What is the terminal velocity of mass falling toward earth?

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Discussion Overview

The discussion revolves around the concept of terminal velocity for a mass falling toward Earth, specifically under the assumption of no atmospheric drag, friction, or other extraneous factors. Participants explore the implications of these assumptions on the definition and calculation of terminal velocity, as well as the concept of escape velocity.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that terminal velocity requires a drag force, implying that without such a force, terminal velocity cannot exist.
  • One participant questions the meaning of "the edge of Earth's gravity," suggesting that it should be defined as infinitely far from Earth, where gravitational influence is negligible.
  • Another participant introduces the concept of escape velocity, arguing that a mass falling from rest at infinity would hit Earth with this velocity, which they suggest is mischaracterized as terminal velocity.
  • One participant predicts a maximum velocity of 40,200 km/h upon impact with Earth, linking this to the concept of escape velocity.
  • Another participant challenges this prediction, stating that the calculations presented are incorrect and asks for clarification on the reasoning behind the claim.
  • A later reply acknowledges a misunderstanding regarding the velocity figures, confirming that escape velocity is approximately 40,000 km/h, but does not resolve the broader discussion about terminal velocity.
  • One participant suggests that specifying the starting distance from Earth's surface or the initial acceleration rate would clarify the discussion, emphasizing the role of distance in determining the final velocity.

Areas of Agreement / Disagreement

Participants express disagreement on the definitions and calculations related to terminal velocity and escape velocity. There is no consensus on the correct interpretation of these concepts, and multiple competing views remain throughout the discussion.

Contextual Notes

The discussion includes assumptions about the absence of atmospheric effects and friction, which may limit the applicability of the arguments presented. The definitions of terminal velocity and escape velocity are also contested, leading to potential misunderstandings.

rwjefferson
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Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of Earth's gravity well to Earth's surface?

Thank you in advance for your answer.

Peace
rwj
 
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rwjefferson said:
Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of Earth's gravity well to Earth's surface?

Thank you in advance for your answer.

Peace
rwj
Terminal velocity by definition requires that there be a drag force. Therefore, no drag force - no terminal velocity.
 
rwjefferson said:
Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of Earth's gravity well to Earth's surface?

Thank you in advance for your answer.

Peace
rwj
What do you mean by "the edge of Earth's gravity"??

As modeled by classical Newtonian mechanics, the "edge" where there is zero influence from Earth's gravity must be placed infinitely far away from the Earth.

If we imagine a a particle starting at rest at infinity, and then is solely influenced by Earth's gravity, then it will hit Earth with the velocity known as "escape velocity".

Perhaps you might call this a "terminal velocity", but that would be an abuse of terms, as Hootenanny has told you already.
 
Is the maximum velocity of a falling mass 40,200 km/h @ Earth's surface?

arildno said:
What do you mean by "the edge of Earth's gravity"??
If we imagine a a particle starting at rest at infinity, and then is solely influenced by Earth's gravity, then it will hit Earth with the velocity known as "escape velocity".
Perhaps you might call this a "terminal velocity", but that would be an abuse of terms, as Hootenanny has told you already.

A plot of gravitational potential of the Earth generates a hyperbolic cross section. The sudden dip in the center is the origin of the name 'gravity well'. The 'edge' of that well occurs where minimal perpendicular velocity counters the force of gravity. I agree that the 'edge' of that well is as arbitrary as 'minimal perpendicular velocity'.

I commend you on your insight.
I will predict that a free-falling mass will reach maximum velocity of 40,200 km/h as it hits the surface of the earth.

Thanks
rwj
 


rwjefferson said:
I will predict that a free-falling mass will reach maximum velocity of 40,200 km/h as it hits the surface of the earth.

Thanks
rwj
I'd have to disagree with you there. Your calculations are incorrect.
 


Hootenanny said:
I'd have to disagree with you there. Your calculations are incorrect.

What, may I ask, are your better reasons and and calculations that I should doubt equal to escape velocity?

Peace
rwj
 


rwjefferson said:
What, may I ask, are your better reasons and and calculations that I should doubt equal to escape velocity?

Peace
rwj
Whoops! I beg your pardon, I thought you had 40 000 km/s.

You are indeed correct, the escape velocity from Earth is indeed approximately 40 000 km/h.

Apologies for the mix-up!
 
rwjefferson said:
Assume no atmosphere; no friction; no extraneous factors.

What is the terminal velocity of a mass that falls from the edge of Earth's gravity well to Earth's surface?

Thank you in advance for your answer.

Peace
rwj

It would probably be best that you specified either an object's starting distance from the Earth's surface or a point beginning at a given rate of acceleration m/s^2, as in theory, the further an object is placed from the Earth (and still capable of accelerating towards it), the more time it is given to accelerate and gain a higher end velocity especially considering your "no atmosphere", "no friction", "no extraneous factors" clause. :wink:
 

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