ScienceMathFilter: Please help me identify these equations of motion...

September 11, 2023 8:48 PM

I was give a snapshot of a whiteboard with a series of equations that am trying to identify. The writing is illegible in a number of places, but some of it I can make out. It is obviously some sort of equations of motion involving the gravitational acceleration on some mass m, versus another force Fw, and some velocities - here are a few things I can make out: ma = mg - Fw v(t) = vT*(1 - e^(-b*A*t/m))

a being acceleration; g being gravitational acceleration; v(t) being the velocity function with respect to time t; e being Euler's number; m being mass

I'm guessing A might be Area, and I don't know what b is. Could this be related to a falling object and it's velocity over time as it falls and as it approaches terminal velocity (vT, which seems to be used as a constant)? It's been too many decades since college physics...

posted by kjl291 to Science & Nature (4 answers total)

Response by poster: NOTE: I have no idea if this relates to terminal velocity or not. That was just a guess.

ALSO: The equations written as: ma = mg - Fw v(t) = vT*(1 - e^(-b*A*t/m)) are two separate equations - beter to be shown on two separate lines, like this:

ma = mg - Fw;

v(t) = vT*(1 - e^(-b*A*t/m));
posted by kjl291 at 9:03 PM on September 11, 2023

I think it's something like the equation for object falling through a fluid. The first line is showing that the opposing forces are the weight of the object (m*g) in the downward direction, and some kind of drag/friction in the upward direction. W could stand for wind?

There's probably other systems with a similar form.
posted by muddgirl at 9:17 PM on September 11, 2023 [1 favorite]

Best answer: b is the drag coefficient, I believe, and this is indeed describing a falling object's velocity over time as a proportion of its eventual terminal velocity (V_T).

Here's a pdf showing how to derive your equation (which finally shows up at the top of page 4). The only difference is that they've defined the drag coefficient b to already include its reliance on the object's area (A), making it a bit cleaner than your whiteboard's version.

Oh, and I agree with mudgirl that F_w is probably being used to mean Force due to wind resistance.
posted by nobody at 9:42 PM on September 11, 2023

Response by poster: Many thanks to both of you!
posted by kjl291 at 10:39 PM on September 11, 2023