Lab # 3 Non constant acceleration problem/activity (Daniel Guzman)

Daniel Guzman

Lab#3 Non constant acceleration problem/ activity

Physics 4A.


The purpose of this problem activity was to approach a kinematics problem numerically, instead of solving it analytically, due that there are some problems, which are very tedious, time consuming , and sometimes very difficult when they are solved analytically;  due that the mathematical functions of this problems cannot be integrated sometimes. Nevertheless, when problems are solved using the numerical approach, one is likely to find or get the desired answer due that one is able to use the data provided in the problem in different ways until the answer is achieved. For instance, in this problem only a few values were given, and using them correctly and applying the correct logic we were able to solve the problem obtaining the same results as it was to be dome analytically.

There was not apparatus in this particular experiment, the only piece of equipment used in this activity was the computer, which has Microsoft excel.

Experimental Procedure: the first step in this experiment was to  analyze and read the problem carefully, so one would know what the problem was asking and what important values were given. After the problem was read and analyze we would look at the analytical approach of solving this problem in, which we would find out that solving it analytically is very tedious and time consuming. Once the problem is understood and is solved analytically, we could proceed and solve the problem numerically. To solve the problem numerically we had to use and understood how the data provided in the experiment could be used to solve it, after this is understood one can use excel and list all the values provided such as, the mass of the elephant  the mass of the rocket, the mass of the elephant, the initial of velocity of the elephant, the thrust of the rocket and the fuel rate of the rocket. Once this values are listed and organized I proceeded and made a table of other values which were : time, acceleration, average acceleration, change in velocity, average velocity, change in displacement and displacement. After this is done I put the correct values for vo and displacement and from here I started to make the respective calculations which allow me to get the desired answer. only the first calculations for the first values have to be done because since one is using excel, excel would do the other calculations as long as the calculations and equations for the first calculation are correct. for time I used the value established for the interval and added the previous number to it. for the acceleration I used the force/ (total mass- burnt rate(t)). for average acceleration I used  the average between the last two previous acceleration * time. for delta v I used the sum between the previous two average acceleration and multiply it by time. for velocity I used the change in velocity+ the initial velocity, for v average i used the sum of the previous two velocities and multiple by time, and for delta x I used the average of velocity and multiply it by time and for position i used the sum of the two previous values for delta x.

Data tables : the spread sheets were made making the time intervals : 1 second, 0.1 seconds and 0.05

Conclusion

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

Doing the problem numerically is much easier due that the integration sometimes can get really difficult and might be tedious. Another problem that one might encounter when doing it analytically is that the function cannot even be integrated. therefore approaching the problems numerically  is much easier. The results obtained doing analytically and numerically give one the same result.
2. How do you know when the time interval you chose for doing the integration is small enough ? how do you tell if you didn't have the analytical result to which you could compare your numerical result?
To know if the time interval is small enough one how to see if the change in velocity stabilizes or reaches a constant number, or if the change in this result is small enough were the changes are irrelevant or insignificant. when this is reached the time interval has been made small enough.
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 full burn rate is kg/sec and the thrust force is 13000 N
when the time interval is 1 second the elephant goes 163.53 meters and when the time is 0,01 the displacement is 163.84 meters.