September 11,2014- Non-Constant Acceleration

Purpose: We were given a problem involving a 5000 Kg elephant that was rolling down a hill in skates and we were asked to figure out how far the elephant rolled before coming to rest. This lab was created so that we could learn to solve kinematic equations of non-constant acceleration analytically and numerically.

Apparatus used: We did not use any apparatus in this lab. We were simply asked to find the answer to the problem given by the professor using calculus and then solve it using excel.

How we approached the problem Mathematically: This was by far one of the most difficult problems I have been exposed to. Thankfully the professor Wolf solved the problem step by step with us. Initially I was overwhelmed by how easily and how fast the professor knew what to do since, I knew i would not have been able to come up with the answer so easily. I was relived of some stress when the instructor told us not to fret if we aren't sure how this whole process that was being unfolded. He reassured us that he was able to breeze through the problem since he had solved it several times.(more than 5 times) After arriving to an answer we began part two of the lab. Solving the equation using excel.

How we approached the problem numerically: The second part of the lab had us use excel to see if our answer that we would obtain using the formulas derived onto our excel spread sheet would match up to the answer we obtained analytically.
Our hand out had us enter information for 6 different variables as well as with 6 different formulas for each column. These variables were as followed.

1. t= Time
2. a=Acceleration 
3. a_avg= Average acceleration
4. Delta V= Change in Velocity
5. V=Velocity
6. X=Distance the Elephant Traveled. 

After we developed our excel spreadsheet we were asked to fill them down far enough to figure out the distance the elephant traveled. We used three different time intervals. We used the time intervals of .01 seconds, .5 seconds, and 1 second. Our data/excel spread sheet look as followed.

 Time Interval of .01 

 Time Interval of .05 

 Time Interval of 1 second

what this data shows: This data is telling us that it takes between 19-20 seconds for the elephant to reach a final distance of 248 feet.

summary: We were able to obtain consistent Numbers using our numerical approach of excel to get a total distance of 248 m. which took between 19-20 seconds. To be more accurate we would use the time interval of .01 seconds which tells us it takes between 19.6-29.7 seconds to reach a distance of 248.69m. The data that we obtained numerically is consistent with the number we obtained analytically. With this lab we come to realize that there are several approaches one can take to solve a problem. However, you must always be careful when computing your data. One wrong number or rounding error in both the numerical or analytical approach can really fudge your answer.

We were also asked how would we know if the time interval we chose for the integration or excel small enough? We know that the results are correct if the numbers converge to a specific number.