Work Energy Theorem.com

 

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=½mv2. 

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.