I have ten apples. I eat two apples. I now have 8 apples. I can write that story as 10 – 2 = 8
Let me retell that story. I had ten apples on the table and zero apples in my belly. Now, I have 8 apples on the table and 2 apples in my belly. I can write that story as 10 + 0 = 8 + 2
Let me retell that story. Today I ate two apples. I started with ten apples, but later I only had eight apples. I can tell that story 2 = 10 -8
If someone wanted, they could rewrite either of these expressions to be 10 = 8 – (-2). But just because you can do something, doesn’t mean you should.
For that reason, I don’t like this physics equation,
Ei = Ef – Wnc
It doesn’t tell a very good story.
It makes way more sense (to me) to write it as Ef = Ei + ΔE. This simply says the energy you have later is just whatever the energy you started with plus the change, or write it as Ei¹ + Ei² = Ef¹ + Ef² This says that what you start with is what you end with, even if you rearrange things to be in different places. I’d even be OK with ΔE = Ef-Ei = Wnc because then its clear that the work quantifies that amount of energy coming in or going out.
Any else think that writing KEi + PEi = KEf + PEf – Wnc is a bad story?