Hypothesis .. Raising GPE without using Law of Levers ? ..

[johannesbender]

1st leg 15.95 of work done for the control assembly and 17.04 of work done for the second assembly with the lifting weights , with a difference of 17.04 - 15.95 = 1.09 j which is equal to the gpe of the second assembly's lifted weight .

[Fletcher]

Fletcher: .. with passion comes inaccuracy,…

Never heard that before.

I keep looking at your Sims Fletcher and all I see is the start of Moment of Inertia it's rotational intertwined with energy and torque.

I don’t see any difference to the roller racers starts. The ability to manipulate MOI during motion.

2 and 3 sims are not rigid bodies - therefore their MOI changes when set in motion and this effects their outputs, and imo violates the Work-Energy Theorem ( WEEP ) ..

The roller races are quite different - their MOI's do not change while translating, whether they are a disk or a ring etc .. at any height lost they have the same total KE ( KE translation + KE rotation ) - and this KE equals the GPE lost ( mgh ) ..

For any time period the disk will be ahead of the ring ..

[Fletcher]

1st leg 15.95 of work done for the control assembly and 17.04 of work done for the second assembly with the lifting weights , with a difference of 17.04 - 15.95 = 1.09 j which is equal to the gpe of the second assembly's lifted weight .

And in the 2nd leg the work done is 14.848 J ( N.m ) for a GPE gain of 1.078 J .. 14.848 + 1.078 = 15. 926 J of Energy - yet in both legs 15.95 J is first given then taken away, same as for all 3 experiments including the rigid body CONTROL experiment ..

Table coming up ..

[Fletcher]

Here's the twist Gregory .. the dimensions and masses are much closer to your recent 1 Leg experiments ..

Here I compare 3 Swingers against WEEP Theorem - 1 is the Control - 2 is able to raise up its pend bobs - 3's pend bobs are able to fall ..

** I have taken out much of the Outputs and let the visuals speak for themselves ** i.e. doesn't clutter the sim to the same degree ..

Hey Fletcher,

Interesting sim...

So, basically in all 3 cases you invested the same amount of energy to accelerate/decelerate the carts ( yes, exactly the same amount for each swinger experiment ), and at the end the main difference between the carts is the change in GPE? Am I interpreting this right? Yes, the swingers have the same investment of Energy of Motion ( KE translational ) imparted to them, and at the end of leg 1 they all have the same velocity and 100% of that energy has been transferred ( assuming ideal sim ) - but sim 2 has a significant gain in GPE - the lifting was not done thru classical mechanics work done = f * d ..

Also, the distance traveled by the swingers might be different when they allowed to swing at acceleration or deceleration... Yes- total distance over 2 legs is identical ..

However, if you consider the cart plus the swingers as one 8 Kg object, then it does not really matter how much each swinger actually traveled. After all each cart plus swingers team can be considered a single object when the swingers are locked/latched... Yes, when locked out they become rigid bodies, and then IMO Work-Energy Theorem is valid and from this viewpoint the travel of the cart itself is what really matters. Does this way of thinking makes sense? If we were to use combined average distances of the swinger components at end of each leg then WEEP would be valid/consistent - BUT, that is not what Work_Energy says to do - it says from where the force is applied ( not a average distance ) ..

Below is a Results Summary Table I decided to make of the 3 sims comparison experiments ..

I give my "Conclusions" below the table ..

I'd be interested to see if after having studied the numbers anyone draws different conclusions to me ( probably ) .. always willing to consider a different point of view because you may have a better argument than me Gregory, or more accurate insight ..

P.S. Momentum and Kinetic Energy are different faces of the same coin - I used Impulse transfer in the sims because it assumes a 100% transfer of momentum - and that m*v has KEt - I could have just used KEt - but I used m*v transfer because a runner needs to have its energy source explained - and m*v can come from the connection to the earth as I theorized previously ..

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[Fletcher]

CONCLUSIONS .. wrt. Transactional Flow Dynamics of KEt passing thru a system compared to the Work-Energy Theorem ( WEEP ) ..

* Kinetic Energy ( KEt ) is the Energy of Motion .. Energy is also the Capacity to do Work .. Work Done = Force x Distance .. m*v and KEt are different sides of the same coin ..

* Swinger 2 sim shows PACKETS OF ENERGY transacted ( handed-off ) linearly * Follow the Energy i.e. the KEt ( energy of motion ) .. KE & WD are scalar - momentum is a vector ..

=> Initial KEt of 15.913 J is given / handed off to the swinger in Leg 1 & it acquires 15.913 J of KEt ( energy of motion ) - In Leg 2 this KEt of 15.913 is then taken away returning the swinger to zero KEt and zero momentum .. According to WEEP 17.047 J was spent in Leg 1 as Work Done on the swinger & the pendulum bob was raised up and gained PE of 1.091 J while 14.848 J was spent in Leg 2 as WD on the swinger & the pendulum bob was raised up and gained 1.078 J .

* Leg 1 .. WD 17.047 J - PE 1.091 J = 15.956 J - CLOSE to our transacted 15.913 J energy of motion ( KEt ) Input ..

* Leg 2 .. WD 14.848 J - PE 1.078 J = 13.770 J - NOT CLOSE to our transacted 15.913 J energy of motion ( KEt ) Input ..

=> Under Classical Mechanics we expect that to raise pendulums up requires work to be done ( i.e. WD = f * d ), and this must be paid for to maintain equivalency ..

Total WD = 17.047 J + 14.848 J = 31.895 J ( similar to Energy of Motion KEt 15.913 J + 15.913 J = 31.826 J ) ..

'=> However using transacted Energy of Motion ( KEt ) we get a free lift of 1.091 J + 1.078 J = 2.169 J PE gain where no extra work was done over the 2 Legs for the surplus of GPE ..

* This is due to swinger inertia delay as It Is not a rigid body .. wrt. Work-Energy Theorem, Work Done thru both Legs is not consistent at all times with the Energy of Motion ( KEt ) ..

[daxwc]

I keep looking at your Sims Fletcher and all I see is the start of Moment of Inertia it's rotational intertwined with energy and torque.

I don’t see any difference to the roller racers starts. The ability to manipulate MOI during motion.

2 and 3 sims are not rigid bodies - therefore their MOI changes when set in motion and this effects their outputs, and imo violates the Work-Energy Theorem ( WEEP ) .

The roller races are quite different - their MOI's do not change while translating, whether they are a disk or a ring etc .. at any height lost they have the same total KE ( KE translation + KE rotation ) - and this KE equals the GPE lost ( mgh ) ...

Yes; it was wrong to compare them to the roller racers directly. I meant more along the lines of a disk morphing to a ring. If a disk gradually morphs into a ring, its MOI increases since more mass is distributed farther from the axis of rotation. This means that for the same angular velocity, the rotational kinetic energy would increase, potentially impacting the system's total kinetic energy distribution and energy conservation dynamics?

Any ideas on how to harvest your PE gain?

[johannesbender]

In leg 2 you have negative work because of cos θ the direction of the force is in the opposed direction of motion , so WD = -14.848 .

Leg 2 , WD (-14.848) - PE (1.078) = -15.926 J .

Or , am i doing it wrong ?

[johannesbender]

As dumb as this may sound , i admittedly did not fully realize how negative work can be at play and how it is calculated until yesterday after a few youtube videos , so if i am mistaken in how the final energy should be calculated then i would not be surprised .

As i understand (might be in denial) even though work is a scalar it can have a negative sign for negative work , and negative work is force * distance where the force is in the opposite direction of the object's motion , such as friction however the direction is not entered in to the equation as a negative but as i understand , it is the cos(theta's) of the equation that changes the sign of the answer .

[Georg Künstler]

Now look at the apologia wheel again.
It is a walker mechanism which makes 3 bounces/impacts on the ground while turning 360 degrees.

Now we can calculate the size of the wheel in wheel construction.
8 impacts on the downgoing side, the apologia wheel delivers 3 impacts per turn.
The apologia wheel has the diameter of 3/8 of the main wheel.

Imbalance is created by the first motion, like when you standing on a carpet and someone is pulling the carpet.
It is bi directional.

The next step is to determine the inertia of the two wheels.

[Fletcher]

Yes; it was wrong to compare them to the roller racers directly. I meant more along the lines of a disk morphing to a ring. If a disk gradually morphs into a ring, its MOI increases since more mass is distributed farther from the axis of rotation. This means that for the same angular velocity, the rotational kinetic energy would increase, potentially impacting the system's total kinetic energy distribution and energy conservation dynamics?

Any ideas on how to harvest your PE gain?

If you don't get too close to it dax it potentially becomes a lot more clearer and easier to think thru imo - so if we take your morphing roller racer thought experiment and we figuratively stand well back, we can then imagine it rolling down the slope and morphing to a higher MOI as it goes, and we know it will increase its inertia - that means the proportions of total energy at any vertical height will change - proportionately it will then have more KEr and less KEt ( total KE is the same for any height loss ) - iows it will roll with less forward velocity .. at any height, whether morphed or not, it requires the same WD to lift it back up to start height ..

Q. Any ideas on how to harvest your PE gain?

The sim experiment is a euphemism for two oppositely placed one-way swingers reacting to an equal and opposite impulse ( the bounce, or pump and dump, analogies ) to potentially show the physical benefit of a free and fast lifting outside of classical mechanics WD and Law of Levers constraints - and in my mind-sim this gives rise to an inevitable increase in GPE to be put to useful purpose as free torque, and down-streaming it a wheel that must gain in angular momentum and KEr ..

The ' trick ' is in how mechanically the repeating " bounce and recovery " input is generated and managed in a dynamic revolving environment - not all bounce mechanisms are created equal .. imo ..

[Fletcher]

In leg 2 you have negative work because of cos θ the direction of the force is in the opposed direction of motion , so WD = -14.848 .

Leg 2 , WD (-14.848) - PE (1.078) = -15.926 J .

Or , am i doing it wrong ?

... I admittedly did not fully realize how negative work can be at play and how it is calculated until yesterday after a few youtube videos , so if i am mistaken in how the final energy should be calculated then i would not be surprised .

As i understand (might be in denial) even though work is a scalar it can have a negative sign for negative work , and negative work is force * distance where the force is in the opposite direction of the object's motion , such as friction however the direction is not entered in to the equation as a negative but as i understand , it is the cos(theta's) of the equation that changes the sign of the answer .

That's the crux of it jb - WD is a scalar just like Energy - and Energy is capacity to do Work - therefore Work is capacity to transform into mechanical Energy - in the maths as you say we use cosine to denote negative Work etc as a means to try and use more instinctive and familiar vector analogies - it also helps keep the accountants math books tidy ..

So I give the same suggestion to you as I did to dax above ..

Stand well back, squint a little if it helps, and let your intuition simplify it down and walk you thru the sim ..

It is about packets of Energy flowing thru an open system - a simple, but not accurate, metaphor is a relay race where the baton is the scalar Energy Of Motion ( KEt ) - at the gun the first runner sprints off getting up to full speed ( velocity ) - the baton has received Energy of Motion which is translation velocity dependent - however this is when the simple analogy breaks down somewhat - when the runner arrives at the interchange area he is met by another runner running backwards at the same speed and keeping pace with our first runner - the hand-off of the packet of Energy Of Motion occurs to the second backward running runner who then puts on the breaks and gently slows to a stop ( that is the imaginary finish line which he doesn't actually cross ) .. so all scalar Energy Of Motion ( KEt ), positive and negative ( given externally from another source i.e. the bookends analogy ), is given to the baton and then taken away again .. all that happened was the baton went some distance around the track ..

But in our sim the baton also went some distance down the track and gained and lost the same Energy Of Motion received at the start, and it had at the interchange moment, and was spent slowing it back down to zero velocity ( and zero KEt ) again - but as a result of the swinger not being a rigid body it could partially delay its inertial effects resulting in it gaining GPE for no apparent classical mechanical cost to the dynamics of the swinger still reaching the same translational velocities at each stage, as the KEt flowed ( see velocities ) thru the system from start to finish ..

Hope this helps ..

[Fletcher]

OK .. simplifying the mind-sim right down jb ..

A couple of bookends of Energy/Momentum are external to the closed swinger system - they in turn give equal and opposite impulses to the swinger so that it gains and loses the same Energy of Motion - but because it is not a rigid body it raises up its GPE during the transaction locking it into torque ..

[Gregory]

Hi all,

I tried to think through this in more detail, and arrived somewhere.
Yes, johannesbender, you are right that work done can be a positive or a negative value as well.

For example if you lift a weight with your hands, then work done on the weight will be a positive number, and work done on your muscles will be a negative number.
Or we can envision a point mass going through a force field, which can be gravity, CF, magnetic, or anything... From the perspective of the point mass, if it is accelerated, then WD is positive on the mass, but if it's decelerated then WD is negative on the mass.

After that, I think the correct way to understand this cart & swingers experiment is as follows:
- We have a cart with two swingers, this is the first component of the experiment. (Cart)
- We also have a driver/controller system, this is represented by the accelerating/decelerating forces, this is the second component. (System)

Now, let's analyse the case of the second cart (from Fletcher's table), where the masses can swing up and gaining GPE.

From the perspective of the System:
1. The Cart is accelerated by the System, this means a negative amount of work done on the System.
2. The Cart's kinetic energy is absorbed by the System, this means a positive amount of work done on the System.
3. The Swingers will fall down in gravity field and give back potential energy, this means a positive amount of work done on the System.

-17.047 + 14.848 + 2.199 = 0
The System can gain back the same amount of energy which it loses first by accelerating the Cart.


From the perspective of the Cart:
1. The Cart is accelerated by the System, this means a positive amount of work done on the Cart.
2. The Cart is decelerated by the System, this means a negative amount of work done on the Cart.
3. The Swingers swing up in gravity field means a positive amount of work done on the masses, represented by the gained GPE.

17.047 - 14.848 = 2.199
The gained GPE of the Swingers is caused by the uneven WD distribution of the accelerating/decelerating forces.


So, If I see it right, this is most likely comes back to a zero sum game at the end, but in a weird way…

And except perhaps for one thing...
In a rotational form the cart will become a wheel with many swingers, and if those swingers are locked into an OOB position most of the time, then they will produce a continuous torque, which will modify the accelerations and maybe that will be a different situation. Will that produce a different outcome?

Actually, I have an exact wheel idea for this, so I will check that some time later...
I also created an interesting formula magic version of this two-leg swinger cart experiment, will post it soon.

P.S. Forgive me if my analysis is wrong, this swinger & cart experiment is still not really my territory...

[Gregory]

Ok, in this experiment I used a cart with two swingers, plus two spring terminals to start and stop the cart.
The cart is started by a compressed spring, and later stopped by another identical spring, and in the process both swingers rise up reacting to the acceleration/deceleration, same as before.

The twist is that at the second terminal I added an additional violet color spring which is enchanted with the amount of energy as the collected GPE. So, the cart will be also accelerated backward to its starting position by this additional spring force. If there is a gain the first spring should become compressed somewhat more compared to the starting condition. But unfortunately, it doesn't happen.

I tried to make this work as a continuous loop, so we can watch the cart go back and forth dozens of times. However there is a catch, the violet spring's formula contains a constant which I couldn't represent with a variable so far, and for that reason it won't be accurate after the first 1-2 cycle.

Basically, that's all. It was quite a challenge to tame wm2d to make this work. Perhaps still could be improved.

[daxwc]

Fletcher: so if we take your morphing roller racer thought experiment and we figuratively stand well back, we can then imagine it rolling down the slope and morphing to a higher MOI as it goes, and we know it will increase its inertia - that means the proportions of total energy at any vertical height will change - proportionately it will then have more KEr and less KEt ( total KE is the same for any height loss ) - iows it will roll with less forward velocity .. at any height, whether morphed or not, it requires the same WD to lift it back up to start height ..

If a non-morphing disk and a morphing 'disk-to-ring' raced down a ramp, the non-morphing disk would reach the bottom first. This is because its Moment of Inertia (MOI) remains constant, allowing it to convert gravitational potential energy (GPE) into translational kinetic energy (KET) more effectively. Meanwhile, the morphing disk’s increasing MOI diverts more energy into rotational kinetic energy (KER), resulting in slower forward velocity.

Now, if raising both objects back to the start height truly required the same work (based solely on restoring GPE), then we would be implying that time is irrelevant to the system. However, time clearly holds physical significance. For example, if you were lying under the ramp at the finish line, the morphing disk’s delayed arrival would represent a tangible, measurable difference. You would be wishing it got the fuck off sooner. The extra time is a direct consequence of how energy is distributed during motion, highlighting that time is not merely an abstract concept but a critical parameter in understanding the dynamics of energy and motion.