2008 Lab 5

Abstract: We performed measuring experiments of the relationships between diameters and masses using calipers and a balance scale. Through a series of measurements, we were able to mathematically calculate the density of wet clay to be around a multiple of 2, which is definitely higher than substances like water, and lower than substances like chromium. The most important exercise begotten from this experiment is the skill of modeling, which we used to apply our lab data in an attempt to gain a general formula. Objectives: In this lab, we will determine the density of clay through measurements of diameter and mass of a set of handmade clay spheres. We also hope to learn more about ?modeling? as a means of fitting our collected data to a formula, which is achieved in this case through linearization of the data. Procedure: Measure the diameters of a series of six clay balls with calipers. Make six measurements of each ball and distribute the measuring so that each person measures each ball twice with his or her own caliper. Record findings. Next weigh the clay balls to obtain the masses of each of them. Record findings. Reform any deformities in the balls during measurements and clean up respective lab area. Results: See lab sheet attached. Table 1: Measurements of two properties of clay balls Data Analysis: See graphs attached. Mass versus diameter ? original data; no calculations necessary. Cubic diameter versus mass ? The measured value for density is: The experimental error for our measured density is: Natural log of diameter versus natural log of mass ? The measured value of the exponent of diameter is: The measured value of the density is: The experimental error for the density is: Looking at the calculations, the density does indeed come within a factor of two, with P = 1.81·10-3 g/mm3 from part i. It seems that wet clay is denser than water but not as dense as material such as chromium. The ln-ln plot fits very well with our model function, which in turn helped us learn the technique of ?modeling? as well as linearization during laboratory experiments. We found n to be somewhere around 3 (2.75) , indicating good accuracy as well as the apparent human errors that caused this problem. Next, we found the density, through curve fitting as well as linearization, which yielded 1.81*10-3 and 1.68*10-3 g/mm3. Our errors for density are 2*10-5 and 4*10-5 g/mm3, which can be accounted for through human error. Possible reasons for the errors include imprecise measurements of mass and diameter, or errors in the making of the clay spheres. Discussion and Conclusion: To sum up, we measured a series of clay balls with radii from 1 cm to 6 cm for the physical properties of diameter and mass. We utilized our information to test out the skill of ?modeling,? which takes data and uses it to model a line of fit for such data. This is especially helpful as adults learn by relevance and example. During modeling, we started with the equation We used log-log fitting to try and find n as a means of using our data to determine a formula. We also perfected our linearization skills by attempting to find lines of linear fit for the collected data. This lab achieved its aims in teaching modeling and reviewing linearization, analytical practices in addition to the direct aim of finding the density of clay. Ball (#) Average Diameter (mm) Mass (g) 1 10.17 1.6 2 19.23 7.4 3 29.93 26.0 4 39.17 52.1 5 50.17 117.5 6 61.43 220.0