Old Measurements 010422

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University of Central Arkansas *

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1400

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Mechanical Engineering

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Feb 20, 2024

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Measurements 1 Measurements v010422_PD Objectives: The student will become familiar with some key pieces of glassware and instrumentation. The student will learn to record measurements correctly, assess the precision of a piece of glassware or instrument, and identify possible errors that can occur. Background: (Section E.2-E.4 in Tro 2 nd Edition) The quality of experimental measurements is affected by the number of digits that can be reported for the equipment used for the measurement, the number of measurements made, and the experimenter. When making a measurement, the investigator should report all digits that can be read with certainty plus one additional digit that is the estimated or uncertain digit. The meaningful digits of a measurement are called significant figures. Precision refers to the reproducibility of measurements. The closer the measurements are to one another, the greater the precision. Increased precision can be observed in measurements obtained from instruments that can be read to a greater number decimal places with certainty. Accuracy refers to how close a measurement is to the real value. The accuracy of the measurement reflects the quality of the instrument. An instrument that can be read with more digits of certainty typically yields a more accurate value assuming that the instrument has been properly calibrated. Errors occur during the collection of data. Errors are of two types: systematic and random. Systematic errors are caused by a defect in the analytical method, by an improperly functioning instrument, or by the analyst. Systematic errors cause a decrease in the accuracy of a set of measurements. Systematic errors can be corrected by calibration of instrumentation, alteration of the procedure, use of glassware and instruments that can be read to a greater number of significant figures, and by attentiveness of the analyst. Random errors cause a reduction in the precision of a series of measurements. Random errors are uncontrollable errors such as electrical fluctuations experienced by balances. A single measurement is insufficient to determine the accuracy and precision of an instrument. It is therefore common practice to make repetitive measurements for a value. The precision of a series of measurements is indicated using the mean of the results ± the error. Example: A student measured the mass of a tennis ball three times on a lab balance that read to the first decimal place. They recorded the mass as 54.4 g, 54.7 g, and 54.1 g. The mean of all of these values is 54.4 g. Assuming reasonable balance calibration, it can be concluded that the true mass of the ball is the range of 54.1 g and 54.7 g. The student reports this more succinctly as 54.4 ± 0.3 g. The accuracy of a series of measurements can only be assessed if the true value is known. But, by using a calibrated instrument and making several measurements the probability that the mean of the measurements and the real value will be the same is improved. https://youtu.be/sX_op1xBaHY https://youtu.be/Y5sUB0suJ9A

Measurements 2 Safety: Wear safety goggles. Wash your hands thoroughly before leaving the lab. Procedure: Measuring Lengths with Rulers (Rulers 1, 2, and 3 are printed on the next page) 1. On your data sheet, indicate the number of digits past the decimal that a measurement made with Ruler 1 should contain. 2. Use Ruler 1 to measure the length of the wooden block. Record you value, including units. 3. Repeat steps 1 and 2 for Ruler 2 and Ruler 3. 4. Report your data to the instructor. 5. Once all measurements have been obtained the class results will be posted. Record the class results and determine the mean and ± error for each ruler. Measuring Liquid Volumes using a Buret and Graduated Cylinder 1. On your data sheet, indicate the number of decimal places that should be recorded for the buret and the number of decimal places that should be recorded for a 10-mL graduated cylinder. 2. Fill the buret to approximately the 0 mL mark with tap water. 3. Read the initial water level of the buret (using the appropriate number of digits). Record this under Trial 1. Include units. 4. Dispense about 5 mL of tap water from the buret into a 10-mL graduated cylinder. 5. Record the new volume of the buret under Trial 1. Include units. 6. Record the volume of the water in the graduated cylinder under Trial 1. Include units. 7. Empty and dry the graduated cylinder. 8. Repeat steps 3-7 for Trial 2 and Trial 3 beginning with the current volume in the buret. 9. Determine the difference between the buret and graduated cylinder readings. Measuring Masses with Balances 1. On your data sheet indicate the number of places past the decimal that should be recorded for the balance. 2. Tare the balance. 3. Place a rubber stopper on the balance and record the mass as mass 1, balance 1. Include units. 4. Remove the object. Let the balance come to zero and tare balance again. 5. Replace the stopper on the same balance and record the mass as mass 2, balance 1. Include units. 6. Remove the object. Let the balance come to zero and tare balance for a third time. 7. Replace the stopper on the same balance and record the mass as mass 3, balance 1. Include units. 8. Repeat steps 2-7 two more times using two other balances but the same rubber stopper. The second balance used should be balance 2, and the third balance used should be balance 3. https://youtu.be/t4K-3_H5kxU F

Measurements 3 Data and

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Measurements 4 Results Measuring Lengths with Rulers # of decimal places expected using Ruler 1 ________ reading 1 st ruler ________ # of decimal places expected using Ruler 2 ________ reading 2 nd ruler ________ # of decimal places expected using Ruler 3 ________ reading 3 rd ruler ________ Class Results Ruler 1 Ruler 2 Ruler 3 ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ Mean Measurement Difference between Mean Measurement and Lowest Measurement Difference between Mean Measurement and Highest Measurement Mean ± Error Ruler 1 ________ ________ ________ _________________ Ruler 2 ________ ________ ________ _________________ Ruler 3 ________ ________ ________ _________________

Measurements 5 Measuring Liquid Volumes using a Buret and Graduated Cylinder # of places past the decimal that should be listed from a buret ________ # of places past the decimal that should be listed from a 10-mL graduated cylinder ________ Trial 1 Trial 2 Trial 3 Initial Buret Reading __________ __________ __________ Final Buret Reading __________ __________ __________ Volume of Water Dispensed by Buret __________ __________ __________ Volume of Water in Graduated Cylinder __________ __________ __________ Difference between the Buret and Graduated cylinder readings (abs. value) __________ __________ __________ Measuring Masses with Balances # of places past the that should be listed for a reading from the laboratory balance ________ Balance 1 Balance 2 Balance 3 Mass 1 ____________ ____________ ____________ Mass 2 ____________ ____________ ____________ Mass 3 ____________ ____________ ____________ Mean Measurement Difference between Mean Measurement and Lowest Measurement Difference between Mean Measurement and Highest Measurement Mean ± Error Balance 1 ________ ________ ________ _________________ Balance 2 ________ ________ ________ _________________ Balance 3 ________ ________ ________ _________________

Measurements 6 Pre-laboratory Assignment 1. Errors in measurements can be classified as random or systematic. a. Define random error. b. Define systematic error. 2. A sample of salt was massed three times. The readings were 1.0639 g, 1.0636 g and 1.0642 g. Express the mass of the salt with the correct number of significant figures. Include the error of the measurement in your answer. 3. A student measured the same block with two different rulers to obtain a length of 20.6 cm and 20.55 cm. Which of these measurements is more precise? Explain. 4. A disreputable grocer places their thumb on the scale every time they weigh produce to sell to a customer. This introduces an obvious error in the measured mass of the produce. What kind: systematic or random?

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Measurements 7 Post-Laboratory Questions 1. Which ruler, ruler 2 or ruler 3, from Part I exhibited the greatest amount of precision? Explain. 2. What type of error, random or systematic, is responsible for the different readings obtained by the class for Ruler 3? Explain. 3. (a) Which volume reading is more precise, that obtained from the buret or the 10-mL graduated cylinder? Explain. (b) Compare the differences between the buret and graduated cylinder readings. Does your cylinder consistently read more than or less than the buret for the same volume? (c) If you failed to properly dry the cylinder prior to dispensing the next trial from the buret, does this represent systematic or a random error? 4. List 2 errors likely responsible for the fluctuation in readings obtained for mass of the stopper taken on balance 1. State whether these errors are random or systematic. Explain.

Measurements 8 5. What error is likely responsible for the mass of the stopper changing depending on the balance used? Is it a random error or systematic error? Explain. 6. Identify each of the following as being due to random error or systematic error. i. A student was massing a block. As a classmate passed the balance the student noticed that the mass changed. Random Systematic ii. A student massed a block on one balance; he then massed it again on a different balance. The mass changed. Random Systematic iii. Two students read the same buret. One read the volume of liquid as 10.91 mL, the other read the volume as 10.89 mL. Random Systematic Explain your answer to question 6 part III.