Error Propagation: Volumes Linearized plot: Density - Lab Report Example

In most cases, a pair of variables under analysis may portray a non-linear relationship. Such non-linear relationships are usually encountered when studying variables with exponential functions (Bevington and Robinson 23). In order to enhance simplicity of variable relationships, it is appropriate to develop linear graphs assuming the equation y = mx + c. This process of simplification is referred to as graph linearization. In this lab report, both concepts of error propagation and graph linearization will be utilized intensively in enhancing data analysis.

One aim of this experiment involved practice and comprehension of error analysis in volume lab measurements through the process of error propagation. Secondly, the experiment aimed at establishing simplified relationship between the physical quantities of mass and density through graph linearization. Theoretically, density is given by mass/volume. In this context, values from sphere 2 yield a mean diameter of 3.21 cm. With respect to the relevant formula, volume of the sphere is 33.28 cm3. Therefore, theoretical density is given by mass/volume = 30.29/33.28.

The resultant value is 0.912 g/ cm3. This part highlights on the error propagation results developed from the analysis section. Results tabulated below portray combined uncertainty values of both parts of the experiment. In addition, three graphs of mass against diameter of spheres were plotted to establish the relationship between the density variables. In order to establish the relationship between mass and diameter of the spheres, three graphs were plotted. In this context, mass (g) and diameter (cm) are the only variables under consideration.

The first graph below indicates the non-linear relationship between mass (y-axis) against diameter (x-axis). The relationship is a curve signifying exponential increase in diameter with respect to a corresponding increase in mass. This second graph shows a plot of mass against