Imaginary momentum, represented by a j


The momentum of the Atwood is not 40kg moving down
It is the difference between the two masses.
They each move a momentum in opposite directions
Smaller mass moving up
Larger mass moving down
Gravity accelerates both downward
The net acceleration is on the difference
The momentum is also the difference as both masses are joined
via the string
They subtract from each other because the mass is balanced out
How much does a kid weigh on a teeter totter?
Why can they jump so high?


I admire your enthusiasm, but you have to understand what is being
conserved.
all the momentum is there, it is just not all in the same direction

What is the momentum of two cars tied to a chain
Driving away from each other?

With an acceleration rate of 4.905 m/sec/sec it will take the 20 kilograms .63855 seconds (d = 1/2at²) to accelerate down one meter.

The other twenty kilograms is balanced and its center of mass does not rise or lower.  

Twenty kilograms exerts a force of 196.2 newtons. So 196.2 newton applied for .63855 seconds is 125.28 units of momentum.

The final velocity is 3.132 meters per second.

A newton * second = kg * m/sec.

Ten kilogram moving up at 3.132 m/sec is 31.32 units of momentum:

10 kilograms moving down at 3.132 m/sec is 31.32 units of momentum:

Twenty kilograms moving down at 3.132 m/sec is 62.64 units of momentum.

And 62.64 + 31.32 + 31.32 = 125.28. The momentums are added in Newtonian Physics.

The fact is that Newtonian Physics works for every type of motion in the lab; but not everyone will properly use it.

One thing that helps verify that the starting rotational momentum in the double stop cylinder and spheres   https://youtu.be/YaUmzekdxTQ   experiment is that four frame per second is what you get in all the throws all the time. Of all the throws I have done I don't remember any faster than 3.5 frames to cross the 20 mm black square. And I do not remember any slower than 5 frames to cross the black square. It seems like the wrist is fairly consistent in producing a relatively slow spin. And I have done hundreds of spins.

Massive quantities of energy are observed when the ballistic pendulum is taken as a proof of Newtonian momentum conservation; and when Newtonian math is used appropriately. 

Quote from: sm0ky2 on February 16, 2017, 10:51:27 PM

Excellent!


Now comes the important part


E = (m2-m1)gh
Where h is the distance downward the large mass moves
during the experiment.


You see that energy is conserved

Totally agree sm0ky2. This topic, as "all" other topics, there are a confusion between force and energy. Energy is what we want at the end of the road. Forces tells nothing about the energy unless we apply displacement.
Energy is conserved even if it doesn't look like it when the experiment is only dealing with forces alone.
I can lift a bulldozer with my finger if I use enough pulleys to do it, but I need to displace hundreds of meters of rope with my finger to lift the dozer a few centimeters. 10 000 kg displaced 1cm require the same energy as displacing 1 kg 100 meters.


The confusion about forces and energy is the one and only reason why all gravity- or permanent magnet over unity experiments fail.
Conservation of energy is always the partykiller - not the naysayers ;-)


Vidar

If you apply 10 newtons for one second to a mass of 10 kilograms you get 5 joules of energy.  (½ mv²)

If you apply 10 newtons for one second to a mass of 1 kilograms you get 50 joules of energy.

If you transfer all the motion of 10 kilograms moving 1 m/sec to one kilogram; the energy changes from 5 J to 50 J.

This is exactly what happen in the video; The motion of a massive object is given to a small object and the small object gives the motion all back; twice. The same quantity of motion is contained in the small object as is contained in the large object.

The small object with the same quantity of motion contains significantly more energy.