Lab 3: Non-Constant Acceleration Problem:
Rocket-Powered Elephant
Joel Cook
Nina Song
Lab performed March 8, 2016
In this lab, we have been given a physics problem in which an elephant on skates rolls down a hill with a rocket on his back pointing backwards. At the bottom of the hill the rocket fires and we are tasked with finding how far the elephant will travel before it stops and how long it will take. We are using Microsoft Excel to perform the calculations.
Introduction: Performing the calculations requested in this lab involve using calculus in order to calculate distance travelled and time with an acceleration that is changing. The professor has performed the calculus and provided the solution to the problem. The intent of the lab is to use Microsoft Excel to perform the calculations quickly and efficiently to reach the same solutions.
Procedure: A computer with Microsoft Excel was used to perform the calculations. The initial conditions and formulas were input into the spreadsheet and the computer generates the results. We then reduced the time interval incrementally to find a more precise answer to the question. In the last part of the lab, we changed the initial conditions in the problem and found a different set of solutions. The results are shown below:
The first set of data shows the result for a time interval of 1 second. The distance traveled is shown as 247.9 meters in 20 seconds. The second set shows the result for a time interval of 0.1 seconds. The distance traveled is shown as 248.6 meters in 19.7 seconds. The third set shows the result for a time interval of 0.05 seconds. The distance traveled is shown as 248.66 meters in 19.70 seconds.
Questions:
1. The solution that was provided analytically is 248.7 meters in 19.69075 seconds. The answer we achieved numerically is 248.66 meters in 19.70 seconds. Essentially the same answer.
2. We had the analytical solution to compare our value against. We were able to change the time interval to achieve a similar accuracy to the analytical solution. To determine the time interval is small enough in the numerical approach with the analytical approach to compare to, we can change the time interval in the spreadsheet until the number in the decimal place we are interested in (i.e. hundredths place) stops changing. It is not necessary to achieve a precision that takes the answer to 5 or 10 decimal places.
3. The last set of data pictured above shows the results for a different set of initial conditions. The distance travelled would be 163.99 meters in 12.95 seconds before the elephant stops.
Conclusion: In this experiment, we showed that Microsoft Excel can be used to perform calculations for distance travelled and time with a changing acceleration and achieve the same solution one would arrive at using calculus and an analytical method. The experiment was a resounding success.
1. The solution that was provided analytically is 248.7 meters in 19.69075 seconds. The answer we achieved numerically is 248.66 meters in 19.70 seconds. Essentially the same answer.
2. We had the analytical solution to compare our value against. We were able to change the time interval to achieve a similar accuracy to the analytical solution. To determine the time interval is small enough in the numerical approach with the analytical approach to compare to, we can change the time interval in the spreadsheet until the number in the decimal place we are interested in (i.e. hundredths place) stops changing. It is not necessary to achieve a precision that takes the answer to 5 or 10 decimal places.
3. The last set of data pictured above shows the results for a different set of initial conditions. The distance travelled would be 163.99 meters in 12.95 seconds before the elephant stops.
Conclusion: In this experiment, we showed that Microsoft Excel can be used to perform calculations for distance travelled and time with a changing acceleration and achieve the same solution one would arrive at using calculus and an analytical method. The experiment was a resounding success.
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