Does Kinetic Energy Loss Equation Hold When Both Objects Are Moving?

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Discussion Overview

The discussion revolves around the application of the kinetic energy loss equation in perfectly inelastic collisions, specifically questioning whether the equation holds when both colliding objects are in motion prior to the collision. The scope includes theoretical considerations and mathematical reasoning related to kinetic energy in collision scenarios.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions if the equation for kinetic energy loss, which is derived from a stationary object colliding with a moving object, requires the second object to be stationary for its validity.
  • Another participant suggests that the situation becomes more complex when both objects are moving prior to the collision, indicating that the analysis may require additional considerations.
  • A participant mentions that they have worked through the mathematics and found it to make sense, implying that there may be a way to reconcile the equation with moving objects.
  • It is noted that the ratio M1/(M1+M2) is used because it provides a simple mathematical form, which some participants agree is a special case that is easier to handle.

Areas of Agreement / Disagreement

Participants express differing views on whether the kinetic energy loss equation can be applied when both objects are moving, indicating that the discussion remains unresolved and complex.

Contextual Notes

The discussion highlights the limitations of the kinetic energy loss equation in scenarios involving moving objects, with participants acknowledging that additional mathematical analysis may be necessary to fully understand the implications.

MotoPayton
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http://hyperphysics.phy-astr.gsu.edu/hbase/inecol.html

When a block in motion(M1) collides with a a stationary object (M2) in a perfectly inelastic collision, the fraction of KE final/KE initial can be modeled as M2/M1+M2.

My question is if M2 has to be stationary for this equation to work.

If both objects are moving before the collide in a perfectly inelastic collision does the ratio of lost kinetic energy still hold?
 
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MotoPayton said:
My question is if M2 has to be stationary for this equation to work.
Yes.
If both objects are moving before the collide in a perfectly inelastic collision does the ratio of lost kinetic energy still hold?
It's a bit more complicated when both blocks are initially moving. But it's easy enough to work it out.
 
I ran the math and it makes sense now.

The only reason we use the M1/M1+M2 is because it is the only ratio of energies that has a simple mathematical form.
 
MotoPayton said:
The only reason we use the M1/M1+M2 is because it is the only ratio of energies that has a simple mathematical form.
Yes. It's a special case that is particularly easy to deal with.
 

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