8-March-2017: Lab 3: Non-Constant acceleration problem/Activity

Lab 1: Finding a relationship between mass and period for an inertial balance

Author: Tian Cih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: March 8, 2017

Purpose of the lab: The purpose of the lab is to find out how far an elephant goes before coming to rest with the given scenario. A 5000-kg elephant frictionless roller skates in going 25m/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 8000N 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 20kg/s) so that m(t) = 1500 kg – 20 kg/s * t (rocket).

Theory/Introduction:

We create a new Excel spreadsheet and input all the parameters and formulas into it. Then we can see the change of acceleration, velocity and distance.

Summary of apparatus/experimental procedure:

We use one groupmate's laptop doing the lab. He used excel to get the result of the lab.

Measured data: There is no measured data for this lab. Everything is carried out based on the known parameters in the scenario.

Calculated result(s)/Graph: 

Analysis:

After we put formula for every variables, we can just change the dt smaller to make the result more accurate. Then we just fill down the table so that we get the v=0 at rest.

Questions:

1. Compare the results you get from doing the problem analytically and doing it numerically.

By looking at the table whose dt is 1s, it makes sense since the results match almost perfectly.

2. How do you know when the time interval you chose for doing the integration is “small enough”? How would you tell if you didn’t have the analytical result to which you could compare your numerical result?

By solving the problem analytically, the integration is “small enough” when the time interval chosen is relatively small comparing to the theoretical “whole” time it takes. Without the analytical result, we can look at the velocity volume. If it quickly decreases to something below zero, then we can tell that the time interval chosen is too large.

3. Determine how far the elephant would go if its initial mass were 5500 kg, the rocket mass is still 1500 kg, but now the fuel burn rate is 40kg/s and the thrust force is 13000N.

By doing the integral from 0 to x, dv = 325ln(175-x)-325ln(175), v=v0+dv=25-325ln(175)+325ln(175-x)

By doing the integral for the distance.

We can use small number of time interval to fill down the table, then we get that the elephant will stop at 119 meters.

Conclusion:

In this lab, we get the result by setting equation of velocity and acceleration. Then we use excel to fill down the table to find the changing of variables.