Conservation of linear momentum

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Discussion Overview

The discussion revolves around the application of the law of conservation of linear momentum in the context of a body that explodes in air while an external gravitational force is acting on it. Participants explore the conditions under which momentum is considered conserved during such events, addressing both theoretical and conceptual aspects.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question the applicability of the conservation of linear momentum when an external gravitational force is present during an explosion.
  • One participant suggests that the force due to gravity is negligible during the short duration of an explosion, allowing for momentum conservation.
  • Another participant emphasizes that explosions are treated as instantaneous events, implying that the gravitational force does not significantly affect momentum during that brief time frame.
  • There is a suggestion that the change in momentum due to gravity is small compared to the initial momentum, making it an acceptable approximation.
  • Some participants discuss the representation of extended objects as mass-points, noting that the center of mass follows an undisturbed trajectory despite the explosion.
  • The impulse due to gravity is described as very small, reinforcing the idea that it does not affect momentum during the explosion.

Areas of Agreement / Disagreement

Participants express differing views on the impact of gravitational force on momentum conservation during explosions. While some agree that the effect is negligible, others question the validity of applying the conservation law under these conditions, indicating that the discussion remains unresolved.

Contextual Notes

Participants acknowledge that the discussion involves approximations and assumptions regarding the duration of the explosion and the relative magnitudes of forces involved. The treatment of explosions as instantaneous events is also a point of contention.

G.Chandra
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Why do we apply law of conservation of linear momentum on a body that explodes in air when an external force, gravittional force- mg, is acting on it? The law says that the linear momentum is conserved in absence of the external forces.
 
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hmm that's because the force [tex]mg[/tex] into the time for which the explaosion happens [tex]dt=mgdt[/tex] is aver small qty so
[tex]P_{f}-P_{i}=mgdt \approx 0[/tex]
 
Welcome to PF!

G.Chandra said:
Why do we apply law of conservation of linear momentum on a body that explodes in air when an external force, gravittional force- mg, is acting on it? The law says that only in absence of external forces the linear momentum remains conserved.

Hi G.Chandra! Welcome to PF! :smile:

Because an explosion, like a collision, is taken to be instantaneous.

So the force from gravity (which takes time!) is zero. :smile:
 


tiny-tim said:
So the force from gravity (which takes time!) is zero. :smile:
hmmmm i don't get this explanation of urs?
 
This means that the law will not be applicable if duration of explosion is longer?
 
no see it's an approximatiion!
so don't wry about the "law holding" or not
what's assumed is that the momentum change due to gravity is negligible as comapred to the initial momentum
say if the intial momentum was some 500 untis and the change sone 1 or 2 units then it shud hardly matter u
it's an approximation and works real well
 
G.Chandra said:
Why do we apply law of conservation of linear momentum on a body that explodes in air when an external force, gravittional force- mg, is acting on it? The law says that the linear momentum is conserved in absence of the external forces.

That's the magic of representing extended objects as mass-points. The center of mass will follow the undisturbed trajectory (within reason- a mid-air collision is different than a 'simple explosion'), even though all the little pieces will tumble hither and yon.
 


tiny-tim said:
So the force from gravity (which takes time!) is zero. :smile:

A better way to say it might be that the impulse due to gravity,

[tex] F \Delta t = m \ g \ \Delta t[/tex]

is very small since delta-t is small. Equating impulse with change in momentum, we can also say this does not affect the momentum during a collision or explosion.
 
yeah perfect that's hwy i had questioned "tiny-tim"!
 

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