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.

I understand that you're feeling confused and want to understand the concepts of energy, work, and their relationship. Let's break it down and clarify some of your concerns.

First, the principle of energy conservation states that energy cannot be created or destroyed, only transferred from one form to another. This principle allows us to set up equations to describe the different forms of energy in a system.

When friction is involved, we need to account for the work done by friction in our energy equation. Friction is a force that opposes motion and does work on an object, so we include it in the equation to ensure that energy is conserved.

The equation you mentioned, Work = Fd, defines the work done by a force. This equation states that the work done is equal to the force applied multiplied by the distance over which the force is applied. So, when we calculate the work done by friction, it is equal to the force of friction multiplied by the displacement.

The work done by a force is indeed equal to the change in potential energy when considering conservative forces, like gravity. For example, when an object is lifted against gravity, the work done by the force of gravity is equal to the change in potential energy, which is given by mgh.

For a spring, the equation for the work done (W) is derived as W = (1/2)kx^2. Here, k represents the spring constant, and x represents the displacement from the equilibrium position. This equation shows that the work done by the spring force is equal to (1/2)kx^2. This quantity is often called the "potential energy of the spring" or simply "spring energy" because it represents the energy stored in the spring due to its deformation.

It's important to note that the reason we call certain quantities "kinetic energy" or "potential energy" is because these names have been given based on their observed behavior and mathematical relationships. The concept of energy arises from extensive experiments and observations, and the terms used to describe different forms of energy have been defined to represent those relationships.

Regarding your example of pushing a block, you're correct that the work done by your push (4J) is not typically considered as a distinct form of energy. In this case, the work done by your push would be transferred into the kinetic energy of the block.

I hope this explanation helps clarify your questions. If you have any further doubts or need additional clarification, please let me know.