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I am not defying any law here just asking.

Energy conservation.

I was really wondering, How physicists arrived to this law?

I was fine with it, solving problems and stuff. But sometimes things click in my mind.

Perhaps confusionleads to a better understanding...

We can prove mathematically that energy is conserved for example a falling object or for some easy problems.

But how about complex mechanics? Can we prove it mathematically too? or should we just generalize it? Have we arrived to this law by experimenting? for example this

I can keep track of the forces and say that momentum is conserved (Newton third law, However I am also confused why the wedge wouldn't move at an angle because there is some parts where the force acting on it is has a Y component. Perhaps the ground is pushing upward? but that wouldnt be conserved for the system of block and wedge.. ??)

Anyway, I can use the same way above to show the energy is conserved, Can't I ?

Also, I have read on some articles. That our energy conservation principle doesn't happen all the time in the universe and there is in some condition some energy lost. What does this mean to you (The person who is answering) as a physicist? That our laws aren't right enough to be applied universally?

I know it is a foundation of a lots of fields of science we have today, That is why I am trying to get full prospective of it.

Energy conservation.

I was really wondering, How physicists arrived to this law?

I was fine with it, solving problems and stuff. But sometimes things click in my mind.

Perhaps confusionleads to a better understanding...

We can prove mathematically that energy is conserved for example a falling object or for some easy problems.

But how about complex mechanics? Can we prove it mathematically too? or should we just generalize it? Have we arrived to this law by experimenting? for example this

I can keep track of the forces and say that momentum is conserved (Newton third law, However I am also confused why the wedge wouldn't move at an angle because there is some parts where the force acting on it is has a Y component. Perhaps the ground is pushing upward? but that wouldnt be conserved for the system of block and wedge.. ??)

Anyway, I can use the same way above to show the energy is conserved, Can't I ?

Also, I have read on some articles. That our energy conservation principle doesn't happen all the time in the universe and there is in some condition some energy lost. What does this mean to you (The person who is answering) as a physicist? That our laws aren't right enough to be applied universally?

I know it is a foundation of a lots of fields of science we have today, That is why I am trying to get full prospective of it.

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