Confused about the difference between impulse momentum and kinetic energy

quirck

1. The problem statement, all variables and given/known data

1 mass M1 of 1 kg moves frictionless at V1 1 meter per second to the right. It fuses with mass M2 of 2 kg and together they keep moving frictionless to the right. What is the speed V2 of the fused objects?


2. Relevant equations

Impulse mass * Velocity
Kinetic energy mass * velocity^2

3. The attempt at a solution

Conservation of energy 1/2*M1*V1*V1 = 1/2 [Joule] = 1/2*(M1+M2)*V2*V2
V2=SQRT (1/3) [m/s]

Conservation of momentum M1*V1 = (M1+M2)*V2
V2=1/3 [m/s]

My confusion is.
When and why should I conserve momentum and when and why should I conserve energy?
I think I can imagine what is energy of a moving object, however I think that somehow I cannot imagine what is momentum.

Doc Al

Remember that momentum is conserved in any collision, but kinetic energy is only conserved in some collisions. When the masses bounce apart and energy is conserved, that's called an elastic collision; when they stick together, that's called an inelastic collision (and energy is not conserved).

In this problem, energy is not conserved.

quirck

[q]In this problem, energy is not conserved.[/q]

Thank you for the quick reply. Very kind.
I understand you want to stay simple here and this rule of thumb is applicable here, however I want to get a deep understanding of this. Most of all I want to try to get a grasp on what is momentum. Like understanding it so much that even my stomach also understands.

We understand of course that also energy of a closed system is always conserved. So the energy must have gone somewhere. I suspect some kinetic energy was transformed from kinetic to heat or deformation. That would be an answer to the question where the energy would have gone.

But then why is momentum conserved? For me it is still is a rule that is just applied and seems to work in the real world. I have a vivid imagination about how energy is conserved. I just like to have the same vivid imagination about momentum conservation.
Do you have any idea how to explain?

Doc Al

Good!

If you understand that the force on an object tells you the rate of change of its momentum, and you understand that whenever two objects collide they exert equal and opposite forces on each other (as per Newton's 3rd law), then perhaps the fact that total momentum is always conserved in a collision will make more sense.

Read this tutorial: Momentum and Its Conservation