Non Constant Acceleration Sept 7

Non-Constant Acceleration Lab (Elephant)

Carlos H., Dahlia T., Ariel D.

Sept 7, 2016

1.So in this lab we will the difference in working out a problem analytically and numerically using excel.

2. So we are given a problem involving an elephant with a rocket booster . The elephant has an initial velocity going down the slope. The rocket booster turns on in the opposite direction stopping the elephant. We need to find how far it will go before coming to rest. First analytically (analyze as the professor has done it for us ) then in excel where it would be easy to change numbers (mass, Vo, etc.). Hence- an important note to the reason why this problem is tougher is because the acceleration isn't constant nor the mass as the rocket fuel burns off as it produces its thrust. 

Elephant Problem Photo

3. We looked and analyzed the solution in an analytical approach . Since numbers weren't constant there had to be an integral approach which was very hard and long. Although in this case possible the professor said sometimes it would be extremely hard to get an answer. Ultimately the solution was found . Now we would try on our own (in our groups) to solve and set up a table where we could solve for this numerically piece by piece. Finding the average acceleration for the time interval then the change in velocity followed by the speed at the end of the interval then the average speed at the end of the time interval lastly finding the position change, we would be able o find the position the elephant would be at.

Analytical Approach

Numerical Approach

4. To find the final value for distance we put the time to increase every .1 seconds ( we belived the accuracy would be good enough ) and look for when the velocity became zero. It is good to keep in mind the the velocity would eventually become negative as the thrust would push the elephant back still after the velocity became zero. Here is a picture of the lab when we found the velocity to become zero. 

5. In conclusion sometimes problems are tough to solve analytically. Although I'm sure after this lab we should know how to approach or understand how the analytical solution would be, the numerical approach with excel gives us many advantages. Advantages where we could easily change the inputs to find different outputs. Cheers.