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dracayr
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Homework Statement
I want to numerically simulate a fall with air drag. In class, we used these equations to produce a table simulating free fall (using a ti calculator):
Code:
dt=0.1s
a=9.81m/s²
t[SUB]n+1[/SUB]=t[SUB]n[/SUB]+dt
v[SUB]n+1[/SUB]=v[SUB]n[/SUB]+a*dt
x[SUB]n+1[/SUB]=x[SUB]n[/SUB]+v[SUB]n[/SUB]*dt
When I compared that system with the curve produced by the direct equation, x=1/2at², I noticed a slight error. After looking at the equations again, I figured that the error came from the fact that I used vn, so the curve would always be a bit lower than 1/2at². So I fixed that by changing the Equation to
Code:
x[SUB]n+1[/SUB]=x[SUB]n[/SUB]+((v[SUB]n+1[/SUB]+v[SUB]n[/SUB])/2)*dt
Now I want to create a similar system but with air drag. As before, my physics book says that I should use vn and not (vn+vn+1)/2. But the book was wrong when it came to free fall, so I don't know which value to use for v. I think I should use (vn+vn+1)/2. But since I don't know the direct equation this time (if there is one), I can't compare to the correct solution..
2a. Relevant equations
v=x/t
a=v/t
F=ma
Fd=b|v|m
vE=(mg/b)1/m
a=g(1-vm/vEm)
Fd is the air drag
b and m are constants depending on the drag (I think in the case of air, m is about 2)
vE is the end velocity the falling body will achieve
The Attempt at a Solution
These are the spreadsheets with the 2 systems:
http://dracayr.awardspace.com/physik.ods"
http://dracayr.awardspace.com/physik.xls"
dracayr
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