One of the earliest set of lessons in physics
involves three simple ideas / formulas - **momentum, work**
and **kinetic energy**.
When combined, work and kinetic energy form the basis of the Work Energy
Theorem.

**Consider what happens when electrical energy is converted
into mechanical.**

A quantity of electrical energy is defined by the product of
voltage, current, and
time. Electrical
power can be converted to mechanical by applying a __voltage__ that
causes __current__ to flow; think of such things as an electrical
motor, solenoid, and so on.
In other words, voltage and current equate to mechanical force.
When this is done, mechanical energy becomes defined by the product of
force and __time__.
(voltage x
current x time =
force x
time).

The Work Energy Theorem defines mechanical energy by the product of
force and __distance__. Mechanical energy is either a function of
*force and time* __or__
*force and distance*, not both.

**And to illustrate how this conflict manifests whenever electrical
energy is converted into mechanical, consider the following very simple
mathematical exercise. **

Imagine converting a
known quantity of electrical energy into mechanical.
And to make this very easy to follow,
we will use the simplest case possible — accelerating an object from
rest.
Electrical energy could be configured
to provide a mechanical force of 10 newtons that acts for 1 second.
This amount of electrical energy will
first be used to accelerate a 1 kg object and then the exact same amount
will be used on a 2 kg object.

The equations that apply are
*F=ma*,
*
v=ta*,
and *
ke=½mv ^{2}*.

__The one-kilogram object__

It will accelerate at:

Its final velocity will be:

It experiences a change in Kinetic Energy of:

__
The two-kilogram object__

It will accelerate at:

Its final velocity will be:

It experiences a change in Kinetic Energy of:

The final values do not match
even though the exact same amount of electrical energy was applied to
both.

**The Obvious Obscured**

Without question, a problem exists and it exists primarily because no one believes it could exist in today's modern world. Upon seeing the obvious conflict between electrical and mechanical energy, the go-to reaction is to find some way of reconciling the paradox of how energy is quantified - force time versus force displacement. This is accomplished by adding complications whose sole purpose is to protect the status quo in physics; experiments are not done.

If one is only skeptical to new ideas and discoveries, he is not a true skeptic or a real scientist. Ask yourself how many times has conventional wisdom been wrong.

**Origins**

When a physicist seeks to defend the Work Energy Theorem, he can only guess which came first - the formula for work or kinetic energy. And if he knows which came first, he will not know of the experiment that "confirmed" the formula. And even if he knows all about the original experiment, he cannot see the error it contains for if he did, he would not be defending the Work Energy Theorem.

Click on this "history" link to see how the Work Energy Theorem came to be and the mistakes that were made along the way.