Hooke’s Law and the Missing Energy of Gravity.

Recently I’ve been going back and forth with various folks in the twitter realm about the fundamentals of physics.  The biggest stumbling block is the issue of forces and how to define them.  I stated in a previous post that you need 3 specific attributes to calculate any force equation:

  1. Magnitude
  2. Vector (or Direction)
  3. Time

I then present a simple example of a 4000kg car accelerating at 10 m/s² for 10s.  The Impulse of Force of the car at each second is:

Mass x acceleration x time¹ = Impulse of Force¹ (¹ is all reference frames from 1 – 10 seconds).  Multiplying Force · Time is known as impulse and is a valid way of expressing a force.

  • 4000kg · 10m/s² · 1s = 40,000 kg·m/s (velocity = 10 m/s) = 200,000 Joules
  • 4000kg · 10m/s² · 2s = 80,000 kg·m/s (velocity = 20 m/s) = 400,000 Joules
  • 4000kg · 10m/s² · 3s = 120,000 kg·m/s (velocity = 30 m/s) = 600,000 Joules
  • 4000kg · 10m/s² · 4s = 160,000 kg·m/s (velocity = 40 m/s) = 800,000 Joules
  • 4000kg · 10m/s² · 5s = 200,000 kg·m/s (velocity = 50 m/s) = 1,000,000 Joules
  • etc…
  • 4000kg · 10m/s² · 10s = 400,000 kg·m/s (velocity = 100 m/s) = 2,000,000 Joules

However, where I caught the consternation of others in the twitter realm was due to confounding of terms that are very specific in the physics world.  We all experience  the affects of forces all day, everyday in our lives and we generally don’t break them down into units of measurement, types of units, work vs. force, etc.  So my way of describing what I see as a fatal flaw in gravity was met with irate rantings.

For one, I was pointing out a potential problem with something they hold in an almost sacred sense (gravity).  And secondly, I was not using terminology correctly for their taste.  I don’t necessarily blame them for wanting exact language, but I would argue that they most likely understood the point I was trying to make but did not want point me in the right direction.  But, for the most part however, they were decent.  In a way, by them resisting what I was presenting forced me to fix and clarify my position.

Force, rate of change, work and energy

What I saw was that over time the acceleration due to gravity should equate to an increase in force on the mass involved.  However, the concept of force is important since in the case of gravity it is, indeed, constant.  I wasn’t arguing that gravity is increasing but the net forces are increasing.  I kept arguing that time must be included in the equation or it doesn’t represent reality (though it was valid see impulse of the force).  But again, my use of the words net force with time was incorrect with respect to physics as we are taught today and net forces has a specific meaning.  It wasn’t until I recalled kinetic and potential energy (work) and how it relates back to force that I was able to present my case in a language that would be acceptable.

From the car example above, if F = ma, then the rate of change is 40,000 N which means the force is constant.  But this is counter-intuitive to most people since they know the car is traveling faster with each second.  However, for acceleration to exist at all,  energy must be constantly applied.  If we accept the conservation of energy law, then that energy must be going somewhere.  In this case it is being expressed as kinetic energy.

In the case of gravity acting on an object or a person on the earth’s surface, gravity is that constant force or energy that is supplying the acceleration.  Either the object or person needs to move or the energy needs to be converted into something else like heat or sound or whatever.  It is the amount of energy that is increasing not the force itself.  We can conclude then, that time multiplies how much energy is in a system with respect to the force being applied.

We can all bear witness to the fact that we are not heating up or emitting noise or expressing some other form of energy release under the stress if gravity.  The counter argument is that since there is no movement there can be no acceleration.  But this is a fallacy since the height of the person is equal to the “x” value in Hooke’s law and the motion is expressed as the compression of the human frame.

There is also a distinction between kinetic energy and potential energy.  A car driving at 100 km/h has a specific amount of kinetic energy but a spring under increasing compression has potential energy that is being stored in the spring itself.  The spring has a maximum compression it can reach before it will begin to become crushed under an increasing load.

Hooke’s law is only a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It must eventually fail once the forces exceed some limit, since no material can be compressed beyond a certain minimum size, or stretched beyond a maximum size, without some permanent deformation or change of state. Many materials will noticeably deviate from Hooke’s law well before those elastic limits are reached.

Wikipedia

Even though the spring no longer has motion the amount energy will increase as the load capacity is transferred to less elastic structures like the metal of the spring or the surface the spring is sitting on.

In other words, the increase of potential energy will propagate to the surrounding environment and begin to compress the weakest structures first.  In the case of a human being standing on the surface of the earth, the acceleration due to gravity would continue to propagate through the human frame as per Hooke’s law.  I have had many discussions with folks who insist that the forces between the earth and the human being cancel each other out.  But they are confusing force with work.

Any equal and opposite reaction is within the frame of the human being (like a spring) and the ground they are standing on.  The opposing forces balance out, but this would not stop the acceleration; the balanced forces would only resist the downward pull of gravity and subsequently increase the potential energy. Since gravity is supposed to be an acceleration and is supposed to be pulling at a force proportional to the mass of the earth, the human being wouldn’t stand a chance.  It is precisely because of the equal and opposite reaction and the balancing of forces that potential energy is possible.  So they are confusing the forces involved with the energy (work) being applied to the mass.

Potential Energy

assuming conservation of energy: if F=ma and a = 9.8 m/s² and m > 0 then ΔPE > 0. where’s all that energy going? We should all be crushed by now.

Spring energy

The potential energy Uel(x) stored in a spring is given by

{\displaystyle U_{\mathrm {el} }(x)={\tfrac {1}{2}}kx^{2}}

which comes from adding up the energy it takes to incrementally compress the spring. That is, the integral of force over displacement. Since the external force has the same general direction as the displacement, the potential energy of a spring is always non-negative.

This potential Uel can be visualized as a parabola on the Ux-plane such that Uel(x) = 1/2kx2. As the spring is stretched in the positive x-direction, the potential energy increases parabolically (the same thing happens as the spring is compressed). Since the change in potential energy changes at a constant rate:

{\displaystyle {\frac {d^{2}U_{\mathrm {el} }}{dx^{2}}}=k\,.}

Note that the change in the change in U is constant even when the displacement and acceleration are zero.

What does this mean?  It means, a constant and catastrophic amount of potential energy should be building up in every object on the earth’s surface.  As mentioned above, this does not violate F=ma since we are not talking about an increase in the force of gravity but an increase in potential energy due to that constant force.

If we calculate the “elastic” capacity of the human frame and equate it to “k” and multiplied that by “x” which would be the height of the person (since they should be getting compressed by gravity) and then multiply by 1/2 we should get the potential energy stored or expressed within the human frame.  Also, since the value for “k” of the human being is less than “k” for ground, the human being would be crushed into the ground.  However, as we all know, we aren’t springs, and won’t bounce back from such an event.  Most of the energy will be released in the form of noise and heat.  Not a pretty picture.

The modern theory of elasticity generalizes Hooke’s law to say that the strain (deformation) of an elastic object or material is proportional to the stress applied to it. However, since general stresses and strains may have multiple independent components, the “proportionality factor” may no longer be just a single real number, but rather a linear map (a tensor) that can be represented by a matrix of real numbers.

Wikipedia

So we can all say with a high level of certainty that we are not being crushed by gravity, therefore, gravity must be falsified.  We exist in a non-gravitational realm.

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A Discrepancy in the use of the Centripetal Force

This is a re-post of an article I wrote in reply to JimSmithInChiapas.  He has been kind enough to respond to some of my ideas on gravity, centrifugal and centripetal force.  Though he does not agree with my assessment of these forces, we continue to communicate in a respectful manner.  Below is a recent reply to a comment he had on centripetal forces.  Ultimately, I feel that the centripetal force has been fundamentally misapplied in spinning frames of reference.  It is my contention that a single frame of reference for spinning body requires that for any object to be apart of that frame, it must be attached directly to that spinning body.  This has massive (no pun intended) implications.  You can read my argument below:

Jim…thank you for your reply.  I initially wanted to clarify a slight misrepresentation in your article.  My article is called “Does Gravity Make Sense?” not “does gravity exist?”.  They are different concepts.  I’m questioning how gravity is being represented by mainstream science today not that objects have mass or that they fall from the sky.

In any event, the example that I used provided a single frame of reference with respect to a spinning disk.  I used a disk with a 10m radius that spins at 10 m/s with a person of 72kg on the outer rim.  The person would experience 720N/kg of centrifugal force.  I don’t think that is in question.  I then go onto saying that unless the person holds onto the disk (via an attached handle of some kind), they would be flung from the disk at 720N/kg.  Again, I don’t think that is in question either.  The centripetal force is an inward force that requires the handle and the person to be attached to the disk at all times.

A more illustrative example would be the Olympic hammer throw.  The athlete is holding onto a tether which is attached to heavy weight.  The spinning motion of the athlete creates the centrifugal force which flings the weight outwards.  The strength of the athlete keeps the hammer from leaving a circular orbit via a centripetal force.  The inward force (centripetal) is provided by the athlete which is ‘balance’ by the centrifugal force.  But all the spinning objects in that frame of reference are and must be attached together. 

There is no empirical evidence of a centripetal force acting on a body that is not attached to the spinning body.  How could it?

There are no real world examples of a free floating object being acted on by a centripetal force.  You can mathematically present a centripetal force acting on an object but it is missing the real world necessity of being attached to or apart of the spinning object.  The centripetal force is a function of a spinning object; it is not a separate force that can be applied to an object outside that frame of reference.  To be part of that frame of reference, an object would, by necessity, need to be attached to the spinning object. 

For example, the person in the disk example above, is not part of the frame of reference unless they hold onto the disk with sufficient force.  They are literally removed from the frame via the centrifugal force.

Therefore, I would conclude that any object that is rotating around the earth must, by necessity, be attached to the earth to be part of that frame of reference for any object not attached is subject to the centrifugal force and will be removed from the frame. 

If we take a real world example of a person of 72kg standing on the surface of the earth and if they are standing at the equator and if the earth is spinning at 1000miles/hr then they are subject to a centrifugal force of 2.2N/kg.  If gravity is acting on the person with 9.8N/kg then a total force of 7.6N/kg is present.  The centripetal force is not part of the frame of reference for that person as shown above.

As the mass of the object increases, the centrifugal force increases.  Therefore, an object greater than ~330kg should become “weightless” on the surface of the earth.  This is obviously not happening nor are people 22% lighter at the equator than they are at the north pole.  Additionally, the person would not feel heavier if they grabbed hold of something attached to the earth. 

What I’m showing is that there is a discrepancy between real world situations and the mathematical examples presented by modern science.  At this juncture I can only conclude that the centripetal force is being improperly applied across multiple spinning  frames of reference to account for the discrepancy and if that is the case then we cannot be in a spinning frame of reference (as shown above).

The Impossible Flight of the ISS

I was looking at some additional sites from NASA that try to explain the nature of gravity at certain altitudes.  https://www.grc.nasa.gov/www/K-12/airplane/wteq.html

The final sentence of the explanation is “…But the high orbital speed, tangent to the surface of the earth, causes the fall towards the surface to be exactly matched by the curvature of the earth away from the shuttle. In essence, the shuttle is constantly falling all around the earth.”

As mentioned in my previous posts, the centripetal force only makes sense for something that is tethered to the spinning body  (If you feel that the centripetal force *does* have special powers, please provide a clear empirical example that can be tested). Neither the space shuttle nor the ISS are tethered to the earth unless we grant the centripetal magical grappling abilities (see hammer throw). https://www.youtube.com/watch?v=KnHUAc20WEU

As well, for the shuttle to be constantly “falling” but not actually falling downwards, a constant acceleration would need to be applied (ie. rockets) plus a continual adjustment of direction or the shuttle would fly off into space (see what happens when the hammer is released).  Again, for apparent “weightlessness” in space, it would require objects to be falling at a rate of 9.8N/kg (or m/s/s) which would mean a constant counter-force of equal value would need to be applied or they would rapidly fall to earth.  So the “floating” objects and people in space would need to be in a free fall all the time.  This is obviously not the case since the ISS would have crashed to earth a long time ago.  In essence the ISS is just like a airplane at a higher altitude and would require constant thrust to stay in “orbit”.  If you turn off the engines of an airplane at 30,000 feet will it stay in “orbit” because “…the high orbital speed, tangent to the surface of the earth, causes the fall towards the surface to be exactly matched by the curvature of the earth away from the [airplane]? ”  I don’t think any scientist would want to be in that airplane at 30,000 feet.   It should be noted that the standard equation for centrifugal force for any object at the equator great than ~317kg would have a centrifugal force greater than gravity.  Unless the centripetal force is magically grappling those objects, they should all start floating and since objects like elephants weigh ~4000-7000kg, they should all be floating thousands of miles above the earth.

If we grant the ISS a value of 3217N/kg (centrifugal force) due to its orbit around the earth (@ 17,150 miles/h & 4200 miles & ~331,000kg) – what force was initially used to get it to that speed?), then an equivalent (but opposite direction) for it must be present via the centripetal force.  In order for a centripetal force to be present the object must be tethered to the earth.  However, to obtain 3217N/kg, this would require the object to be traveling at a faster rate than the earth’s rate of spin.  So an object that travels faster than the earth’s rate of spin *must* be under its own propulsion and not tethered to the earth.  Since the ISS is traveling at such a high rate of speed and is not tethered to the earth, then it *must* be under its own propulsion and heading.  This is plainly not the case.  If the centripetal and centrifugal forces are equal but opposite directions, then we are left with 9.8N/kg (the force of gravity) on all objects.

In conclusion, if the centripetal force only applies to objects that are tethered to a spinning object (ie. Earth) then objects above the earth’s surface must be constantly under their own propulsion (like an airplane) to stay above the earth’s surface.  In other words, the ISS should be falling out of the sky.

Forces – Where do they originate?

If you open any physics text book you will notice the use of the word force (as in F=ma).  However, what is being described in this equation is not a force at all but a relationship between two other measurements.  The variable ‘m’ or ‘mass’ is a measurement which requires its own force and ‘a’ or ‘acceleration’ which also requires it’s own force.  The problem is in trying to define mass and acceleration.

These definitions refer back to each other in a self-referential manner.  For example, one definition (there are many) says:

In physics, the property of matter that measures its resistance to acceleration.

So mass, in this instance, refers to acceleration and acceleration is defined as:

Mechanics. the time rate of change of velocity with respect to magnitude or direction; the derivative of velocity with respect to time.
Now acceleration refers to velocity and velocity is defined as:
Mechanics. the time rate of change of position of a body in a specified direction.
Now if velocity is defined as above, then in no way has any force been defined or measured since we are simply left with ‘time’ which is also a relationship between what was before and what is now.  No forces have been directly measured.  If we then look at the concept of ‘gravity‘, we are left working with the mass of two object in relation to radius of those objects.  Again, there is no inherent force in the ‘radius’ of an object and as we’ve seen above, the mass of an object has no inherent force.  Therefore, ‘gravity‘ cannot be a force but only a definition of a relationship between objects.
So the question that arises is: What is a force and where does it originate?
Forces have their origin in the hidden (occult) or unmeasured worlds.  As previously written, hidden forces are real and have a direct, meaningful and potent affect on our lives.  As Goethe’s Faust says:
In thy Naught I hope to find the All.
This brings us to the most difficult of places.  We are crossing over into the threshold of the ‘naught’ and most are terrified to venture there.  We have ask ourselves why it is so uncomfortable to look into a region that is our true origin?  In most cases we have been conditioned to seek the ‘hidden’ through authoritative paths (ie. religion) or to dismiss it completely (ie. scientism).   But why have we been ‘directed’ into these paths?  That is an even more complicate answer.