Conservation of momentum and conservation of energy details

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SUMMARY

The discussion focuses on the principles of conservation of momentum and conservation of energy, particularly in the context of a ball dropped from a height. It clarifies that conservation of energy cannot be applied when the ball reaches the ground with zero velocity, as this implies an initial height of zero. The conversation also emphasizes that momentum is conserved in collisions, even when external forces are present, such as the Earth’s mass affecting the ball's momentum during impact. The participants conclude that mechanical energy is not conserved in inelastic collisions, but total energy, including all forms, remains conserved.

PREREQUISITES
  • Understanding of gravitational potential energy (GPE) and kinetic energy (KE)
  • Familiarity with the concepts of inelastic and elastic collisions
  • Knowledge of momentum conservation principles
  • Basic physics equations involving mass, velocity, and energy
NEXT STEPS
  • Study the differences between elastic and inelastic collisions in detail
  • Learn about the mathematical derivation of conservation laws in physics
  • Explore the implications of external forces on energy conservation
  • Investigate real-world applications of momentum conservation in collisions
USEFUL FOR

Physics students, educators, and anyone interested in understanding the fundamental principles of mechanics, particularly in relation to energy and momentum conservation.

  • #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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