Momentum of two colliding trollies.

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The discussion centers on solving a problem involving the momentum of two colliding trolleys, with an emphasis on the principles of conservation of momentum and energy. The initial attempts to solve the problem were incorrect due to the misunderstanding that kinetic energy is conserved in inelastic collisions, where the trolleys stick together. It is clarified that mechanical energy is not conserved in this scenario, as some kinetic energy is lost. A question arises about the possibility of one trolley transferring all its kinetic energy to another while sticking together, but it is concluded that this is not feasible. The conversation highlights the importance of understanding the nature of inelastic collisions in physics.
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The question is shown in the first image attached.

I did three ways to solve it, and all three answers were wrong. After some trial and errors, I found the correct solution, which is written in the little box in the second image.

However, I still find my three solutions reasonable. I used both Principle of Conservation of Momentum and Principle of Conservation of Energy. I substituted everything correctly too. Why are they wrong?
 

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Kinetic energy is not conserved here since it is an inelastic collision.
For your first attempt, just use the first equation you've written down, remembering that mA = mB
 
coconut62 said:
I used both Principle of Conservation of Momentum and Principle of Conservation of Energy.
Mechanical energy is not conserved--the cars stick together. In fact, one of the questions asks for the fraction of KE lost.
 
ap123, thank you.

Doc Al said:
Mechanical energy is not conserved--the cars stick together.

Is it possible for one of the trolley to transfer all of its kinetic energy to another trolley while still being able to stick together with it? I mean like, when the first trolley hits the other, in that fraction of a second before any sound energy could be produced, the second trolley just starts moving and kinetic energy is conserved?
 
coconut62 said:
Is it possible for one of the trolley to transfer all of its kinetic energy to another trolley while still being able to stick together with it? I mean like, when the first trolley hits the other, in that fraction of a second before any sound energy could be produced, the second trolley just starts moving and kinetic energy is conserved?
No, not if they stick together.
 
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