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My physics book defines energy like this:

"Everything that works has energy, energy $E$ of a system is a function of state and its variation $\Delta E = W$ ($W$ is work done on system)".

After that, it said that energy of a system is sum of its mechanical energy and its internal energy. I have 2 questions about this:

  1. Why Energy = Mechanical Energy + Internal Energy. Is it inferred from the definition?

  2. Why there is only 2 main kinds of energy is potential energy and kinetic energy? And how do we classify energy?

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    $\begingroup$ About second question. Potential energy measures what work system can do potentially. Imagine $1~kg$ brick laying on the roof of $100~m$ height building,- if would be falling from that roof to the ground,- could do about $1~kJ$ work upon touching ground. That's why it's potential energy, energy that's "in there" but not used still. Kinetic energy (btw, kinesis in Greek means "motion") means that some other form of energy was converted for speeding object. Usually it can be potential, but also can be internal/heat (from heat engine), etc. $\endgroup$
    – Agnius Vasiliauskas
    Nov 18, 2022 at 18:33

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Strictly speaking, energy is capacity to do work for a given system. However, I think you are versed in this definition so I would like you to give you other intuition.

Typically, we often are interested in 'change in energy'. Absolute energy has to do very little with our lives. For example, our body's atoms has absolute energy $E=mc^2$, but you can't use it or transfer it in any way realistically possible. By doing work we are basically transferring energy to other mediums, in different forms.

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  1. Yes, it can be inferred from the definition you gave but one needs more knowledge of physics to understand what it means: Typically in classical mechanics you consider an object as a point mass and define it's mechanical energy as E_kin=0.5mv^2. But that's not the whole story because the object can have a substructure, for example if you consider an atom it can move around which contributes to the mechanical energy but it also has internal energy levels (see for example https://en.wikipedia.org/wiki/Energy_level). Or you can consider a gas ensemble where it's center of mass velocity defines the mechanical energy and the internal energy is given by the velocity of the particles and their potential energy in the frame of center of mass (https://en.wikipedia.org/wiki/Internal_energy).

  2. There are only the types kinetic and potential energy because your system needs to be able to provide work as in the definition said. This can be only given by these two types.

I hope I could help you with my explanations. If you have more question do not hesitate to ask :)

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    $\begingroup$ Re, "There are only the types kinetic and potential..." That's one way of classifying it. But you might consider that there are other axes of classification. Some scientist might find it useful, for example, to notice the distinction between chemical potential energy, and the binding energy of an atomic nucleus. Another might find it useful to distinguish the energy carried by a photon from the the energy carried by a pitched baseball. Energy is what it is. Types are our own inventions which we use in trying to understand it. $\endgroup$
    – Solomon Slow
    Nov 18, 2022 at 15:21

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