Conservation of momentum and conservation of energy details

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Discussion Overview

The discussion revolves around the principles of conservation of momentum and conservation of energy, particularly in the context of collisions and falling objects. Participants explore scenarios involving a ball dropped from a height, the effects of initial velocity, and the implications of external forces on these conservation laws.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants question why the conservation of energy equation cannot be set to zero when a ball dropped from height h reaches the ground with zero velocity, suggesting that mgh = 0 implies h = 0.
  • Others propose that if a ball has an initial velocity v, the conservation of energy equation should include both potential and kinetic energy, leading to mgh + (1/2)mv^2 = 0.
  • Concerns are raised about the applicability of conservation of energy when external forces are involved, particularly in cases of inelastic collisions.
  • Some participants argue that two masses colliding and coming to rest together would violate conservation of momentum, while others assert that momentum can be conserved if the system includes all relevant masses, such as the Earth.
  • There is a discussion about how mechanical energy is not conserved in inelastic collisions, as kinetic energy is transformed into internal energy.
  • Participants explore the concept that even if the ball comes to rest, the Earth must move slightly due to the collision, thus conserving momentum when considering the entire system.

Areas of Agreement / Disagreement

Participants express differing views on the conservation of momentum and energy, with no consensus reached on the implications of external forces or the conditions under which these conservation laws apply. The discussion remains unresolved regarding specific scenarios and interpretations.

Contextual Notes

Limitations include assumptions about the system boundaries, the treatment of external forces, and the definitions of energy forms involved in collisions. The discussion does not resolve these complexities.

  • #31
Rather than focus on "forces", it might be better to focus on the
"transfer of momentum [from one object to another]"...
one object gaining momentum ##\Delta \vec p_1\stackrel{Newton2nd}{=} \Delta \vec p_{1\mbox{ from 2}}##
because the other object transferred momentum to it: ##\Delta \vec p_{2\mbox{ from 1}} \stackrel{Newton3rd}{=} - \Delta \vec p_{1\mbox{ from 2}}## .

Yes, it deals with the impulse and the time-integral of the force...
but, as others have tried to emphasize,
it's more than a formula, a "change", or a sign.
It's about what object is applying the force (the source of the force.. source of the momentum-transfer)
and what object is receiving that force (the target of the force.. target of the momentum-transfer).
Think of it as an accounting problem.
 
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