[Pmb]

There is no scientific principle involved in the naming of quantities.

I believe that this has gotten off track. My purpose was to demonstrate that quantities which have momentum and quantities which have energy both have the ability to do work and therefore "the ability to do work" doesn't uniquely define energy. That is one of the reasons it can't be used to define energy.

[alancalverd]

I agree with your conclusion - almost. It's a fatuous definition.

However, whilst anything that has mass and velocity has the ability to do work, a coiled spring and a charged battery also have the ability to do work, unrelated to their mass or speed. Therefore energy is always the ability to do work, and anything that has momentum also has energy, but the converse is not necessarily true. 

And by the way, both energy and momentum are conserved in a pure inelastic collision. In the example you gave (#14), the system momentum was zero before and afterwards, and inelastic collisions of macroscopic bodies result in an increase in temperature of the bodies. I'll leave you to work out what happens when a neutron is absorbed by a nucleus!

[Pmb]

However, whilst anything that has mass and velocity has the ability to do work, a coiled spring and a charged battery also have the ability to do work, unrelated to their mass or speed. Therefore energy is always the ability to do work, and anything that has momentum also has energy, but the converse is not necessarily true.

I knew this when I came up with that example. The so-called “definition” energy is the ability to do work is flawed in other ways since there are instances where there is no ability to do work yet there is energy present. Consider a neutron. It has rest energy due to its proper mass. However by itself it does not have the ability to do work when its at rest. This is example when the definition of “ability to do work” won’t work.

[alancalverd]

But when your stationary neutron decays, the sum of the pion and proton masses is less than the rest mass of the proton and they have kinetic energy equal to the mass difference. The same as a spring, sort of, and a radium nucleus even more so.

However your underlying point remains true, as does my preferred definition: energy is one of the conserved quantities in a closed system. This may beg the question of "what is a closed system?" where the obvious answer is "one in which energy and momentum are conserved" but if we add "and entropy increases" it's a fairly complete definition that allows us to solve all the physics equations. 

[Pmb]

But when your stationary neutron decays, the sum of the pion and proton masses is less than the rest mass of the proton and they have kinetic energy equal to the mass difference.

I blame it on fatigue but I didn't mean neutron but meant neutrino for just this reason. Or even zero-point energy etc.

[SimpleEngineer]

Maybe the definition of energy having the ability to do work, then contradicts the ideas of zero point energies?

For me.. Energy means its going to do something even if I dont know what that something is.. a potential by all means and purposes..

your zero point mass.. sitting there (or moving there) is going to do something at some point.. so it has/is energy!

if its not going to do anything

a) how do you know its there
b) what is the point of it being there

[Pmb]

Maybe the definition of energy having the ability to do work, then contradicts the ideas of zero point energies?

I fully agree. E.g. How can an atom in its ground state be said to have energy?

I’ve addressed your concern in the webpage I posted earlier in this thread, i.e.
http://home.comcast.net/~peter.m.brown/mech/what_is_energy.htm

Suppose we were to define energy as the ability to do work and you were asked I have in mind a quantity which has the ability to do work. What is that quantity?  What would your answer be? I addressed this point right above Figure 1.

For me.. Energy means its going to do something even if I dont know what that something is.. a potential by all means and purposes..

A rock sits at rest on the top of a hill. It has energy by virtue of its position. Why would you expect it to do something?  A stable particle at rest in an inertial frame has energy by virtue of its mass. Again, why would you expect it to do something?

[SimpleEngineer]

that rock IS doing something.. its pushing down on the hill.. it may not look like its doing something but it IS doing something. (and will do other things if interfered with)

And the something may be a reaction to outside forces, without energy there can be no interaction.. (i.e. if something hits it, it will change the velocity/momentum of that something)