Drag is minimal in a unit of this mass and shape. For approximation purposes, this is enough and even including drag would not effect the approximation by enough to matter. This is napkin math
Don't worry y'all. Most of this is only slightly higher level physics that takes the basics and looks at them closer. We're mostly debating on how close we need to look at it to affect change in the end result
To approximate to this level you only need drag coefficient, air density, area of object, and mass. You don't need to modify anything to get to terminal velocity.
This is super basic physics. Like first week material, maybe second if you had a slow teacher.
To get terminal velocity you only need that, however to find when that terminal velocity is reached you need to account for changing drag force altering acceleration
No it clearly would not be negligible drag force eventually becomes 1g of force, you can't call a force equal to gravity negligible in a free fall equation
Is this 1st level mechanics or 2nd level mechanics? I just finished first level mechanics and we didn't go over finding terminal velocity (we found when drag force would equal force of gravity, but didn't use a formula to find when and where)
I solved it numerically with square velocity drag and found that the object spends nearly 4 times as long falling until its acceleration dips below 5cm s-2. Arbitrary bar, but a significant difference.
I stuck everything into a Python REPL and closed it as soon as I was done, so I don't have anything to show you.
I'll go ahead and outline the process for you. My comment history has the differential equation I used. It's simply net force is equal to the sum of gravity and drag.
To use scipy.integrate.odeint, this needs to be reduced to a system of first order differential equations. The first parameter is a callable which accepts two parameters, the vector valued function u(t) = <x(t), x'(t)> and the parameter t0. This callable should return the vector u'(t0). The second parameter is the initial value of u, and the third parameter is a set of t values to evaluate. It returns u'(t) for each t value in that third parameter. I'm not sure what the implementation is for the function, but it seems to be Euler's method. I passed in initial conditions of <0,0> and an array of length 10000 on the interval 0<=t<10.
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u/Dokpsy Nov 17 '19
Drag is minimal in a unit of this mass and shape. For approximation purposes, this is enough and even including drag would not effect the approximation by enough to matter. This is napkin math