12-Sep-2016: Lab 3 Non-Constant Acceleration Problem/Activity

1. Title: Lab 3 Non-Constant Acceleration Problem/Activity
    Name: Qiwen Ye (Sherry)
    Lab partners names: Eugene, Chandler
    Date: 12-Sep-2016

2. Purpose
To used excel to solve problem by using the numerical approach because some physic problem are extremely difficult to solve analytically if it is even possible at all. 

3. Introduction
A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a fill and arrives on level ground. At that point a rocket mounted on the elephant's back generates a constant 8000 N thrust opposite the elephant's direction of motion. The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the: 

m(t) = 1500 kg - 20 kg/s*t.

Find how far the elephant goes before coming to rest.

4. Apparatus/Experimental Procedure

To figure out how far the elephant goes before coming to rest we can use calculus to integrate the acceleration function into a velocity function and further integrate that to come up with a position function. Though the functions were able to be integrated, which is not always the case, we are now left with an incredibly hard function to solve. Using calculus we can solve for the time when the velocity of the elephant equals zero. We then plug that time into our position function to come up with x=248.7 m, and the time is 19.690575 second.

5. Data

Used the Excel spreadsheet and enter the following:

6. Calculated Results 
Here is the data that we entered into Excel spreadsheet by changing the time interval in order to  in order to find where was the elephant stopped.

1) the time interval in 1 second

2) the time interval in 0.1 second

3) the time interval in 0.05 second

Here is the data about changed the mass into 7000 kg, the fuel burn rate is 40 kg/s, and the thrust force is 13000 N.

7. Explanation/Analysis

Even though we changed the time interval from 1 second to 0.1 second and to 0.05 second, we still got the same distance that the elephant stopped and its stopped time is around 19 to 20 second, the distance that the elephant stopped is around 248.6 m. However, when we changed the fuel burn rate and the thrust, but keep the same mass, the distance of stopping is became 164 m and the time became 13 second. 

8. Conclusion

In this experimental, we learned how to use the Excel to solve problems numerically. The error percent of the time is 0.65%, the error percent of the distance is 0.01018%. For a complication problem, we can use the Excel by entering the equation that we can get more values in order to analysis the results easily. Also, this method is a great alternative to solve the difficult integration problems.