12-Sept-2016: Non-Constant acceleration problem/Activity

Lab 3 Non-Constant Acceleration
Date: 12 September 2016
Name: Andrew Martinez
Lab Partner: Richard Mendoza

Introduction: Using analytical and numerical approach determine how far the elephant goes before coming to rest.

Apparatus: While there is no apparatus we are given a problem to solve. "A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a 1500-kg 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." Two ways to do this are through analytical means or numerical means.

Measured Data:
Elephant Mass: 5000-kg
Initial Velocity: 25 m/s
Rocket Mass: 1500-kg
Rocket Force: 8000 N opposite elephant's direction
Rocket Fuel Depletion: 20 kg/s

Analytical Method:

1. Set as a function of time

2. Find delta V and then derive an equation for V(t)

3. Integrate the velocity from 0 to T to find delta x and then derive an equation for x(t)

Plug it all in and you get time 19.6 seconds and distance 248.7 meters

Numerical Method:

By opening up an excel spreadsheet and plug the equations into there appropriate columns  

Once everything is plugged in and the relevant data has been inputted the distances can be determined by dragging down

 At 19.6 seconds the distance is 248.5 meters

Conclusion: 

1. Comparing the results it is clear that both analytically and numerically results are reasonably close to one another. Though numerically requires less work on the user.

2. By obtaining the time given in the analytical approach or by seeing when the velocity reaches zero

3. Time 13 seconds and distance 164 meters