Physic Laboratory 6Section: 4061

Introduction to the Lab: Measurement Lab # 1

RODNEY PUJADAPartners:

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Performance Date : 08/31/2011, Submission Date: 09/07/2011

Professor: Miguel Angel Moreno, Ph.D.

TABLE OF CONTENTS

1. Introduction ……………………………………………………………………………………………………………………… 1

2. Purpose ………………………………………………………………………………………………………………………….… 2

3. Equipment ……………………………………………………………………………………………………………..………… 2

4. Procedure ……………………………………………………………………………………………………………..………… 2

4.1. Dimensional measurement for the three objects.

4.2 Calculate the density for the three objects

5. Formulas and Calculations …………………………………………………………………………………….………. 3

5.1 Using the following formulas for each object.5.2 Calculate the volume of the three objects: using the table No 25.3 Measure the mass for three objects using the double pan balance.5.4 d Calculate the density for iron objects.

A) Using the caliper and micrometer, and the mass from the calculation in part 6.2:5,5, Calculate the Percentage of Error5.6 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. IntroductionAccurate measurement requires appropriate tools. When measuring a tabletop, for

instance, one could use a meter stick to produce a suitable measurement. The meter stick has gradations small enough to 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 reasoning one can see that measuring something like 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 1) is a fairly simple measurement 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

Micrometer caliperAnother type of caliper is known as the micrometer caliper. Often times these calipers consist of a barrel and shaft. As the barrel is turn the caliper opens and 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, 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 shaft. Finally, we add this number together. If we examine 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, we write our measurement as 8:769mm 0:005mm

Figure 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 equations for volume and density. Finally the experimental value of the density will be compares to the theoretical density of the three objects.

3. EquipmentCaliper, micrometer, ruler, 100mL graduated cylinder, double pan balance, and distilled water.4. Procedure

a. Dimensional measurement for the three objects.i. Measure three (3) objects using the vernier caliper

and three (3) objects using the micrometer caliper.ii. Weight the three objects using the double pan

balance.iii. Record the data

b. Calculate the density for the three objectsiv. Measure the volume from two objects (cylinder and sphere) using the 100

mL graduated cylinder.

v. Record the data.

5. Formulas and Calculations

5.1 Using the following formulas for each object.

Table No 2 : Experimental Data using the caliper and micrometerObjects Diameter Height Width Length Formula Volumen

(cm) (cm) (cm) (cm) cm³

Cylinder1.25 5.07 6.222

Block 3.58 0.64 3.80 V= H*W*L 8.707

Sphere2.530 8.479

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

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

Formula volume: V= diameter2

* π *height / 4 = (5.07 cm)2

* π * 1.25 cm/ 6 =6.22 cmᵌFor block: Data: length = 3.80 cm; Height = 3.58 cm; Width= 0.64 cm using the caliper

Formula volume: V= length * Height * Width = 3.80 cm * 3.58 cm * 0.64 cm= 8.70 cmᵌFor sphere: Data: Diameter = 2.530 cm using the micrometer

Formula volume: V= diameterᵌ * π / 6 = (2.530 cm)ᵌ * π / 6 = 8.48 cmᵌ5.3. Measure the mass for three objects using the double pan balance.

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

Table No 3: Mass of three objects (g)

5.4. Calculate the density 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

From caliper and scale measurements Objects Volumen Mass Density Theorical Density % Error

cm³ g g/cm³ g/mL Cylinder 6.22 56.7 9.11 Copper 8.97 -1.59

Block 8.71 23.6 2.71 Aluminum 2.70 -0.39Sphere 8.479 67.0 7.90 Steel 7.8 -1.31

For cylinder: Data: mass = 56.7 g.; volume = 6.22 cmᵌ Formula density : D= mass/ volume = 56.7 cm /6.22 cmᵌ = 9.11 g/mL

For block: Data: mass = 23.6 g.; volume = 8.71 cmᵌ Formula density : D= mass/ volume = 23.6 cm / 8.71 cmᵌ = 2.71 g/mL

For sphere: Data: mass = 67.0 g.; volume = 8.479 cmᵌ Formula density : D= mass/ volume = 67.0 cm / 8.479 cmᵌ = 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 mLMass of the sphere = 8.0 mL

From Graduated cylinder and scale measurements

Objects Volumen Mass Density Theorical Density % Error

cm³ g g/cm³ g/mL Cylinder 6.0 56.7 9.45 Copper 8.97 -5.35

Block 23.6 Aluminum 2.70 Sphere 8.0 67.0 8.38 Steel 7.8 -7.37

Objects Volumen Mass cm³ g

Cylinder 6.22 56.7Block 8.71 23.6

Sphere 8.479 67.0

For cylinder: Data: mass = 56.7 g.; volume = 6.0 cmᵌ

Formula density : D= mass/ volume = 56.7 cm /6.0 cmᵌ = 9.45 g/mL

For sphere: Data: mass = 67.0 g.; volume = 8.0 cmᵌ

Formula density : D= mass/ volume = 67.0 cm / 8.0 cmᵌ = 8.38 g/mL

5.5. Calculate the Percentage of Error: 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 = -1.59 %

B) For the table 4: For the sphere of steel% Error = (Experimental Density - Accepted density) *100 / Accepted density% Error = (Experimental Density – 7.8) *100 / 7.8 =% Error = ( 7.90– 7.8) *100 / 7.8 =% Error = -1.31 %

5.6. Relative Error Estimate and Analysis

A) Volume of the Block.Measure valued (MV) user a ruler to measure length, width, and heightAccepted valued (AV) uses a Vernier caliper to measure length, width, and height.% error = (MV – AV) *100 / AV% error =

B) Volume of the cylinder.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 of a sphereMeasure 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 OF THE EXPERIMENT

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 From caliper and scale measurements

Objects Volumen Mass Density Theorical Density % Error cm³ g g/cm³ g/mL

Cylinder 6.22 56.7 9.11 Copper 8.97 -1.59Block 8.71 23.6 2.71 Aluminum 2.70 -0.39

Sphere 8.479 67.0 7.90 Steel 7.8 -1.31A) 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.

From Graduated cylinder and scale measurements

Objects Volumen Mass Density Theorical Density % Error

cm³ g g/cm³ g/mL Cylinder 6.0 56.7 9.45 Copper 8.97 -5.35

Block 23.6 Aluminum 2.70 Sphere 8.0 67.0 8.38 Steel 7.8 -7.37

7. Conclusions 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.