Understanding the Impact of Mass and Dimension Measurements on Density Calculation

Determining the Contribution of Mass and Dimension on Coefficient of Variation (CV)

In many methods that employ multiple measurements, one particular type of measurement may be the "weak link" that limits overall precision. For the density measurements you made here, you will determine what contributes most to the CV of your calculated density - the measurements of mass or of dimensions. Typical standard deviation for length and mass using the equipment employed in this lab are the following:

Dimensions: 0.01 cm

Mass: 0.002 g

Select the data for your lightest object, focusing on its mass and its shortest dimension, and answer the following two questions:

Questions:

1. What is the CV for the mass value? (2pts)
2. What is the CV for the measurement of its shortest dimension? (2pts)

Answers:

e. Which type of measurements (mass or dimensions) had the greatest impact on the CV of the measured density? Choose the explanation

1. Mass measurements have the greater impact because the mass CV with the lightest object was greater than its dimension CV.
2. Dimension measurements have the greater impact because the dimension CV with the lightest object was lesser than its mass CV.
3. Dimension measurements have the greater impact because the dimension CV with the lightest object was greater than its mass CV.
4. Dimension measurements have the greater impact because the dimension CV with the lightest object was lesser than its mass CV.

We can draw the conclusion that compared to dimension measurements, mass readings had a smaller effect on the CV of the measured density. To determine the contribution of mass and dimensions on the coefficient of variation (CV) of the calculated density, we can calculate the CV for both mass and dimension measurements separately for the lightest object.

Let's assume that the mass of the lightest object is 0.5 g and its shortest dimension is 1.0 cm. The CV for mass can be calculated as follows:

CV for mass = (standard deviation of mass / mean mass) x 100%

CV for mass = (0.002 g / 0.5 g) x 100%

CV for mass = 0.4%

Similarly, the CV for dimension can be calculated as follows:

CV for dimension = (standard deviation of dimension / mean dimension) x 100%

CV for dimension = (0.01 cm / 1.0 cm) x 100%

CV for dimension = 1.0%

From these calculations, we can see that the CV for mass is lower than the CV for dimension, indicating that mass measurements are more precise than dimension measurements for this particular object.

Therefore, we can conclude that mass measurements had a lesser impact on the CV of the measured density compared to dimension measurements. This is because the contribution of mass measurement uncertainty to the overall CV is lower than that of the dimension measurement uncertainty.