The Two Flavours of Work

[Grimer]

The Two Flavours of Work


I've finally managed to sort out what is going in the Keenie and the RAR.

Work comes in two flavours,

Force x distance

d²x...........................d³x
----....x....dx.....=.......----.... ....... ...........
dt² ...........................dt²
This is the expression for work we are familiar with, i.e. work viewed from the inside of a system.

and the other flavour is

Jerk x time

d³x...........................d³x
----....x....dt.....=.......----.... ....... ...........
dt³ ...........................dt²
This is work viewed from the outside of a system.

In the Keenie and the RAR gravity is doing work inside the system on the side where the weight is dropping and work on the outside of the system where the weight is earthed.


If you want to understand the foundations of this insight you need to read the note: Iterative Hierarchical Mechanics which you will find on my website.

[Grimer]

It's interesting to note that greendoor had got hold of the importance of "Force" x time.
The only problem was he was still thinking in terms of the second derivative and not the third.

[Mark]

Velocity - the rate of change of the position of an object, equivalent to a specification of its speed and direction of motion.

Acceleration - the rate at which the velocity of an object changes with time.

Jerk [ aka, jolt or surge or lurch ] - the rate of change of acceleration; that is, the derivative of acceleration with respect to time, the 2nd derivative of velocity, the 3rd derivative of position.

An object can be stationary or in motion, depending on the frame of reference.
A stationary object can be put into motion by applying a force to it.
When in motion, its acceleration can be constant or changing. A change in acceleration requires an additional force, either positive or negative (in relation to its direction of travel).

Are we in agreement so far?

I understand Jerk to be nothing more than the mathematical and physical resultant of the application of force.

What I fail to see is how one might extract useful energy/work from merely the change of the rate of an object's acceleration.

[Grimer]

Mark

Are you familiar with elementary calculus?

[Mark]

For the sake of argument, let's say I'm not familiar with [even elementary] calculus. I believe you'll reach a larger audience if you are able to keep the discussion on an fundamental level. You know, layman's terms. One needn't know mathematics to understand the concept of a jerk [that's verb, not noun :-)].

You have used the term/phrase "jerk energy" several times in the past. In my previous post, I questioned the extraction of useful work that might be derived from tapping just the rate of change of an object's acceleration. The keywords there being 'useful' and 'just'.

Don't get me wrong, I understand that a moving object's kinetic energy can be tapped from any point between slightly altering it's velocity, and bringing it to a halt. But I guess my real question, Frank, is how much energy are you talking about? Are you talking about turning a generator, pumping water, lifting a box of rocks? Are you talking about closing the loop on an overbalanced wheel?

Help me, please, to understand the bigger picture of where are you heading with "jerk energy" and it's potential to help solve 'the puzzle'.

n.b. - If it is your intention to limit this thread to a math-only discussion [which, of course, you have every right to do] I'll back out and follow along quietly. However, I would still appreciate your addressing my inquiry.

[Grimer]

I've only just come across your post, Mark. I've been busy on the Overunity.com forum.

I'll do the best I can to answer it in layman's terms.

Firstly, the amount of energy I'm talking about.

Bessler has given us evidence of a minimum value. Though not much compared to a steam engine - which is presumably why people lost interest in it - that energy is free and available everywhere on earth - even under the earth.

The energy you are familiar with is the second derivative, force x distance energy known as kinetic energy.

But there are other forms of energy, thermal energy, radiation energy, etc. These can be transformed (I prefer the word transduced to avoid confusion with electrical transformation) into mechanical energy for running steam engines for example or used directly without transducing them into their mechanical equivalent (you've no doubt heard of the mechanical equivalent of heat) to keep us warm for instance.

Now Jerk is as independent a source of energy from the second derivative as heat is. But because it is so close in hierarchical order to the second derivative, Force x distance, people don't seem to realise this. They accept heat (the nth derivative) and light (the mth derivative) as being different because they are zillions of derivatives away from KE. But jerk is so close that it seems just an aspect of KE.

There is one clue however which should give them pause for thought and that is the conservation aspect. The first derivative, momentum is conserved, the second derivative, kinetic energy is conserved, and jerk (angular momentum) is conserved. All three conservation laws are independent like independent nations bordering each other.

Another problem that arises is the use of the word "energy". It can be used in the global sense of ENERGY which includes heat, light, atomic, etc. or it can be used in the local sense of second derivative, Force x distance energy. It's a language problem.

We should really think of the first three derivatives as velocity energy, acceleration energy, and jerk energy. Then each would have its own name, its own nationality, like Italy. France and Germany.

But you might protest - but what about mass - where does mass come in?

Well we can think of these three as having unit mass - After all a velocity has to be the velocity of something. We can't have a grin without a Cheshire cat (except in Wonderland). So we can think of them as specific velocity, specific acceleration and specific jerk.

(If you wanted to go further, specific snap, specific crackle and specific pop)

Now I see gravitational "acceleration" energy as being mechanically transduced into jerk energy. This jerk energy is split into two.
One half goes off to earth and reduces the angular momentum of the earth by an infintesimal fraction of its total angular momentum.

The other half is left behind as useful angular momentum which powers a mechanical device such as a wheel.

After all, we are already tapping the earth's angular momentum with space vehicles so we know it can be done.

It's called the slingshot effect though NASA prefers the term "gravity assist".

I hope that goes some way to answering your question.

[Grimer]

To enlarge upon my previous post.

What is Force?

Force is defined as Mass x acceleration. It substitutes a single word for two other words. And if we have a unit mass we can think of Force as units of specific acceleration, units of things moving with increasing velocity.

But what about the forces in the ties and struts of a structure, say. These aren't moving. Nothing is accelerating - not at engineering scales at any event.

So what's the difference between a moving force and a stationary force?

Jerk x time doesn't involve movement so maybe we would do better to think of static forces as jerk actions rather than acceleration actions.

As Stafford Beer said,

"It's all a question of finding the right language." or words to that effect.

[cbucket]

but how do you convert from a static force (j * t) to a dynamic force (m * a) ?

[Tarsier79]

Jerk x time doesn't involve movement

As Mark stated, Jerk is the change of acceleration. Acceleration involves movement. Please explain, is this a contradiction?

[daanopperman]

Jerk is the magnifying glass of velocity X time .

[daanopperman]

I can do 600 Km on one tank fuel , or I can use the tank of fuel as a canon , but I will not reach 600 Km . I think jerk is a wast of energy .

[Grimer]

but how do you convert from a static force (j * t) to a dynamic force (m * a) ?

Good to see you Charlie.

You convert it by hitting it with a hammer.

Nitro has a quasi-fluid phase in tension and a quasi-solid phase in compression.
It's prestressed structure on an atomic scale.

If you put a drop on an anvil and hit it with a hammer then you've converted the tension in the fluid phase and the tension in the solid phase to KE and you'll be very lucky if the hammer head misses yours.

Remember a static force always has an equal and opposite static force and within a closed system one has to be a tensile force and the other a compressive force.



Prestressed concrete buildings have to be dismantled very carefully because they are in effect macro explosives.

That's why I always though England's AGRs were a daft idea when I was at BRS. Of course no one took any notice and they won't until one of them goes pop and they have to shut the others down. Lay in a good stock of candles.

[Grimer]

I can do 600 Km on one tank fuel , or I can use the tank of fuel as a cannon , but I will not reach 600 Km . I think jerk is a waste of energy .

How do you know? Have you ever tried it?

I think Clarkson has a video in which he demonstrates a cannon with a puff of hairspray. You should watch it.

http://www.youtube.com/watch?v=xai1GjLzKsg

Think how many puffs of petrol there are in a whole tankful.

[Grimer]

Jerk x time doesn't involve movement

As Mark stated, Jerk is the change of acceleration. Acceleration involves movement. Please explain, is this a contradiction?

Acceleration is a vector. if at a point you have two equal and opposite accelerations then you have no movement, have you.

Where did you learn your mechanics?

Force is only a convenient name for specific acceleration.

[daanopperman]

Hi Grimer ,

Made myself a Patato Gun with PVC fittings , combustion chamber 100mm concentric reducer to 40 mm stock 500 mm long , used under arm deodorant as propellant , immense fun , immense power .