Why Do Different Conservation Laws Give Different Results in SHM Problems?

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Homework Help Overview

The discussion revolves around a problem involving simple harmonic motion (SHM) and the application of conservation laws. The original poster is examining the effects of adding a smaller mass to a larger mass attached to a spring while it is in motion, specifically looking at the resulting amplitudes and the ratios derived from conservation of momentum and energy.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • The original poster attempts to apply both conservation of momentum and conservation of energy to analyze the system but finds differing results. Some participants question the assumptions regarding energy conservation in the context of the interaction between the two masses.

Discussion Status

Participants are exploring the implications of the interaction between the masses and how it affects energy conservation. One participant suggests that the work done during the interaction alters the energy balance, drawing a parallel to inelastic collisions. There is no explicit consensus yet on the resolution of the original poster's confusion.

Contextual Notes

The problem involves assumptions about energy conservation in a dynamic system where an external force acts during the interaction of the masses. The original poster's inquiry highlights the complexities of applying conservation laws in non-ideal scenarios.

kushan
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Conservation of energy ?

Homework Statement


I was trying to solve this question
" A mass M , attached to a horizontal spring , executes SHM with Amplitude A1 , when the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with Amplitude A2 , ratio of A1/A2 "
when i apply conservation of Momentum i get
(M/(m+M))^(1/2)
and if i apply conservation of energy
i get (M/(m+M)

Can somebody help me figure out what is going wrong ?
Thank you
 
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When you place the small mass on the big one while it is in motion, the small mass has to accelerate up, the bigger mass has to decelerate to the common speed. For that, some force of interaction is needed, and that force does work. Because of the work done by something else than the spring, the sum of the elastic energy and kinetic energy is not conserved.
The situation is similar to inelastic collision. If the small mass were put in front of the big one it would be exactly an inelastic collision. The momentum conserves but the energy does not.

ehild
 


thank you ehild :D
 
Last edited:


You are welcome.:smile:
 

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