Problem: 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/) so that the m(t) = 1500 kg - 20 kg/s*t.
The objective of the problem is to find how far the elephant goes before coming to rest. Now there two ways we can find the distance of the elephant, an analytical approach and a numerical approach.
Analytical approach: This method involves using the Newton's 2nd law giving us the acceleration of the elephant + rocket system as a function of time. a(t) = Fnet / m(t). Next we can integrate the acceleration from 0 to t to find 🔼v and then derive an equation for v(t). Then we can integrate the acceleration from 0 to t to find 🔼x and then derive an equation for x(t), were we can use integration by parts. Once all the integration is all done and we can add all the elements to find the distance the elephant travels until the rocket runs out of fuel.
Numerical approach: As we can see from above, the analytical approach is time consuming. It turns out we can do it faster by using the numerical approach.
Conclusions:
1. When doing it numerically it was faster and more simple to use then the analytical approach, the former method allowed us to retain most of the original data, while the latter method allowed forced to us alter our data to fit the parameters of the problem, as when we did the numerical approach using Excel, our values for 🔼v and 🔼x were inconsistent with each other.
You can move the propagated uncertainty picture out.
ReplyDeleteYou are welcome to photograph the calculations from the lab handout and just paste that in here. THe important part especially is the analytical result, which we are trying to approach by using the spreadsheet analysis instead.
Describe the numerical approach. How do you go from one column to the next? For a student who missed class and who is counting on your lab report to understand what they missed, right now it is a list of labeled columns but not a context on how you got them.
There were some questions in the lab about using ∆t less than 1 second and how you know when the ∆t you are using is small enough.
THere was also a question asking you to use the spreadsheet for a different set of initial conditions (diff elephant mass, diff thrust, diff burn rate.)