Does a Falling Object Ever Truly Reach Terminal Velocity?

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SUMMARY

Terminal velocity is definitively reached by a falling object when its speed becomes constant, contrary to the belief that it is only approached asymptotically. The term "terminal" signifies a final value, not an asymptote. Factors such as the orientation of the falling object can influence the terminal velocity, but in an ideal scenario with no air currents and a stable object, such as a parachute, it will achieve and maintain this velocity. The discussion emphasizes the importance of understanding the definition and conditions surrounding terminal velocity.

PREREQUISITES
  • Understanding of basic physics concepts, particularly forces and motion.
  • Familiarity with the concept of air resistance and its effects on falling objects.
  • Knowledge of the definition and implications of terminal velocity.
  • Basic graphing skills to visualize velocity versus time relationships.
NEXT STEPS
  • Research the physics of air resistance and its impact on different shapes and orientations of falling objects.
  • Study the mathematical modeling of terminal velocity in various mediums.
  • Explore the dynamics of parachute descent and how design affects terminal velocity.
  • Learn about experimental methods to measure terminal velocity in controlled environments.
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This discussion is beneficial for physics students, educators, and anyone interested in the principles of motion and forces, particularly in relation to falling objects and terminal velocity.

Peter Frame
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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.
 
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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.
 
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.
 
DaveC426913 said:
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.
 
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.
 
Also i meant this more as a conceptual question. In practice I am sure it would reach a number.
 
phinds said:
I see we disagree.
And thus I have edited my response to account for that. :)

phinds said:
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.
 
Peter Frame said:
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.
 
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.
 
  • #10
DaveC426913 said:
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 ;)
 
  • #11
DaveC426913 said:
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.
 
  • #12
Peter Frame said:
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.
 
  • #13
Peter Frame said:
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.
 
Last edited:
  • #14
Thanks
 
  • #15
DaveC426913 said:
[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.
Are you getting old? Your text is starting to turn grey...
 

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