Inegnuity v's Entropy 2 - Observations & Questions

[Fletcher]

Hi all ..

As mentioned I've been thinking about a couple of questions regarding my understanding of Classical Physics mechanical interactions and my Sim Program predictions v's Real World results for those interactions.

It has caused me to wonder many times what Conservation Law was most fundamental in the Real World and what Conservation Law priority the Sim takes to solve collision problems (if it does) ?

The two Conservation Laws in question being ... Conservation of Linear Momentum ... AND ... Conservation of Energy (specifically KE for collisions where elasticity is 100%). Normally both are conserved.

I will introduce in this thread different collision scenarios that I hope will cause everybody to scratch their heads along with me, or not ;7)

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Let me start the ball rolling by introducing a collision scenario we are all familiar with. This is a real world scenario that I can also reproduce in Sim world (pics attached).

In pic one (Momentum1_Start) I have two masses, only able to move horizontally. The left hand green mass is 4kgs and is moving to the right at 1m/s velocity. Therefore green mass mv = 4 kg-m/s. It impacts a stationary mass of 1kg with mv = 0 kg-m/s. Total system momentum before collision is 4kg-m/s. The green mass has KE = 2 J's before collision.

After collision (Momentum1_End) the two masses move to the right, the yellow mass quite fast at 1.6 m/s and the green mass at 0.6 m/s, slower than initial velocity. The Sim predicts the new velocity and momentum of each mass. It predicts that momentum is conserved at system mv = 4 kg-m/s and energy is also conserved at KE = 2 J's.

ETA: That is the green rolling mass has mv = 2.4 kg-m/s and KE = 0.720 J's; and the yellow rolling mass has mv = 1.6 kg-m/s and KE = 1.280 J's.

I trust that if you were presented with this scenario and asked to solve for the Total System Momentum and Total System Energy before and after collision you would use this equation (see Linear Calculator attachment pic) to find the relative velocities after collision ? Then take those velocities and find mv and KE for each mass and the Total System ?

e.g. v1 = (( m1 - m2 ) x um1 + 2 x m2 x um2 ) / ( m1 + m2 )

e.g. v2 = ( 2 x m1 x um1 - ( m1 - m2 ) x um2 ) / ( m1 + m2 )

Please note that for Linear interactions I (inertia) = m (mass).

OK .. all seems reasonable. The Sim could be doing what we are doing and just predicting some velocities then calculating mv and KE's. Don't need to prioritize Conservation Laws for that, right ?

[Fletcher]

OK .. just to be clear. The heavy green mass rolling forward collides with the lighter stationary yellow mass. After collision System Momentum and KE is conserved at 4.0 kg-m/s and 2.0 J's respectively.

The green mass was unable to transfer ALL its momentum to the stationary yellow mass and that is why it continues to roll forward albeit at a slower velocity than initial velocity.

It was unable to transfer ALL its KE either.

The transfers were proportional to their respective masses where I = m and is a linear relationship.

[daxwc]

Fletcher:

OK .. all seems reasonable. The Sim could be doing what we are doing and just predicting some velocities then calculating mv and KE's. Don't need to prioritize Conservation Laws for that, right ?

You don’t believe they would input a formula of approximate values of transfer losses from real world testing?

[ME]

OK Check- have the same values here. Next?

[Silvertiger]

OK .. just to be clear. The heavy green mass rolling forward collides with the lighter stationary yellow mass. After collision System Momentum and KE is conserved at 4.0 kg-m/s and 2.0 J's respectively.

The green mass was unable to transfer ALL its momentum to the stationary yellow mass and that is why it continues to roll forward albeit at a slower velocity than initial velocity.

It was unable to transfer ALL its KE either.

The transfers were proportional to their respective masses where I = m and is a linear relationship.

Would this be the culprit responsible for WM2D's inability to simulate a Newton's Cradle? If so, is there a workaround?

[Ed]

Silvertiger,

Please have a look at this thread.

http://www.besslerwheel.com/forum/viewt ... 6479#16479

[Silvertiger]

Even with accurate settings, they still exhibit interactions that are not the mirror effect you see in the real thing.

[Ed]

That's why simulation should be used as a tool and not a replacement for reality.

[eccentrically1]

Programs do what they're told. Formulas in, formulas out. So in this scenario, it's been given two masses that lose no energy or momentum to friction. It takes the simple equations for energy and momentum (or vice versa) and plugs in the values for the masses, and solves them simultaneously; or at least as simultaneously as possible. That might be where a sim is limited in representing real world results. It has to execute one line of code for energy and then one for momentum, take those results and place the masses in their new locations with the new values, and repeat; whereas in the real world, those executions occur simultaneously. Meaning, there isn't a priority for one over the other, energy and momentum are conserved simultaneously.
Yes? Or BS?

[ME]

I'm not really fond of integrals, as I tend to mess those things up in mysterious ways; but the attached picture should solve that.
Conclusion: kinetic energy is the change in momentum.

[Tarsier79]

S. I had no trouble modelling Newtons Cradle. You don't need a work around, just use the correct settings for elasticity.

[Fletcher]

Fletcher:

OK .. all seems reasonable. The Sim could be doing what we are doing and just predicting some velocities then calculating mv and KE's. Don't need to prioritize Conservation Laws for that, right ?

You don’t believe they would input a formula of approximate values of transfer losses from real world testing?

Thanks for the replies guys.

ME .. I reached the same conclusion that KE was a change in mv. ie. that mv comes first; was more fundamental (at least in real world).

I'm going to continue today and build on the above scenario but introduce non momentum elements. Then we see a problem with that assumption for sim world I think.

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dax .. no, I don't believe the programers took real world testing and then built a formula like I used in the Linear Calculator that would work in every example of Linear collisions. Simply because as the sims get more an more complex it becomes inconceivable to me that a one-fits-all formula was encoded for every potential situation that a user might dream up.

As this thread develops I put up different sims and the complexity of that approach becomes apparent. Added to that the real world is not discrete packets of information following a time line and is contiguous while a sim is an approximation of that using discrete steps by necessity.

I think the sim calculates forces ( m x a ) and since the mass is invariable for classic physics then it calculates fundamental accelerations. Just a guess at this stage. Later you'll perhaps see why I think this.

P.S. this exchange of ideas helps me sort wheat from chaff, so my ideas might change to chaff as we go on, or not.

[ME]

Well, I don't think one is first or second; it's more a mathematical consequence (as my current humble opinion).

KE can be explained by the change of momentum (and the conservation of it).
KE is just easier to use for not doing integrals all the time.
PE can also be explained by momentum when applying it as a continuous force over time.

Something I think about:
Perhaps one could consider energy as non-existing at all, only that it is easier to talk about what is required to change some desired momentum (like motion) at the cost of undesired momentum (like another motion, friction, heat, sound).
So that's why energy can't be created or destroyed, as it only 'fictitiously appears' when something goes from one kind of momentum to another?

Marchello E.

[Fletcher]

There's the problem. Two different masses can have the same momentum.

The force x time to stop them is the same i.e. f x t = m v

N.B. See the bottom segment in my Linear Calculator where I explore this. There I compare 4kg at 1m/s v's 2kg at 2m/s. Both have the same momentum of 4 kg-m/s. The same deceleration vector is applied to both masses to bring them to a stop in the same time interval.

However because the 2kg mass is going twice as fast it travels twice the displacement before being brought to a stop.

Therefore thru the Work Energy Equivalence Principle (WEEP) the f x d = J's is twice as much for the lesser mass traveling twice as fast initially i.e. 4 J's v's 2 J's.

We know it instinctively because whilst these two masses have the same momentum twice as much 'Work' can be done with the lesser faster mass. And energy is the capacity to do Work in mechanical systems and unfortunately it is not momentum.

Somewhat circular logic.

[Fletcher]

OK .. continuing on.

In the below pics I have the same set-up as previous.

This time I have placed a Spring Intervention between the 4kg green mass and the 1kg yellow mass. The green mass will impact the spring, which will compress, then the spring will release its stored energy into the stationary yellow mass.

N.B. this is a somewhat hypothetical spring (springs, rods, ropes have no mass in WM2D). The stops I've built have tiny mass (1 gram) just so that they operate as they should (can't have no mass for interactions). The spring is special because when the green mass connects the lhs stop it compresses while the rhs stop is locked. When the green mass has zero velocity (and spring compressed) the lhs stop locks in position and the rhs stop unlocks allowing the spring to expand. So the spring sort of creeps to the right slightly. This was necessary to fully capture and release the energy of the green mass and allow it to come to a stop.

The sim shows that the green mass has zero velocity after impact with spring and the yellow mass has velocity of 2m/s after spring fires. So we have affected a full transfer of energy i.e. the green mass has 0 J's and the yellow mass 2 J's of KE. N.B. for the purists the sim shows a very slight gain in energy (3 decimal places) which can't be helped. I had to increase accuracy from my standard 1,000 fps to 2,000 fps else the frame steps would allow parts to move inside boundaries and extra energy is produced as they are expelled (bug known to most WM users, but not a show stopper).

*What the sim shows is that the system momentum is halved to 2 kg-m/s whilst the system KE is conserved at 2 J's. So in sim world in this instance I think Energy was conserved but momentum wasn't.*

1. How did the sim treat the analysis problem when a non momentum intervention is in the sequence ?

2. Where did half the momentum go in sim world ?

3. What would happen in the real world ?

My thoughts ...

1. I think the sim conserves KE (possibly because this is the currency for doing 'Work' in mechanical systems and of interest to most engineers) so this appears a Top Down programing over-ride.

2. See answer 1. and P.S below.

3. The same thing would be observed in the real world i.e. a mechanical intervention from a spring stores energy and not momentum, therefore the local system KE is conserved. BUT .. the local system Momentum is also conserved in real world (as is all universal momentum). Half the observable mv went into the earth grounding because the spring stops are periodically anchored to the earth. So Momentum is conserved with the earth datum receiving half the momentum form the green mass thru its connection to the earth.

P.S.1. in the sim analogy the page background is 'assumed' to receive half the system momentum in order to conserve system KE when a spring is used ?!

P.S.2. in the initial experiment the rolling balls were not anchored to the earth at any time, but that is also why the green ball could not transfer all it KE and Momentum to the yellow ball.