Report 1 Measurement Physics 6

Physic Laboratory Laboratory 6 Section: 4061

Introduction to the Lab: Measurement Lab # 1

RODNEY PUJADA Partners: …………………………………….. …………..………………………... Performance Date : 08/31/2011, Submission Date: 09/07/2011 09/07/2011 Professor: Miguel Angel Moreno, Ph.D.

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TABLE OF CONTENTS 1. Introduction ………………………………………………………………………………………………………… …………… 1 2. Purpose ………………………………………………………………………………………………………… ……………….… 2 3. Equipment ………………………………………………………………………………………………………… …..………… 2 4. Procedure ………………………………………………………………………………………………………… …..………… 2

5.

4.1. 4.1.

Dime Dimens nsio iona nall mea measu sure reme ment nt for for the the thre three e obj objec ects ts..

4.2 4.2

Calc Calcu ulate late the the densi ensity ty for for th the thre three e obje object cts s

Formulas and Calculations

…………………………………………………………………………………….………. 3 5.1 5.1 Usin Using g th the fo follow llowin ing g for formu mula las s fo for eac each h obj objec ect. t. 5.2 5.2 Calc Calcul ulat ate e the the vol volum ume e of of the the thre three e obj objec ects ts:: usin using g the the table No 2 5.3 5.3 Meas Measu ure the the mass mass for for thre three e obje object cts s usin using g the the doub double le pan balance. 5.4 5.4 d Cal Calcula culate te the the densi ensity ty for for iro iron objec bjects ts.. A) Using the caliper and micrometer, and the mass from the calculation in part 6.2: 5,5, Calculate the Percentage of Error 5.6 Relative Error Estimate and Analysis





6.

Experimental Results

…………………………………………………………………………………………….………,. 6 A) Using the caliper and micrometer, and the mass from the calculation in part 6.2: B) Using the caliper and micrometer, and graduated cylinder to measure the mass of the three objects: 7. Conclusions …………………………………………………………………………………………………………… ……..… 6





1. Intr Introd oduc ucti tion on Accurate measurement requires appropriate tools. When measuring a tableto tabletop, p, for instance, instance, one could could use a meter meter stick stick to produc produce e a suitab suitable le measu measure reme ment nt.. The The mete meterr stick stick has has grada gradati tion ons s small small enou enough gh to attain attain a measurement to within millimeters. Therefore, one can make a measurement accurate to within a thousandth of a meter. This is good accuracy if the table is roughly a meter or longer. To measure a table top the most appropriate instrument would be: (a) a ruler (b) a micrometer, and (c) a vernier caliper By this this reason reasonin ing g one one can can see that that meas measur urin ing g some someth thin ing g like like the the thickness of a pencil with a meter stick would be inappropriate. Assuming a pencil is roughly 5 millimeters in diameter; one would want a tool that could give measurements accurate to a fraction of a millimeter. The vernier and micrometer calipers were developed to perform such measurements. The vernier caliper (figure (figure 1) is a fairly simple measuremen measurementt tool. It has two parts: a stem with the main scale (cm, mm, and inches) and the vernier, a secondary scale, which slides along the stem and allows for identification of fractions of the main scale. Each part of the caliper culminates in a jaw to grasp the item being measured. Ten vernier scale divisions fit within nine stem divisions (remember the stem is the fixed part), so each vernier division is 9/10 as long as a stem division. When the jaws of the caliper are closed, the first line of the vernier, the zero line, coincides with the zero line of the main scale. This means that the first division of the vernier is 0.1 mm from the first main scale division, the third division of the vernier is 0.3 mm away, etc. To make a measurement with the vernier caliper, the jaws must be tightly closed around an object. Wherever the zero line of the vernier falls indicates the number in the tenths place of the measurement. The next line on the vernier that aligns with the main scale indicates the hundredths place. (Refer to figure 2 for examples)

Figure No1





closes. Each turn is usually one-half of a millimeter. To measure with a caliper, close the caliper gently till it just closes (don't crank it closed). Make a reading, if the caliper is in good shape it will read zero. It is likely that it will not, read the zero value, you will either need to add or subtract this from your final measurement. After this reading is made, made, open the caliper and close it gently on the object you are measuring (don't crank it closed). The shaft will have millimeter and half millimeter marks, read over until you reach the thimble. Next you read the number on the thimble that is aligned with the laterial line on the the shaf shaft. t. Fina Finall lly, y, we add add this this numb number er toge togeth ther er.. If we exam examin ine e the the micrometer scale on in Figure 2, we see that the shaft reads 8.500mm and the thimble reads 0.269mm. The digit 9 is an estimation of the position of the line on the shaft between 0.260mm and 0.270mm. Now we add our two readings 8:500mm+0:269mm = 8:769mm. Since there is no Vernier scale we make a generous estimate of the uncertainty of the last digit, as 1/2 of the smallest division. x = 0:005mm. Now, Now, we write our measurement measurement as 8:769mm 0:005mm

Fig ure No2 2. Purpose: The purpose of this laboratory is to gain experience using the caliper and micrometer to measure length, width, height for the objects. We will do this laboratory by measuring the measures of a copper cylinder, one aluminum block, and steel sphere, using the t he equations for volume and density. Finally the experimental value of the density will be compares to the theoretical density of the three objects. 3. Equi Equipm pmen entt Caliper, micrometer, ruler, 100mL graduated cylinder, double pan balance, and





i. Measure three (3) objects objects using the vernier vernier caliper caliper and three (3) objects using the micrometer caliper. ii. Weight Weight the three objects objects using using the double double pan balance. balance. iii. iii. Reco Record rd the the dat data a b. Calculate the density for the three t hree objects iv. Measure the volume volume from two two objects objects (cylinder (cylinder and and sphere) sphere) using the 100 mL graduated cylinder. v. Reco Record rd the the data data.. 5. Formulas and Calculations

5.1

Usin Us ing g the the foll follow owin ing g form formul ulas as for for each each obje object ct..

Table No 2 : Experimental Data using the caliper and micrometer

Objects

Diamete r

Height

Width

Length

(cm)

(cm)

(cm)

(cm)

1.25

5.07

Cylinder

3.58

Formula

Volum en cm³ 6.222

0.64

3.80

V= H*W*L

8.707

Block 2.530

8.479

Sphere

Calculate the volume of the three objects: using the table No 2 5.2.

For cylinder: Data: height = 5.07 cm; Diameter= 1.25 cm using the caliper 2

2

Formula volume: V= diameter * π *height / 4 = (5.07 cm) * π * 1.25 cm/

ᵌ







Formula volume: V= length * Height * Width = 3.80 cm * 3.58 cm * 0.64

Objects Cylinder Block Sphere

Volum en

Mass

cm³ 6.22 8.71 8.479

g 56.7 23.6 67.0

cm= 8.70 cmᵌ For sphere: Data: Diameter = 2.530 cm using the micrometer Formula volume: V=

diameterᵌ * π / 6 = (2.530 cm)ᵌ * π / 6 = 8.48 cmᵌ

Measure the mass for three objects using the double pan balance. 5.3.

For cylinder: Data: mass = 56.7 g For block: Data: mass = 23.6 For sphere: Data: mass = 67.0

Table No 3: Mass of three objects (g)

5.4. Calculate the density for for iron objects A) Using the caliper and micrometer, and the mass from the calculation in part 6.2: Table No 4: Experimental data using micrometer and caliper with theorical density





Formula density : D= mass/ volume = 67.0 cm / 8.479 cm ᵌ = 7.90 g/mL B) Using the caliper and micrometer, and graduated cylinder

to measure the mass of the three objects: Table No 5: Experimental data using micrometer and caliper and the mass from the graduated cylinder. Mass of the cylinder = 6.0 mL Mass of the sphere = 8.0 mL From Graduated cylinder and scale measurements meas urements

Objects

Cylinder Block Sphere

Volume n cm³ 6.0 8.0

Mass g 56.7 23.6 67.0

Densit y g/cm³ 9.45 8.38

Theorical Density

g/mL Copper Aluminum Steel

% Error 8.97 2.70 7.8

-5.35 -7.37

For cylinder: Data: mass = 56.7 g.; volume = 6.0 cm ᵌ Formula density : D= mass/ volume = 56.7 cm /6.0 cm ᵌ = 9.45 g/mL

For sphere: Data: mass = 67.0 g.; volume = 8.0 cm ᵌ Formula density : D= mass/ volume = 67.0 cm / 8.0 cm ᵌ = 8.38 g/mL

5.5. 5.5. Calc Calcul ulat ate e the the Perc Percen enta tage ge of Erro Error: r: A) For the table 4: For the cylinder of copper. % Error = (Experimental Density - Accepted density) *100 / Accepted density % Error = (Experimental Density – 8.97) *100 / 8.97 = % Error = ( 9.11– 8.97) *100 / 8.97 =





% error =

B) Volume Volume of the the cylind cylinder. er. Measure valued (MV) user a vernier caliper to measure diameter Accepted valued (AV) uses a micrometer to measure diameter. % error = (MV – AV) *100 / AV % error =

C) Volume Volume of a sphe sphere re Measure valued (MV) user a vernier caliper to measure diameter Accepted valued (AV) uses a micrometer to measure diameter. % error = (MV – AV) *100 / AV % error =

6. RESULT RESULT OF THE EXPER EXPERIMEN IMENT T A) Using the caliper and micrometer, and the mass from the calculation in part 6.2: Table No 4: Experimental data using micrometer and caliper with theorical density





Objects

Cylinder Block Sphere

Volume n cm³ 6.0 8.0

Mass g 56.7 23.6 67.0

Densit y g/cm³ 9.45 8.38

Theorical Density

g/mL Copper Aluminum Steel

% Error 8.97 2.70 7.8

-5.35 -7.37

7. Conc Conclu lusi sion ons s When we compare the ruler and the caliper, we find the caliper is more accuracy than the ruler by approximately ten percent of analytical error. •

•

•

When we compare the caliper and the micrometer, we find the caliper is more accuracy than the ruler by approximately ten percent of analytical error. When we compare the density from the measurement from the caliper and micrometer versus the volume from the graduated cylinder we find more percent of error if we take the density of the graduated cylinder.

Report 1 Measurement Physics 6

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