# Confusion with work and energy

• Entr0py
In summary: For example, if you have kinetic energy and potential energy, and you use work to convert one to the other, you've created a new type of energy called "work energy".
Entr0py
This is something that's bugged me since I've read about it. What does it mean to say "energy is the capacity to do work"? I've read somewhere that work is some sort of integral. But I'm still confused, what do we mean when we say "the energy of object x is so and so"? I know the two quantities are related by the work-energy theorem, but I think there's a difference between knowing that such an equation exists and actually understanding it.

You start by defining work as the integral of force over some path:
##W=\int_C Fds##
You get a quantity W out of it - it tells you something about how a force acts on an object. You wonder if it's ever going to be useful to you.

When you calculate this quantity to be non-zero for some system, you also make an observation that some other properties of the analysed system changed at the same time. Be it temperature distribution in the system, position of masses in a force field, velocity of those masses, etc.

You try and quantify by how much these properties change when you do work, and you end up with equations for heat transfer, potential energy, kinetic energy etc.

Since you observe that at least one of these properties changes by the exactly right amount to compensate for the work quantity, you conclude that work cannot be done without expanding those (and vice versa).

You call these properties energy for the lack of a better word. You end up happy you've managed to find a way to connect various properties of a system though the single quantity of work.

Last edited:
Nugatory and Entr0py
Bandersnatch said:
You start by defining work as the integral of force over some path:
##W=\int_C Fds##
You get a quantity W out of it - it tells you something about how a force acts on an object. You wonder if it's ever going to be useful to you.

When you calculate this quantity to be non-zero for some system, you also make an observation that some other properties of the analysed system changed at the same time. Be it temperature distribution in the system, position of masses in a force field, velocity of those masses, etc.

You try and quantify by how much these properties change when you do work, and you end up with equations for heat transfer, potential energy, kinetic energy etc.

Since you observe that at least one of these properties changes by the exactly right amount to compensate for the work quantity, you conclude that work cannot be done without expanding those (and vice versa).

You call these properties energy for the lack of a better word. You end up happy you've managed to find a way to connect various properties of a system though the single quantity of work.
Awesome explanation. You clarified some things for me. Thank you

I've always thought of "energy" as a "bookkeeping device". Any time a new situation occurs in which the previously defined types of energy are not conserved, we define a new kind so that it is!

## What is the difference between work and energy?

Work is the measure of the force applied to an object over a certain distance, while energy is the ability of an object to do work. In other words, work is the action, while energy is the result of that action.

## How are work and energy related?

Work and energy are closely related because work is the transfer of energy from one object to another. When work is done on an object, its energy changes.

## Can work be negative?

Yes, work can be negative. This happens when the force and displacement are in opposite directions, resulting in the object losing energy instead of gaining it.

## What is the unit of measurement for work and energy?

The SI unit for work and energy is joule (J). It is equivalent to one newton-meter (N*m).

## How can we calculate work and energy?

Work can be calculated by multiplying the force applied to an object by the distance it moves. Energy can be calculated by multiplying the force applied to an object by the distance it moves, and then subtracting any potential energy or work done by external forces.

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