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I have a problem when it comes to work and energy I honestly cannot get the idea behind them, when I read about work it is defined as the ability to transfer energy, But when I read what energy is I find the definition is: the ability to do work, so what is the meaning of this it is meaningless for me I cannot conceive of this!! what is energy? what is work? and why works' formula is W=FD? and why other formulas of energy are like they are? I want to know the deep meaning behind these.

If my question is hard to answer here or it is too long to answer, can you refer me to a book that would explain all these mysteries to me? please do if you can

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  • $\begingroup$ This is might help with what energy is. Basic energy question $\endgroup$
    – mmesser314
    Commented Jan 6, 2021 at 0:57
  • $\begingroup$ hyperphysics.phy-astr.gsu.edu/hbase/work.html $\endgroup$ Commented Jan 6, 2021 at 1:29
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    $\begingroup$ If you are not comfortable with the definitions, then it might be of help to do some problems involving work/energy. This is the best way to learn these concepts. $\endgroup$
    – joseph h
    Commented Jan 6, 2021 at 1:46
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    $\begingroup$ Your “WARNING!!!” is inappropriate. I suggest removing that word. $\endgroup$
    – G. Smith
    Commented Jan 6, 2021 at 1:54
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    $\begingroup$ Just wait til you see the definition of a tensor $\endgroup$
    – Señor O
    Commented Jan 6, 2021 at 4:41

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when I read about work it is defined as the ability to transfer energy, But when I read what energy is I find the definition is: the ability to do work

The issue that you are running into here is that physics is not one overall field of study, but rather has many smaller subdivisions. Very often one term will be defined differently in different branches of physics. Here you are looking at the thermodynamics definition of work and the mechanical definition of energy.

In mechanics: work is defined as $dW=\vec F \cdot d\vec s $ and energy is the ability to do work. This is an appropriate definition for mechanics because the central topics in mechanics are forces, so it is reasonable to consider a force-based definition as the primitive one.

In thermodynamics: energy is defined as $KE=\frac{1}{2}mv^2$ or anything that can be converted into it, and work is the ability to transfer energy. This is an appropriate definition for thermodynamics because the state variables like energy are the central topics.

The definitions are not circular in either sub-discipline, but if you mix them inappropriately you can get an apparent circularity as you found. Probably more interesting, however, is the fact that the different definitions are consistent with each other. If you start with the thermodynamics definition and calculate how much energy is transferred by a force then you can derive the mechanical definition of work. If you start with the mechanical definitions then you can derive the thermodynamic definition of KE.

Probably neither definition is a good “unity” or “fundamental” definition. In my opinion, the best candidate for that is to use Noether’s theorem to define energy as the conserved quantity associated with the time translation invariance of the laws of physics. Then work is still defined as a transfer of energy.

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  • $\begingroup$ Any set of definitions will become circular if you go deeper. We can define work in terms of force, and force in terms of acceleration and mass, but mass is the property of resisting a force, so we've reached a circle. $\endgroup$ Commented Jan 6, 2021 at 19:09
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I see the difference between work and energy this way. Energy is a state variable. it depends on variables like speed, position, temperature etc. It describes the state of a system or particle. Work is a way to transfer energy from one part of the world to another, via a force. So in mechanics, I can change the energy state of an object, by pushing it and doing work on it. Perhaps, I change its kinetic energy, or I lift it against gravity and change its potential energy. In order to do this, my energy state has to change. So I burn some chemical energy. Perhaps not much, but it has to happen. Work and energy can be confusing, I believe, if it is only discussed in the context of mechanics, without understanding the big picture.

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  • $\begingroup$ Thankyou for your response i highly appreciate it but what I am seeking here is how scientists think of it intuitively and how did they actually form these definitions, in a nutshell: The deep meaning of the ideas. $\endgroup$ Commented Jan 6, 2021 at 2:29
  • $\begingroup$ I don't understand why this was down-voted. Perhaps it's the reference to chemical energy which, I admit, does cloud the argument. $\endgroup$
    – garyp
    Commented Jan 6, 2021 at 3:22
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For starters, energy is just a number that remains the same at any time in the universe, only its distribution changes. That is what energy is in a nutshell. Work is how that distribution can be changed in due course of time. What happened with energy is that we have been able to identify and calculate such a number that always gives us the same answer no matter when or where it is calculated. Now you might believe that there is something much deeper in it but that is what an actual Physicist told me on what he meant by energy.

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I will give a rather unconventional answer. Energy is the 'state' of an object in space and time, which can be defined as a combination of two things: the mass of an object, which is the intrinsic unchanging component of 'state', and its motion in space and time, which is the extrinsic variable component of 'state'. So mass is generally considered to be constant for an object, and motion is variable and represented as distance and time. Motion can be in the form of translational motion(one place to another), vibrational motion or rotational motion. Both mass and motion are needed to accurately describe the total 'state' of an object i.e. its energy, which can be in different forms. For example, at the atomic level, the 3 forms of motion, combined with mass translates into heat energy.

That was the qualitative definition, now for the quantitative definition. The question is how would you mathematically combine the definitions of mass and motion to give an appropriate mathematical definition for energy? The answer is not so straightforward, and this is where the equations come in. So then we come to 2 basic ways to describe useful notions for energy:

$$K.E. = (1/2)mv^2$$ $$E = mc^2$$

The first equation represents dynamic state that depends on motion, and the second equation represents the base invariable state that is independent of motion. They both seem to represent useful values, which are conserved. You may be wondering where the equation for work done is. The equation for work done represents the change in kinetic energy, and are two different aspects of the same thing. In fact one can be derived from the other using $F=ma$ and kinematics, as shown here:Where did the kinetic energy formula come from?

The equation for kinetic energy is better suited for scenarios in which an object is moving at a constant velocity, with no net force acting on it. The equation for work done is better suited when there is a force acting on an object. Potential energy can simply be seen as the potential motion an object can make, arising from multiple forces acting on that object that vary with time.

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understanding work and energy

Work and energy are two intercoiled interconnected highly tangled concepts. But here is an analogy. Energy is like money. Work is a transfer of money(energy).

Imagine a group of 5 people who can only exchange money amoung themselves. Such a system is called an isolated system. Money cannot come in or go out of this 5 people. If you need money, any one amoung the five have to transfer it to you. And you can spend your money by transferring it to someone else.

100% similarly, work is any process that gives a body energy. For you to get energy, something else have to do work on you. Now that you have more energy, you can spend it by doing work on something else.

The problem is that we don't have a mental picture while trying to understand that cyclic definitions. Now that we have a picture (of money and money transfer), we can again define Work and energy.

Work is any process that gives a body energy. Energy is the amount of "ability to do work" that a body has.

Maybe an example also helps : You are pushing a cart. You have done some work on the cart $W = F \ s$ where $F$ is the force you applied and $s$ the displacement of the cart. So now that you have done some work on the cart, cart has more energy and you have less. And the cart can transfer it to something else by colliding (and many other ways to transfer)

Why are the formulas as they are? please wait

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  • $\begingroup$ but for someone to transfer money it needs to have some money and this again comes to the question that what Is energy ? Is it something which tends to be transferred all the time among different forms ? $\endgroup$
    – Ankit
    Commented Jan 6, 2021 at 8:12
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A thing that confused me a lot about transfer of energy:

Work done by a force on an object doesn't transfer energy on the point of contact, nothing material flows to the object. It's like an online transaction going on inside the system. See the picture from Fundamentals of Physics book!

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