## Euler-Alex Cylindrical Paradox

(With permission from Euler)

Wed, Jun 1, 2005 at 3:22 PM

Euler-Alex Cylindrical Paradox. Suppose we have a big vertically

placed hollow cylindrical object with spiral engraving on the surface.

The Spiral paint a trajectory from a point at the top rim of this

object to another point at the bottom of this object. Now we place a

metal ball of a small size that could fit the width of this spiral on

the starting position of the spiral on the top of this object and

release it. Naturally, gravity would pull this object downward. Do the

Math now.

Now the potential energy is Mass * Height * g, assume the ball is

rotating with constant speed, the kinetic energy is centripetal Force

* Distance= Mass* Velocity^2 / Radius* Number of Circle from top to

bottom(n)* 2* Pi* Radius (We assume the Spiral is approximate equal to

the length of a circle, however, the perimeter of this ellipse should

be GREATER than a circle), which we could rewritten to 2* Mass *

Velocity^2* Pi* n. And in textbook Physics we assume all the kinetic

energy is coming from the Gravity, therefore:

Mass * Height * g=Mass * Velocity^2 *n *Pi or

Height* g= Mass* Velocity^2 * n* Pi

Are they TRULY equal each other? It is impossible Mathematically

since the value of n is arbitrary! Theoretically it could equal to any

amount we want it to be. Of course, the result still await experiment

verification.

My prediction is no amount of experiment would prove this equation

right since it is WRONG theoretically. The reason?

Our assumption is wrong because we omit something very important:

The attraction force between the cylindrical object and the metal ball

which PROVIDE the energy which transform an otherwise free fall into

circular motion. It doesn’t matter what material the ball and the

cylindrical object are made of, as long as the spiral trajectory could

keep the ball rolling. We just use Gravitation Energy to Lead Out this

non-obvious energy. The amount of energy lead out depend on the

geometry of the trajectory, has nothing to do with the mass of the

rolling object.

To complete the Paradox, suppose we have a way to transfer the

kinetic energy into other energy, and storing that energy. Then we use

that energy to rise the ball from bottom to the top. However, the

amount of energy is more than adequate to do that. The energy input is

LESS than energy output!

To increase the level of challenge, we could change this rolling

ball into a Magnets, and place coil vertically inside the cylindrical

object. Use the electrical energy produce to move the magnetic from

destination to starting point. Since it is inconceivable that the

rolling Magnet would slow down, we have a very simple Generator which

extract energy from Magnetic Field, Molecular Attraction and

Gravitational Field at the same time. Now Output is far greater than

input.

To increase the level if challenge further, now we use what the

rolling Magnetic to somehow power a Generator of the design in 1. The

Output to Input ratio could be of ANY number we wanted to (greater

than 1).

We start with every working Physics theory to arrive at a result no

conventional Physicist would accept.

I challenge any Physicist to prove me wrong, or to nominate me for

the Nobel Prize on Physics for theorizing on Perpetual Motion Machine.

kinetic energy is centripetal Force * Distance = Mass* Velocity^2 / Radius* Number of Circle from top to bottom(n)* 2* Pi* Radius

<—– Why? How can you assume the centripetal force / velocity is constant?

And CENTRIPETAL FORCE does not do work!

And in textbook Physics we assume all the kinetic

energy is coming from the Gravity, therefore:

Mass * Height * g=Mass * Velocity^2 *n *Pi or

Height* g= Mass* Velocity^2 * n* Pi

<– So what is the INITIAL kinetic energy of the ball? 0?

I think you should read more books and do physics problems, think more detailedly and check your concepts. If you really know why "integral of F dotproduct dx = work done", you will not make mistakes like "kinetic energy = centripetal Force * Distance". I recommend the book "Fundamentals of Physics" by David Halliday and http://www.physicsforums.com to you. Hope you will propose some "deeper" paradoxes in the future!

passby said this on 一月 3, 2010 於 3:23 上午 |

Actually what I want to do is try to account for all energy in this process, I only ASSUME centripetal force as constant because I DO NOT HAVE A WAY to measure that in this thought experiment. I think what we need is a REAL EXPERIMENT to measure all the force acting on the ball.

Also if it is not the centripetal force, that what force is drive the ball downward? Remember that the spiral is curved so it is NOT COMPLETELY perpendicular to the motion of the ball.

If we assume that the spiral could be as infinitely long, then we arrive at the contradiction that no work done is driving the ball downward, what drive the ball downward then?

newnewhkcc1976 said this on 一月 6, 2010 於 3:07 下午 |