Lab M-1 Report

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Community College of Philadelphia *

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Apr 3, 2024

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Community College of Philadelphia Philadelphia, Pennsylvania Experiment Number: M-1 Title: Measurement of Length and Mass Written by: Physics 140, Section 003 Lab Instructor: Professor Indu Das Date: January 20, 2022

Experiment M-1 2 Purpose The purpose of this experiment is to familiarize with several basic but important laboratory measuring devices, to study some of the methods by which laboratory measurements are made, and finally, to study methods for determining the density and specific gravity of a body. Procedure * Part I Vernier Calipers 1. Close the vernier caliper jaws and record the reading. This provides a "zero correction" to be added to or subtracted from subsequent readings. 2. Determine the least count of the vernier scale. The least count is the smallest division which can be read directly on the measuring instrument. 3. Measure the lengths and diameters of the metal cylinders. Record the reading, apply the zero correction, and determine the average. * Part II Micrometer Calipers Caution: Tighten the micrometer only by means of the small ratchet head. Otherwise, the delicate threads may be damaged by excessive torque. 1. Determine the zero reading of the micrometer caliper. Determine the least count of the scale on the thimble. 2. Measure the diameters of the metal cylinders provided. Record the reading, apply the zero correction, and determine the average. * Part III Density as Calculated from Mass and Volume 1. Check the platform, triple-beam balance to see that it is balanced with the platform empty and all the sliding weight/indicators set to zero. The pointer at the end of the beams should point to zero or should oscillate by equal amounts above and below zero. 2. Weigh each metal cylinder. With the cylinder sitting on the platform, adjust the sliding weight/indicators until the beam is balanced. At balance the pointer at the end of the beam

Experiment M-1 3 should point to zero o should oscillate by equal amounts above and below zero. Record the masses of the metal cylinders. 3. Calculate the volume of the cylinders using equation V= π d 2 L 4 , the average lengths from part I, and the average diameters from part II. 4. Calculate the density of each cylinder using equation ρ = m V . 5. Compare these densities with the accepted values and calculate the percent error, using equation % Error Measured Value - Accepted Value Accepted Value   100 . * Part IV Specific Gravity by Archimedes’ Method 1. Check the overhead balance to see that it is balanced at zero. 2. Suspend one of the metal cylinders by a fine wire from the hook above the pan. Weigh the cylinder in air and record the weight in air in gwt. 3. Place a beaker of water on the support provided on the overhead, triple-beam balance. Adjust the apparatus until the metal cylinder is suspended submerged in water without touching the beaker. Find and record the apparent weight of the cylinder in water. 4. Calculate the specific gravity of the sample from equation w a w a − w w . Calculate the percent difference between this result and that implied by the results of part III step 4. 5. Repeat for the other metal cylinder.

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Experiment M-1 4 Data Sheets Part I: Vernier Calipers Zero Reading: _0______________ cm Least count: _0.005___________ cm Sample Material Reading 1 2 3 Average N/A cm cm cm cm Al Diameter 1.905 N/A Diameter, Corrected 1.905 1.905 Length 4.345 N/A Length, Corrected 4.345 4.345 Fe Diameter 1.270 N/A Diameter, Corrected 1.270 1.270 Length 5.095 N/A Length, Corrected 5.095 5.095 Part II: Micrometer Calipers Zero Reading: _0________________ cm Least Count: _0.001_____________ cm Sample Material Reading 1 2 3 Average N/A cm cm cm cm Al Diameter 1.904 N/A Diameter, Corrected 1.904 1.904 Fe Diameter 1.269 N/A Diameter, Corrected 1.269 1.269 Part III: Density as Calculated from Mass and Volume Sample Material Mass Volume Density, Calculated Density, Accepted Percent Error g cm 3 g/ cm 3 g/ cm 3 % Al 37 12.37 2.99 2.70 10.7

Experiment M-1 5 Fe 50 6.44 7.76 7.88 1.52 Part IV: Specific Gravity by Archimedes' Method Sample Material Weight in Air Apparent Weight in Water Specific Gravity Calculated Specific Gravity from Part III Percent Difference gwt gwt % Al 37.36 24.8 2.97 2.99 0.67 Fe 50.03 43.8 8.03 7.76 3.42

Experiment M-1 6 Calculations  Part I: * Aluminum cylinder: Average diameter = 1.905 + 1.905 2 = 1.905 cm Average length = 4.345 + 4.345 2 = 4.345 cm * Steel cylinder: Average diameter = 1.270 + 1.270 2 = 1.270 cm Average length = 5.095 + 5.095 2 = 5.095 cm  Part II: * Aluminum cylinder: Average diameter = 1.904 + 1.904 2 = 1.904 cm * Steel cylinder: Average diameter = 1.269 + 1.269 2 = 1.269 cm  Part III: * Aluminum cylinder: Volume: V Al = π d 2 L 4 = π ( 1.904 ) 2 ( 4.345 ) 4 = 12.37 cm 3 Density: ρ = m Al V Al = 37 12.37 = 2.99 g / cm 3 % Error = MeasuredValue − Accepted Value Accepted Value x 100 = 2.99 − 2.70 2.70 x 100 = 10.7 % * Steel cylinder: Volume: V Fe = π d 2 L 4 = π ( 1.269 ) 2 ( 5.095 ) 4 = 6.44 cm 3 Density: ρ = m Fe V Fe = 50 6.44 = 7.76 g / cm 3 % Error = MeasuredValue − Accepted Value Accepted Value x 100 = | 7.76 − 7.88 7.88 | x 100 = 1.52%  Part IV:

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Experiment M-1 7 * Aluminum cylinder: Specific Gravity Calculated = w a w a − w w = 37.36 37.36 − 24.8 = 2.97 g / cm 3 % Difference = | SecondValue − First Value | | Second Value + First Value | x 200 = | 2.97 − 2.99 | | 2.97 + 2.99 | x 200 = 0.67% * Steel cylinder: Specific Gravity Calculated = w a w a − w w = 50.03 50.03 − 43.8 = 8.03 g / cm 3 % Difference = | SecondValue − First Value | | Second Value + First Value | x 200 = | 8.03 − 7.76 | | 8.03 + 7.76 | x 200 = 3.42%

Experiment M-1 8 Answers to Questions 1. Compare the readings taken with the vernier calipers to those taken with the micrometer caliper. Are there deviations? Discuss reasons. The readings taken with the vernier calipers are different from those taken with the micrometer caliper. For example, the diameter of the steel cylinder was 1.270cm with the vernier caliper and 1.269cm with the micrometer caliper. There are deviations because of the different least counts of these two calipers. The vernier caliper can only measure to the 0.005cm and the micrometer caliper measures to the 0.001cm. 2. What is the numerical least count of each type of caliper? - For Vernier Caliper, the numerical least count of each type of caliper is 0.005 cm. - For Micrometer Caliper, the numerical least count of each type of caliper is 0.001 cm. 3. Why is the concept of "significant figures" important? The concept of “significant figures” is important because it is one of the ways we can determine the accuracy of measurements. 4. The derivation of specific gravity w a w a − w w w w = w a − F b F b = ρ x g xV  w w = w a − ρx g x V  ρ = w a − w w g xV Specific gravity = density of theobject density of the water = ρ o ρ w = ρ o w a − w w g x V = ρ o x g xV w a − w w = w a w a − w w w a = weight of object in air w w = apparent weight of object in water F b = buoyant force ρ = density g = acceleration due to gravity V = submerged volume

Experiment M-1 9

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Experiment M-1 10 Analysis and Discussion of Results Laboratory measuring devices in this experiment are vernier caliper and micrometer caliper, and they were used to measure diameters and lengths of the aluminum cylinder and steel cylinder. The least count of micrometer caliper is less than that of vernier caliper (0.001cm < 0.005cm), so the measurement results of the micrometer caliper are more accurate than those of the vernier caliper. In part III, density of two cylinders was calculated from mass and volume. The percentage error will determine the accuracy of the measurements relative to the acceptable value. The percent error of the aluminum cylinder is high (10.7%), so it shows a large error in the measurements. The percent error of the steel cylinder is low (only 1.52%), so it means the result is close to the accepted measurements. In part IV, the specific gravity of two cylinders was calculated by Archimedes' Method. Thus, there are two experimental measurements (the calculated density specific gravity and the specific gravity using Archimedes’ method), percent difference will compare the results of those two dimensions. The percent difference for the aluminum cylinder is 0.67%, while the percent difference for the steel cylinder is 3.42%. In conclusion, we were introduced to different devices that used to measure object’s length, diameter, and mass. In this experiment, the density calculated from mass and volume is comparable to the specific gravity calculated using Archimedes’ method. Archimedess’ method is useful because it can even determine the specific gravity of oddly shaped objects.

Lab M-1 Report

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