Gummy Bear Lab Report

Because gelatin is found in food and medical products, it is important to understand its behavior in solutions. The objective of this experiment was to determine the best fit of an exponential empirical model for the swelling of gelatin-based gummy bears and determine if changes in solution type or bear color resulted in significant differences. This objective was accomplished by submerging red and green bears in two solutions, tap water and saltwater, and observing the effects of each solution over time. Specifically, analysis of the time-interval data for lengths of one red gummy bear placed in tap water revealed the optimal combination of parameters to fit the data. Excel Solver simulations determined that allowing two degrees of freedom
The L term is the length of the gummy bear when the system has reached equilibrium; according to Equation 1, the bear will grow asymptotically towards this maximum length. The L0 term is the initial length of the gummy bear before submergence when t is equal to 0. The K value represents the rate of mass transfer, which is referred to as the swelling constant.2 The data can be fitted to the model when some or none of these terms are known. By fitting the data to the predetermined equation multiple times and varying which parameters are constrained, the error between modeled values and actual data can be found. This error can be analyzed to determine which constraints and degrees of freedom make the best fit. When the greatest fit is found, t-tests can be performed between the parameters found for different conditions to determine if the differences in data are significant.

APPARATUS & PROCEDURE (150) This experiment requires red and green gummy bears, salt, water, and cups. A saltwater solution was placed in four cups, of which two had red bears and two had green. This step was repeated with four cups of tap water, resulting in eight cups with one bear in each, as shown
This process was repeated with two degrees of freedom where L0 remained constant and with one degree where L0 and L remained constant. This allowed K to vary as a free parameter across all three simulations. When using two degrees of freedom, we decided to add the constraint of L 0 due to the impossibility of having a negative bear length. This constraint allows modeling of both disappearing salt bears and growing tap bears. Comparison between the three models showed that two degrees of freedom with the above constraint yielded the smallest sum of squared error. Table I below compares the values reported from the data analysis. Raw data are available in Appendix A, and more detail on the use of Solver to calculate the parameters is available in Appendix