# Drag Force Acting on an Object with Respect to Velocity

#### haruspex

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taking $$v=ah+b,$$
There is no basis for such an equation, and it is certainly wrong.
An object falling through a dragging medium approaches, but never quite reaches, a "terminal velocity".
The exact relationship to time or distance is not susceptible to algebra - it's very complicated. Typically, drag is roughly a linear function of speed at low speeds, more like a quadratic one at higher speeds.
But we do not need to care about the details here. What matters is that at the start the drag is very small, so v2 is nearly linear with h (the ½v2 line starts tangent to the gh line), but as h increases v2 rises more slowly and approaches a horizontal asymptote.

#### Ray Vickson

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Dearly Missed
That is quite interesting, but I don't think I could do it since I only have one pair of $(T_1,V_1)$, after all the whole experiment is done with a single object.

Down is positive, so both v and dv/dh are positive
You said in your first post that you drop the object from various heights, so that sounds to me like you will obtain several values of terminal speed and fall-time. Yes, you have just a single object, but are you not using it several times to get several data points?

#### Marcell

You said in your first post that you drop the object from various heights, so that sounds to me like you will obtain several values of terminal speed and fall-time. Yes, you have just a single object, but are you not using it several times to get several data points?
ah I see what you mean. No, sorry for the confusion, but that is not the data I have (object doesn't reach terminal velocity), either way I really appreciate your time and effort thanks!

#### Marcell

There is no basis for such an equation, and it is certainly wrong.
An object falling through a dragging medium approaches, but never quite reaches, a "terminal velocity".
The exact relationship to time or distance is not susceptible to algebra - it's very complicated. Typically, drag is roughly a linear function of speed at low speeds, more like a quadratic one at higher speeds.
But we do not need to care about the details here. What matters is that at the start the drag is very small, so v2 is nearly linear with h (the ½v2 line starts tangent to the gh line), but as h increases v2 rises more slowly and approaches a horizontal asymptote.
Thanks for explaining it so many times, I think I finally got it, have a good one!

#### Ray Vickson

Homework Helper
Dearly Missed
ah I see what you mean. No, sorry for the confusion, but that is not the data I have (object doesn't reach terminal velocity), either way I really appreciate your time and effort thanks!
Sorry for the confusion: by "terminal velocity" I do not mean the usual "terminal velocity in air" figure, but rather, the final velocity the of the object just as it hits the ground (which you said you measure).

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#### haruspex

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Gold Member
2018 Award
If the drag force can be defined as 1/2 Cd A v^2, where Cd is coefficient of drag, and A is cross sectional area, then there is a closed form solution for an dropped object with only a vertical component of velocity. Wiki link, click on "show" for the derivation:

https://en.wikipedia.org/wiki/Terminal_velocity#Derivation_for_terminal_velocity
As I understand the purpose of the exercise, it is to estimate the drag forces at various points in the fall based on the measured velocities. There is no suggestion that it should be based on any drag equation or theory.

"Drag Force Acting on an Object with Respect to Velocity"

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