Lab 2 Records

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University of Cincinnati, Main Campus *

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2001L

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Physics

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Apr 3, 2024

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docx

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Uploaded by DukeGrasshopper4065

Lab 02: Introduction to Measurement Uncertainty I. Uncertainty Due to Measuring Techniques  The uncertainty of the stopwatch is ±0.01s A. Data: String length: 0.49 m Mass of the pendulum: 0.050kg Angle of release: 10° Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 1.25s 1.32s 1.28s 1.26s 1.28s Trial 6 Trial 7 Trial 8 Trial 9 Trial 10 1.34s 1.26s 1.33s 1.28s 1.28s B. Standard Deviation: 0.0312s C. More about standard deviation i. Based on the description for standard deviation (σ), what does a small σ indicate about the spread of the data around the mean? Data with a smaller σ contains a smaller spread of data. ii. Are values reported with larger or smaller values for σ more accurate? Explain. Data with smaller values of σ contain more accurate data most of the values are within a close range of each other. D. Uncertainty of scale vs technique You now have two uncertainties associated with the period data collected during Lab 01, including (1) the uncertainty of the stopwatch due to its scale and (2) the uncertainty of the technique whereby a person uses the stopwatch to time an event. Which value for uncertainty makes sense to include with your period measurements collected during Lab 01? Indicate this value in your lab records and provide reasoning for the use of this single value over the other. The uncertainty of the technique whereby a person uses the stopwatch to time an event makes sense to include with the period measurements collected during Lab 01 because some values deviated more than ±0.01s, therefore indicating error on the part of the person operating the stopwatch more than error on the stopwatch itself. E. Add uncertainty values to graphs from Lab 01 E xperiment with mass of the pendulum as an independent variable

In this experiment, the Control Variables are string length (0.533m) and angle of release (20°). The Independent Variable is the mass of the pendulum (0.050kg to 0.130kg). As the mass of the pendulum increased from 0.050kg to 0.090kg, the period of the pendulum's swing did not increase, proving no correlation between the two variables. Experiment with angle of release as an independent variable In this experiment, the Control Variables are string length (0.533m) and mass of the pendulum (0.050kg). The Independent Variable is the angle of release (10° to 50°). As the angle of release increased by 10°, the period of the pendulum's swing did not increase, proving no correlation between the two variables. Experiment with string length as an independent variable

In this experiment, the Control Variables are angle of release (20°) and mass of the pendulum (0.050kg). The Independent Variable is the string length (0.245m to 0.533m). As the string length increased each time, the period of the pendulum's swing increased as well, proving a positive correlation between the two variables. II. Types of measurement uncertainty A. Identify and reduce uncertainty in measurements. When investigating the impact of pendulum length on period, students commonly only measure and record the length of the string. However, the length of the pendulum should be measured to the center of mass of the pendulum bob, as shown in Figure 2. Address the following questions in your lab records. 1. The above mistake leads to systematic measurement uncertainty, as all measurements would be off by a similar length. This uncertainty could be reduced for this scenario by measuring the length of the string from the end of the string to the center of mass of the pendulum bob. 2. Other sources of uncertainty include the measurement of the angle on the protractor, which leads to random uncertainty, the mass of the pendulum bob, which leads to random uncertainty, the tape measure used to measure the length of the string, which leads to random uncertainty, and the beginning and end of the stopwatch time, which leads to random uncertainty. 3. If the pendulum investigation were to be repeated, we could use a protractor with smaller, more accurate measurements to reduce the measurement uncertainty of the angle, a scale that provides a more accurate reading that reduces human error, such as a digital scale, to reduce the measurement uncertainty of the mass of the pendulum bob, a tape measure with smaller, more accurate measurements to reduce the measurement uncertainty of the length of the string, and an automated stopwatch to reduce human error while timing the period of the pendulum.

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