the math is disturbing

[Leafy]

Suppose we have a spring and a mass.
Spring constant k = 2
The mass has 25J in kinetic energy.

What is the maximum displacement of the spring?
E=.5kx^2 So displacement= 5
F= kx So Force = 10

Suppose some point when it about to reach maximum compression, we apply a 1N extra force to the mass. This extra force is added to the maximum spring force.
F= 10+1 = 11
new displacement F=kx ; x=11/2 = 5.5
new energy E=.5kx^2 = 30.25J

Our input energy is Force x distance = 1 x .5 = .5J
Our output energy is 30.25 J minus the kinetic energy of the mass 25J = 5.25J

This is some crazy crackpottery man, smoke?

[Leafy]

A mass of 1kg is dropped at a height of 6m on an ideal spring. Calculate the maximum spring displacement. Spring constant k=20N/m. Spring length is 5m.

so we must take gravity into account during the compression. mg(1m) +mg(x) = .5k(x^2) ---> 0 = 10x^2 - 9.8x - 9.8 x=-.6; x = 1.6 So we take the positive one which is 1.6 m of spring compression?

Can we have a sim to compare with paper answer?

[Fletcher]

See attachments - sim confirms.

Note I had to massage the apparatus to match your requirements in terms of heights and lengths - hence a spring attachment block etc. A frictionless vertical platform guide rail is hidden from view.

[Leafy]

Thank you Fletcher,

I was expecting the mass would dip further than the math and violate energy, but it doesn't. I wonder if the sim programmed using conservation of energy method.

[Fletcher]

It's something I've never been able to establish Leafy. I'm not a programmer.

What I do know is that Working Model 2 Dimensions was designed and beta tested over years by around 10,000 engineers and IT guys etc. Throw in a handful of physicists etc. It would be constructed on logic. The logic of Newton's Laws and Mechanics, and cause and effect relationships. Within the confines of discrete time steps i.e. recalculating every frame. They have served us well, and are used extensively in industry and the commercial world.

You could build a spread sheet model of what you are investigating but that would be laborious and there would not be 10,000 checks and balances to debug it.

ATEOTD 'g' is an acceleration ( field / gradient of potential ) and a conservative force for all intents and purposes, at the macro and local level we are dealing with.

So my issue has been are kinematic sim programs Top-Down, or Bottom-Up ? I would expect that they start building a picture from fundamentals, forces, and map and retain each and every relationship per frame i.e. Bottom-Up building exponentially frame on frame.

What I don't know is if there is some fail-safe routine that oversees the result so it is not gobbledygook (rubbish in rubbish out) i.e. Top-Down approach i.e. make a result fit Conservation Of Energy Law and Conservation of Momentum.

I've come to the conclusion that a Top-Down approach is probably too complex. And importantly it means that there are certain mechanical instances where the legion of 10,000 found an anomalous result which needed a 'gross' work-around to beat it back in the hole. Of course this didn't happen, otherwise we'd all know about it now.

So I am 99.99% certain that the programing is simple step by step Bottom-Up.

And importantly for me it leaves the door open that a sim program could show a Bessler type wheel gaining momentum. And that logically means that it also conforms to Newton's Laws and Mechanics as we know it, IMO !

We just haven't found the right mechanical approach to demonstrate the 'gain' conditions, also IMO !

[Fletcher]

I should add that I can not sim all things - some are too complex for my limited laptop. Some mechanical actions don't translate well to sim program because you are limited by the sim elements you can use built into the program. This means simplifying and having to find a 'cheat' work-around method which can usually be done with a bit of thought. Sometimes with a lot of thought and headache.

[Leafy]

Your knowledge is amazing. I think we'll find the solution.

[Fletcher]

I am certain we will !

[agor95]

It is good you are seeing how bad things look in the world of math's modelling.

Also how disturbing it is when you are unable to see a way forward.

So many people walk passed without noticing and therefore do not challenge what they see.
Their perceived reality is not like yours and by working at your understanding of disturbing facts your reality will grow the richer.

One fact that came to me is an object rolling down a slope increases it's speed as it drops. However not for ever as the acceleration down the slope reduces.

So the rolling object ends with a constant speed.

Therefore a force does not cause an increase in acceleration of a mass in all cases.

All the Best

[Georg Künstler]

by agor95 » Tue Nov 23, 2021 10:39 am
Therefore a force does not cause an increase in acceleration of a mass in all cases.

True, if the fall is ending, the mass will stay on the ground without moving.

But not seeing that the object is not moving it does not mean that it will not move.

A mass on earth is always travelling with its carrier, the earth.
So the mass is moving but your eye can not detect that, because your eye and your body is also travelling with the same speed.

A small mass will, as a consequence, always travel with the same speed of the carrier, the earth, after a short time.