Momentum of two colliding trollies.

[coconut62]

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?

 

[ap123]

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 m_A = m_B

 

[Doc Al]

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.

 

[coconut62]

ap123, thank you.

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?

 

[Doc Al]

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.