Does a Falling Object Ever Truly Reach Terminal Velocity?

[Peter Frame]

Today in physics we talked about terminal velocity. This got me thinking. As air resistance acts on a falling object, the acceleration of that object will decrease. I was wondering if terminal velocity is only approached asymptotically and never technically reached. Please explain this. Thanks.

 

[phinds]

Your question is a reasonable one, but no, terminal velocity IS reached. If the speed does not become constant, you have not reached terminal velocity. That's what the term MEANS. "Terminal" means "final" and is a value, not an asymptote.

 

[DaveC426913]

Tilting my hat to phinds' answer, I guess that depends on how you look at it. Terminal velocity is not a fixed target, since it's dependent on many changing factors, such as orientation of the falling object.

 

[phinds]

You are correct.
Moreso, it is not even a fixed target, since it's dependent on many changing factors, such as orientation of the falling object.

I see we disagree. I think you need to check the definition.

 

[Peter Frame]

But if you graphed the velocity, it would curve to horizontal. Either midway along this curve it would suddenly flat line, or it would approach a number but never quite get there.

 

[Peter Frame]

Also i meant this more as a conceptual question. In practice I am sure it would reach a number.

 

[DaveC426913]

I see we disagree.

And thus I have edited my response to account for that. :)

I think you need to check the definition.

I think you're looking at it simplistically. Terminal velocity can't even be well-defined, since it's not stable.

 

[DaveC426913]

But if you graphed the velocity, it would curve to horizontal. Either midway along this curve it would suddenly flat line, or it would approach a number but never quite get there.

It would approach a value and then wander up and down around as the orientation of the falling object changed from moment to moment.

 

[Peter Frame]

So your saying that in a perfect experiment with no air current, and no wobbling object, it would approach it? This is what makes a lot of scene to me.

 

[phinds]

I think you're looking at it simplistically. Terminal velocity can't even be well-defined, since it's not stable.

Yes, I keep telling you, I am VERY simple-minded ;)

 

[phinds]

It would approach a value and then wander up and down around as the orientation of the falling object changed from moment to moment.

I agree.

 

[phinds]

So your saying that in a perfect experiment with no air current, and no wobbling object, it would approach it? This is what makes a lot of scene to me.

No, in an ideal situation, it would reach it and stay there instead of reaching it and then, as Dave says, wobbling around a bit faster and a bit slower.

 

[DaveC426913]

So your saying that in a perfect experiment with no air current, and no wobbling object, it would approach it? This is what makes a lot of scene to me.

[EDIT Sorry, I did not see that you said an ideal experiment.]

Yes, so, to do so, you use an object that is stable under descent. Such as, say, a parachute.

A parachute, assuming its oscillation is kept down, reaches its terminal velocity quite quickly, and then its velocity will stick very close to that thereafter.

 

[Peter Frame]

Thanks

 

[Danger]

[EDIT Sorry, I did not see that you said an ideal experiment.]

Yes, so, to do so, you use an object that is stable under descent. Such as, say, a parachute.

A parachute, assuming its oscillation is kept down, reaches its terminal velocity quite quickly, and then its velocity will stick very close to that thereafter.

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