Lab Measurement and Uncertainty for Physics

Lab 1 Measurements and Uncertainty “Pre-Lab Questions” 1. “Use Figure 3 to measure the diameter of the quarter (in mm).” 24mm ± 0.025 mm 2. Why is uncertainty important to consider when reporting data?” Uncertainty tells us the possible range of values within which the actual value lies. The smaller the range, the more accurate the measurement. So, it’s important to consider uncertainty when reporting data because it indicates the accuracy. “Experiment 1: Rulers vs. Calipers” “Table 1: Ruler and Caliper Measurements” “Object” “Marble Diameter” “Washer (Outer Diameter)” “Washer (Inner Diameter)” “Washer Thickness” “String Width” “Styrofoam® Cup Height” “Ruler” Measurement Uncertainty (cm) (cm) 1.3 ±0.05 1.8 ±0.05 0.8 ±0.05 0.1 ±0.05 0.2 ±0.05 9.1 ±0.05 “Caliper” Measurement Uncertainty (cm) (cm) 1.38 ±0.0025 1.87 ±0.0025 0.875 ±0.0025 0.15 ±0.0025 0.17 9.14 ±0.0025 ±0.0025 “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 than a caliper.” It’s more beneficial to use a ruler to measure flat (two-dimensional) objects. 2. “Comment on accuracy vs. precision for rulers and calipers.” Accuracy refers to how close a measurement is to the actual value. Precision is a measure of reproducibility of a measurement. Calipers are better than rulers in accuracy. With regards to precision, rulers could be better than calipers because they do not require calibration. However, Lab 1 Measurements and Uncertainty human errors could make rulers imprecise. Calipers, when properly calibrated, could be just as precise. 3. “Where are the sources of uncertainty when using a ruler and caliper?” One major source of uncertainty is that objects in unusual shapes are not amenable to being measured by a ruler or caliper (e.g., the diameter of a sphere is hard to measure by a ruler). Other sources of uncertainty include improper use of a ruler and a caliper (e.g., not measuring the right way), incorrect reading, improper calibration, faulty instruments. The uncertainty was 0.1cm/2 = ± 0.05 cm on a ruler and 0.05mm/2 = ±0.0025 cm on a caliper. “Experiment 2: The Spring Force Scale” “Table 2: Spring Scale Measurements” “Object” Stopwatch Modeling Clay Roll of Masking Tape Single Hole Punch 5 N Spring Scale Weight (g) 210 470 60 50 Uncertainty (g) Uncertainty (g) ±5 ±5 ±5 10 N Spring Scale Weight (g) 160 440 20 ±5 20 ±10 ±10 ±10 ±10 1. “What are the advantages and disadvantages of using a spring scale to measure weight?” Advantages: easy to carry and use; no need to have reference weights; gives relatively accurate results when calibrated properly. Disadvantages: must be continuously calibrated because the stiffness of the spring can decrease over time; not good for measuring heavy and bulky objects. 2. “What are sources of uncertainty when using a spring scale?” Sources of uncertainty include improper calibration of scale and the change of stiffness of the spring. The uncertainty was 5g for a 5N spring scale and 10g for 10N spring scale. “Experiment 3: The Stopwatch” “Table 3: Time Data for Dropped Marble” “Drop (Trail)” “1 ” “2 ” “Time (s)” .57 .50 Lab 1 Measurements and Uncertainty “3 ” “4 ” “5 ” .48 .40 .38 1. “What are the advantages and disadvantages of using a stopwatch to measure time?” Advantages: A stopwatch can be more accurate than a normal clock. Disadvantages: Stopwatches are prone to human errors because they depend on human reflexes and judgment. 2. “What are sources of uncertainty when using a stopwatch?” The major source of uncertainty is human error (human reflexes) in starting and ending at the right time. Another source of uncertainty would be accuracy and precision of the stopwatch itself. The uncertainty for the stopwatch was ± 0.5 seconds. “Experiment 4: Density of the Mass Set” “Table 4: Mass Set Density Data” “Quantity” “Height (cm)” “Base Edge Length, b (cm)” “Volume, V (cm3)” “Mass (g)” “Density (g/cm³)” “Measurement” 2.3 “Uncertainty” ±0.0025 1.5 ±0.0025 13.4 “N/A” 100 7.46 ±10 “N/A” “Post-Lab Questions” 1. “Use Table 5 to determine what material the mass set is made of? Be sure to take your uncertainty into consideration.” “Table 5: Known Densities of Various Materials” “Material” “Aluminum” “Copper” “Lead” “Nickel” “Density at 20°C” “2.70 g/cm³” “8.92 g/cm³” “11.34 g/cm³” “8.90 g/cm³” Lab 1 Measurements and Uncertainty “Silver” “Steel” “Zinc” “10.50 g/cm³” “7.80 g/cm³” “7.14 g/cm³” “The mass set is made of: steel, given that the density is close to 7.8 g/cm3 when we factor in uncertainty (another possibility is zinc because the density is close to 7.14 g/cm3 as well).