scale:Average: L:27.5+27.5+27.5+27.5+27.5 = 137.5
137.5/5 = 27.5 W:21.5+21.5+21.5+21.5+21.5 = 107.5 107.5/5 = 21.5 D: 1+0.9+1+1+1 = 4.9 4.9/5 = 0.98
Average Area: 27.5cm x 21.5cm = 591.25cm2
Average Volume: 27.5cm x 21.5cm x 0.98 cm = 579.43cm3
TABLE 2. Vernier Caliper
Average: Outside Diameter: 2.1+2.1+2.1+2.1+2.1=10.5 10.5/5 = 2.1 Inside Diameter: 1.6+1.6+1.6+1.6+1.6 = 8 8/5 = 1.6 Depth: 4.8+4.8+4.8+4.8+4.8=24 24/5 = 4.8
Experimental Volume :
V= π4
(d 2 outside−d2 inside )h
= 3.14
4 ( (2cm)2 – (1.6 cm)2) 4.8
EV= 5.43 cm3
EV= Volume of the coin + Volume of the water5.43 + 100 = 105.43 cm3
Percentage Error:
100cm−105.43cm3
100×100=5.43 %
TABLE 3. Micrometer Caliper
Volume:
Coin 1: V=π r2h
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= (3.14) (5.7)2 (0.19)
= 19.38 mm3
Coin 2 = V=π r2h
= (3.14) (10.2)2 (0.30)
= 98.01mm3
Metal Sphere: V=16π d3
= (1/6) (3.14) (5.41)3
= 82.86mm3