Does a Falling Object Ever Truly Reach Terminal Velocity?

In summary, in a physics discussion, it was mentioned that terminal velocity is reached by a falling object when its speed becomes constant. However, the definition of terminal velocity can be debated as it is dependent on changing factors such as orientation. In an ideal experiment with no air current or wobbling, the object would reach its terminal velocity and stay there. However, in a real-life scenario, the object may wobble around its terminal velocity due to external factors. A stable object such as a parachute can reach its terminal velocity quickly and maintain it.
  • #1
Peter Frame
6
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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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Also i meant this more as a conceptual question. In practice I am sure it would reach a number.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 
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  • #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...
 

1. What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. It occurs when the force of gravity is balanced by the opposing force of air resistance.

2. How is terminal velocity calculated?

The formula for calculating terminal velocity is Vt = √(2mg/ρACd), where Vt is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and Cd is the drag coefficient.

3. What factors affect terminal velocity?

The factors that affect terminal velocity include the mass and shape of the object, the density and viscosity of the fluid, and the force of gravity. Objects with larger surface areas or higher drag coefficients will have a lower terminal velocity, while objects with smaller surface areas or lower drag coefficients will have a higher terminal velocity.

4. Can an object reach terminal velocity in a vacuum?

No, an object cannot reach terminal velocity in a vacuum because there is no fluid present for the object to fall through. In a vacuum, the only force acting on the object would be gravity, causing it to continue accelerating until it reaches the speed of light.

5. How is terminal velocity different from free fall?

Terminal velocity occurs when the force of gravity is balanced by air resistance, resulting in a constant speed. In free fall, there is no opposing force, so the object continues to accelerate until it reaches the ground or encounters another force. Terminal velocity is a type of free fall, but not all free falls result in terminal velocity.

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