PHYS 253 - Module 1 - Lab 3

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Aerospace Engineering

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Apr 3, 2024

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Measurements and Uncertainty PRE-LAB QUESTIONS 1. Use Figure 4 to measure the diameter of the quarter. Main scale reading: 24 mm Vernier scale reading: 1 ∗ 0.05 = 0.05 mm Main scale + Vernier scale: 24.05 mm 2. Why is uncertainty important to consider when reporting data? Measurement uncertainty is important because it provides an understanding of the limitations and potential errors associated with any measurement. ©eScience Labs, 2014 Figure 4: A quarter being measured by a caliper.

Measurements and Uncertainty EXPERIMENT 1: RULERS VS. CALIPERS Data Sheet Table 1. Ruler and Caliper Measurements Object Ruler Caliper Measurement (cm) Uncertainty (cm) Measurement (cm) Uncertainty (cm) Marble Diameter 1 cm 1.5 ± 0.1 cm 2 cm 2 ± 0.5 cm Washer (Outer Diameter) 1.73 cm 1.73 ± 0.1 cm 1.62 cm 1.62 ± 0.1 cm Washer (Inner Diameter) 0.9 cm 0.9 ± 0.5 cm 0.53 cm 0.53 ± 0.1 cm Washer Thickness 0.5 cm 0.5 ± 0.5 cm 0.03 cm 0.03 ± 0.1 cm String Length 612 cm 612 ± 0.1 cm 599 cm 599 ± 0.1 cm Styrofoam® Cup Height 8.12 cm 8.12 ± 0.1 cm 8 cm 8 ± 0.1 cm Post-Lab Questions 1. Compare the measurements for objects using the ruler and caliper and write a general statement on when it is more beneficial to use a ruler rather than a caliper. Choosing between a ruler and a caliper depends on the specific requirements of the measurement task. Rulers are preferable for quick and simple measurements of larger objects, while calipers are better suited for tasks demanding a higher degree of accuracy, especially for smaller and more intricate dimensions. Selecting the appropriate tool depends on the precision needed for the particular application. 2. Comment on accuracy vs. precision for rulers and calipers. Rulers: Rulers generally offer accuracy for larger measurements but may lack precision due to larger scale increments. They are suitable when a close approximation is sufficient. Calipers: Calipers excel in precision, providing accurate measurements for smaller details. Their fine scale increments make them ideal for tasks requiring a high level of accuracy. Rulers prioritize accuracy over precision, making them suitable for general measurements, ©eScience Labs, 2014

Measurements and Uncertainty while calipers prioritize precision, ensuring accurate readings for more intricate dimensions. 3. What are the sources of uncertainty when using a ruler and caliper? Sources of Uncertainty for Rulers: Parallax Error: Misalignment of the eye with the measurement markings on the ruler can introduce errors, especially when viewing from an angle. Instrumental Limitations: Rulers may have inherent imperfections, such as uneven markings or slight deformities, affecting measurement accuracy. Human Error: Inconsistent or imprecise placement of the ruler on the object or misinterpretation of the markings can contribute to uncertainties. Temperature Effects: Changes in temperature may cause the ruler to expand or contract, leading to variations in measurements. Sources of Uncertainty for Calipers: Zero Error: Calipers may have a zero point that is not perfectly aligned, resulting in systematic errors if not properly calibrated. Instrumental Precision: While calipers are designed for precision, variations in manufacturing quality can affect their accuracy. Friction: Friction in the moving parts of the caliper can lead to inconsistent readings, especially if not properly lubricated. Operator Skill: The accuracy of caliper measurements depends on the skill and experience of the person using them. Temperature Effects: Like rulers, calipers can be sensitive to temperature changes, causing expansion or contraction and influencing measurements. ©eScience Labs, 2014

Measurements and Uncertainty EXPERIMENT 2: THE SPRING FORCE SCALE Data Sheet Table 2. Spring Scale Measurements Object 5 N Spring Scale Weight (g) Uncertainty (g) 10 N Spring Scale Weight (g) Uncertainty (g) Masking Tape 71 g 71 ± 10 g 82 g 71 ± 10 g Stopwatch 32 g 32 ± 10 g 43 g 43 ± 0 g Set of Masses 82 g 82 ± 5 g 91 g 91 ± 5 g Modeling Clay 490 g 490 ± 10 g 498 g 498 ± 5 g Post-Lab Questions 1. What are the advantages and disadvantages of using a spring scale to measure weight? Advantages of Using a Spring Scale to Measure Weight: Ease of Use: Spring scales are user-friendly and straightforward, making them easy for individuals of various skill levels to operate. Portability: Spring scales are often compact and lightweight, making them easily portable for measuring weight in different locations. Cost-Effective: Compared to some other types of scales, spring scales tend to be more affordable, making them accessible for a wide range of applications. Quick Measurements: Spring scales provide rapid measurements, making them suitable for tasks where speed is essential. Durability: Spring scales are generally robust and durable, with fewer delicate components that may be prone to damage. Disadvantages of Using a Spring Scale to Measure Weight: Limited Precision: Spring scales may lack the precision required for highly accurate measurements, especially in scientific or industrial settings. Non-Linearity: The relationship between the force applied and the scale's indication may not be perfectly linear, leading to potential errors, particularly at extreme ends of the scale. Limited Weight Range: Spring scales are typically designed for specific weight ranges, and using them outside these ranges may result in inaccurate measurements. Temperature Sensitivity: Changes in temperature can affect the accuracy of spring scales, as the elasticity of the spring may vary. ©eScience Labs, 2014

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