Everyone talks about energy as if it's going out of style, but what is energy, anyway?
Energy is the ability to do work.
Great! That's a simple enough... But what does that mean? I am young and capable - does that mean that I am full of energy? Well, in this sense, we are talking about mechanical work, and mechanical energy. To get to work and energy, we must first talk about force (from Newton's law):
Force (F)=Mass (m)*(a) Acceleration
The force required to move (accelerate) an object varies by the size of the object (it's mass). Well, given this, mechanical work can be so defined:
Mechanical Work (M)=Force (F)*(d) Distance
The mechanical work done on a system is the product of the force acting on it, and the distance it traveled Here we have some interesting phenomena. You know how sometimes you feel that you are "spinning your wheels" and not getting any work done? Well, from the definition of mechanical work, you aren't: to do mechanical work, the object needs to be moved - and the amount of work done varies directly by the distance traveled! From here, we can talk about the two main types of mechanical energy.
Potential energy:
Ep = m g h
If you lift an object to some height, that object has energy in it proportional to its size (mass) and the height that you lifted the object to (h). We throw in g (acceleration due to gravity) for good measure - but this is fairly constant across the Earth's surface (g ~ 9.81 m/s^2).
Kinetic energy:
Ek = (1/2) m V^2
An object travelling at a certain velocity (speed, V) and a certain mass (m) has energy.
Fairly simple concepts - but you need them later to understand how we change between mechanical work and various other forms of energy (heat, electric energy, radiation, & chemical energy).