Lab 2 Records

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Apr 3, 2024

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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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B. Identify how measurement uncertainty affects interpretation of graphed data 1. Random measurement uncertainty is represented on the graph by error bars that extend above and below each point, indicating a range of values. 2. Reducing the random measurement uncertainty would affect the claims that could be made about the graph because the students could claim that the period of the swing increases more frequently with each increase in string length, therefore indicating a stronger positive correlation than can be claimed with the current values of the random measurement uncertainty. 3. The graph includes only the length of the string as pendulum length. i. How would the graph change if the students had correctly measured the length of the pendulum to the center of mass of the bob? The x-axis values would shift, but the graph will look the same. ii. Would plotting correct length measurements for the pendulum affect any of the claims that could be made from the graph? If so, how? If not, why not? It would not as the correlation and the error bars would remain the same with only the x-axis length values shifting. III. Final Wrap-up A. Update your general claim from Lab 01 Lab 01 Experimental Outcomes Organizer: P Period of Pendulum (DV) Mass of Pendulum (IV 1) Length of String (IV 2) Angle of Release (IV 3) Experimental Outcome: No Correlation found when the length of the string and angle of release held constant Experimental Outcome: Positive Correlation found when the mass of the pendulum and angle of release held constant Experimental Outcome: No Correlation found when the mass of the pendulum and length of the string held constant

Updated Experimental Outcomes Organizer: B. Evaluate the data and any observed patterns or trends i. We are confident in the period values we recorded using the stopwatch as the error bars use a small standard deviation. ii. We are confident that a best fit line would accurately describe the correlation between the IV (Independent Variable) and DV (Dependent Variable) as the graphs indicate a clear positive correlation. C. Consider a hypothetical exercise: Reducing Random Uncertainty We agree with Student 2 because the pendulum w ill no t continue to swing at 10 degrees the more it swings, making it an unreliable control variable and the period inaccurate. P Period of Pendulum (DV) Mass of Pendulum (IV 1) Length of String (IV 2) Angle of Release (IV 3) Experimental Outcome: No Correlation found when the length of the string and angle of release held constant Experimental Outcome: Positive Correlation found when the mass of the pendulum and angle of release held constant Experimental Outcome: No Correlation found when the mass of the pendulum and length of the string held constant

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