What is energy?

1. May 11, 2005

I have heard the definition of energy to be "capacity to do work". However, the term "work" to me seems even more ambiguous than the term "energy" itself. Does anyone have a good answer to the question of what energy actually is?
thanks

2. May 11, 2005

KingNothing

There is one thing you must understand first. Everybody learns in different ways. For some people, the capacity to do work is a good definition. For others, its not. Our minds all make sense out of things differently.

I learn best by example. A battery holds energy because once the energy is released, useful things can happen (running electronics). A ball held up in the air has potential energy because physical energy had to be used to raise it. Once it is dropped, that energy will be released again.

Energy is in many ways an abstract concept. We measure it by observing what it does, not the energy itself (for most purposes). We don't just go out and see energy. Energy does not have its own dimension. You may want to define it for yourself as an arbitrary measurement created simply to say that when you push a box up a hill, it comes back down the hill equally, or to say that when the fuel inside one of your car's cylinders explodes and releases energy, it pushes the car forward.

3. May 11, 2005

Anzas

energy is the ability of an object to do work
an object does work by appying force over a distance
so work is defiend by

$$w=FX \cos \alpha$$

where
w - the amount of work done
F - the force the object applied over the distance X
X - the distance over which the force F was applied
and alpha is the angle between the direction of the applied force and the direction in which the object moved when the force was being applied.

when we say an object has x energy that means it has the ability to do x work

when object A does work on object B (and only on object B) then the work A has done is substracted from its energy and added to the energy of B.

4. May 11, 2005

neutrino

Go through Ch 4, Vol 1 of The Feynman Lecture on Physics.

5. May 11, 2005

thanks for all the help. just one more thing. since your definition of energy uses the term force it would be helpful to have a precise definition for force aswell. I know that F=ma, where m is mass and a is acceleration, but mass is apparantly equivalent to energy and therefore your definition of energy appears to me to be cyclical. ie E=maXcosa where m is actually in a sense E aswell.
I know I am most likely mistaken in this as I dont have a particularly advanced knowledge of physics but I would be interested in hearing your answers. thanks again

6. May 11, 2005

KingNothing

mass is considered a very dense form of energy, but that's way, way beyond the realm of newtonian mechanics, which the old F=ma is.

7. May 12, 2005

Anzas

force is defiend to be any interaction between two objects
m in f=ma is whats called inertial mass
inertial mass is defiend to be the ability of a body to prevent a change in its acceleration thats the definition used no need to involve e=mc^2 .

einsteins infamous e=mc^2 simply states that matter can be converted into energy and energy can be converted into matter. (they aren't the same things one can just be converted to the other).