Conservation of Energy or Momentum?

[i.mehrzad]

Conservation of Energy or Momentum??

A mass M is attatched to a horizontal spring of force constant k fixed on one side to a rigid suppport.(Please imagine the diagram). The mass oscillates on a frictionless surface with time Period T and amplitude A. When The mass is in equilibrium another mass m is gently placed on it. What will be the new amplitude of oscillation.

My approach,
Conservation of energy
1/2 Mw(1)^2A(1)^2= 1/2 (M+m)W(2)^2A(2)^2 where w is omega.
And then on rearranging the terms i got
[A(1)/A(2)]^2 and
w(1)/w(2) on the left hand side i substituted it with (m+M)/(M) since w is inversely proportional to m.
This did not lead me to the right answer.
However if i conserved momentum then i do get the right answer. Question When am i supposd to know when to conserve momentum and when to conserve energy.
Anyone to help since my AIEEE examination is tomorrow.

 

[i.mehrzad]

Note here W(1) A(1) stands for initial amplitude and initial angular velocity.

 

[m2003]

I would say that both conservation of energy and momentum are important concepts to consider in this situation. However, in this specific scenario, it seems that conservation of momentum would be the more appropriate approach.

Conservation of momentum states that the total momentum of a system remains constant unless acted upon by an external force. In this case, when the additional mass m is gently placed on the original mass M, there is no external force acting on the system. Therefore, the total momentum of the system should remain constant.

On the other hand, conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this scenario, the potential energy of the system changes when the additional mass is added, but the total energy should remain constant. This may not necessarily lead to the correct answer for the new amplitude of oscillation.

In general, to determine whether to use conservation of energy or momentum, one must carefully analyze the system and consider the forces acting on it. In this case, since there are no external forces and the masses are not accelerating, conservation of momentum would be the more appropriate approach. However, in other situations where external forces may be present, conservation of energy may be the better approach. It ultimately depends on the specific dynamics of the system in question.