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I'm confused and am hoping someone could help me understand

energy can neither be created nor destroyed...

great...

so in physics classes we can set up problems and stuff were

KEo + PEo = KE + PE

Energy intial equals energy final sense energy is conserved but then when friction is added into the equation

KEo + PEo = KE + PE (plus the work done by friction)

HALT!!!
why would we set into our energy equation
Eo = E
an equation of work???
Work = Fd
work done by friction = Ffr d
Is that to say that the work done by a force equals it's energy??? So like why the energy of friction just equal to the work it does???

ok like I get how the work done by a force is equal to it's potential energy

i understand that work is equal to the change of kinetic energy

Work done by gravity = mgh

work done = delta KE

ok what I also don't understand is that why would we eneter into our energy conservation equatio one half k x^2 for the energy of a spring

ok like I understand the derivation that the work done by a spring does indeed = 1/2 kx^2
ok but why do we consider the work done by the spring "spring energy" and just plug into our equation as if it was an energy when it was just the work done by the spring

like I've been told that "oh well scientists call 1/2 kx^2 spring energy" well that's great I understand the derivation but all it proves is that the work done by a spring = 1/2 kx^2 not that it is equal to spring energy

Why is it that for Friction and Springs we can find the energy they... transfer... by just finding the work that they do and not for other forces

like if you pushed a block lets say with a horizontal force of 4N and for 1 meter at which point you release your hand

the work done by your push is 4J but you wouldn't go on to say that "oh well this is equal to the energy of push" and plug it into your energy conservation equation...

Thanks!
Please help... This has been killing me I've always been told this stuff but never udnerstood it fully like we just call 1/2 mv^2 kinetic energy because... just because... and potential energy equals mgh because I said so... and spring energy is equal to 1/2 kx^2 because god said so.............

Please don't get mad at me i just need to understand this

Newton ponder all this, and had to invent calculus to explain what was happening. Hold your questions until calculus, you will get the answer there.

Work is in calculus terms, the integral of force *dx integrated over the path. Remember that, then in calculus, all your terms and formulas suddenly make sense. Hang on till then.