I've managed to really confuse myself on the conservation of energy in a system. I guess the basic question boils down to why is the total mechanical energy of a system a meaningful quantity.(adsbygoogle = window.adsbygoogle || []).push({});

I understand E for a point particle in a conservative field is constant. I understand E for CoM with only conservative external forces is constant. Why is the sum of E for each element of a system constant? What are the specific conditions under which this is true?

At this point, words are only confusing me more, so I would prefer symbolic explanations using the definitions of work, ke, and potential. Here are some specific examples that confuse me.

#1 Elastic Collision: block 1 moving at speed v hits block 2, which is stationary. Equal mass blocks. Force between them is conservative (e.g. spring).

The following is wrong, but why?: look at block 1 in isolation. It is only subject to a conservative force. Therefore, its energy must be constant, yet it starts with E=KE and ends with E=0.

#2 Block on free wedge: a block slides without friction down a wedge, which slides without friction on the floor.

Is the normal force between block and wedge conservative? If yes, why does the total energy of the block decrease from the top of the wedge to the bottom? What is the PE of the normal force? How is that energy stored?

If no, how can total energy be conserved, since there is a nonconservative force?

Can anyone formulate and prove a statement for when the sum of the energy of each element in a given system must be concerned?

Thanks in advance

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# Homework Help: Total Mech Energy and Conservative forces

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