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Demonstrating an apparent loophole in the law of conservation of linear momentum.


What follows is the description of an experiment that demonstrates an apparent loophole in the law of conservation of linear momentum.


We can use the same classroom elements employed to exhibit the law of conservation of linear momentum (low friction track, low friction carts, a spring and plunger) to demonstrate an apparent loophole in said law with a simple method that in a VERY NON-INTUITIVE manner allows a closed system to apparently disregard said law of conservation of linear momentum.


Fig 1



First we shall replicate the experiment as it is executed in the classroom, for that we will need the following elements:

1 A mass (M1) on a low friction chart.

2 A second mass (M2) also on a low friction chart.

3 A low friction track (Pasco Dynamics Track or equivalent)

4 A compressed spring that can be released remotely by plunger.


The original experiment.


The elements as set up at rest as illustrated in fig 1, with the spring (4) compressed.


When the spring (4) is released (fig 2) the carts (M1) and (M2) are expelled in opposite directions

Fig 2


If the cart’s masses are not equal, their velocity may be different (V2 < V1) but their momentum will always be the same (p2 =p1) see fig 3.


V1 = Velocity of mass M1 in the +X direction.

V2 = Velocity of mass M2 in the –X direction.

Notice that if M1 is not equal to M2 their velocity are not equal, in this example we shall assume M2 > M1.

Therefore the velocity V1 of mass M1 is greater than velocity V2 of mass M2.

If M2 > M1 then V1 > V2.

But the momentum (p1) of mass M1 will always be equal to the momentum (p2) of mass M2 as described in fig 3


Fig 3


You can see this experiment described in greater detail in The Physics Classroom, Momentum Conservation in Explosions

Fig 4



We now modify the test bed by positioning the low friction track (3) on a low friction surface (5) so that it has freedom of movement in the X axis.

Fig 5


When we repeat the experiment the masses M1 and M2 will behave almost exactly as described in fig 2, the low friction track (5) may display some movement on the X axis depending on friction and the position of the masses.

Fig 6


When the masses collide with the low friction track’s borders, even if they do not collide at exactly the same instant, the low friction track’s final velocity will always be 0.

NOTE: this works best when the collisions are inelastic therefore it is recommended you put a small amount of plasticine on the tracks inner borders so the charts “stick” and do not bounce.

Fig 7


We now put mass M1 (on the low friction cart) at the front (+X) end of the low friction track that we will now refer to as mass 2 (M2)

Fig 8


When the spring (4) is released (fig 8) the low friction track or mass 2 (M2) will gain velocity in the +X direction while the cart (M1) will travel in

the –X direction.

Fig 9


When the cart (M1) collides with the track’s –X (rear) end, as both masses have traveled at a constant velocity their momentum is the same, as

p1 = p2 both track (M2) and cart (M1) stop.

NOTE: this works best when the collisions are inelastic therefore it is recommended you put a small amount of plastisine on the tracks inner borders so the charts “stick” do not bounce.


Fig 10



We shall now repeat the experiment as described in figs 7, 8 and 9, but on this occasion we will add an “air brake” (small parachute) to mass 1 (M1, the cart)

Fig 11


While just as in fig 8 mass 2 (M2 the track) is traveling in the +X direction with a constant velocity, mass 1 (M1 the cart) is slowing because of the additional drag created by the air brake, as it loses velocity it loses momentum.


Fig 12


As M1’s velocity is less at the moment of collision than the moment the spring gave it a strong push, it has LESS momentum (p1f >p1a), sufficient to slow mass M2 but not to bring it to a stop, M2 will continue in the +X direction till friction brings the system to a full stop.


NOTE: No momentum has been lost, it has been TRANSFERRED to the air molecules with every collision (between air brake and air molecules), so far we may have had fun playing with carts but nothing surprising has happened yet.


Now comes the interesting part.



Fig 13



We envelope mass 2 (M2) with a lightweight airtight cover (7) and repeat the experiment as in figs 10, 11 1nd 12 we will observe that the end result is the same, when the cycle is completed (spring released, masses travel in opposite directions, masses collide) M2 continues to move at constant velocity in the +X direction.


This is not supposed to happen because M2 is now a closed system and acceleration of a closed system from within is supposed to be impossible.


NOTE: if any alternative method is used to slow M1’s –X velocity, like a contact brake (friction against M2) at the end of the cycle both M1 and M2 finish at full stop


Fig 14 and 15 summarizes what is observed in the experiment when M2 (the low friction track) is fitted with an air tight covering.
Without air brake.
Fig 14
When we execute the experiment without an air brake attached to mass M2 (figs 5, 6 and 7) mass M1 will go thru 3 distinct stages:
(1)    At rest.
(2)    Spring is released and mass M2 gains velocity in the +X direction.
(3)    M2 stops when chart M1 collides against the inner –X side of M2.
With the air brake
Fig 15
Fig 15 illustrates what is observed when we execute the experiment with an air brake attached to mass M1, mass M2 will behave a little differently:
(1) At rest.
(2) Spring is released and mass M2 gains velocity in the +X direction.
(3) As M1 (the chart) travels in the –X direction, drag on the air brake (little parachute) slows it’s –X velocity, the random collisions of air molecules 
      do NOT interact directly on the inner surface of the airtight covering (as the result of the experiment demonstrates).
(4) M1 collides against the inner –X side of M2, but as its velocity (therefore its momentum) has decreased it is not sufficient to stop the system 
      and M2 continues moving in the +X direction until friction stops it’s +X velocity.
But in a 0g and frictionless environment (space) M2 will retain its velocity change in the +X direction and may increment that acceleration in every cycle:
For a better description of the cycle and practical application please see a step by step explanation of the principals involved.
Article on Fortean Times magazine by David Hambling.
Main page with video (somewhat primitive)
Note 1:
The aerodynamic airtight cover (box) must be of sufficient width so that the air brake has plenty of space for the air in the box to behave in a 
turbulent manner, if not the air brake will act as a piston compressing the air against the –X side of the box and the experiment will not give the 
described results.
We have found that the larger the box the better, a 3m (meter) x 0.5m x 0.5m with a 0.4m x 0.4m air brake (fig b) gets the describe results without
 problems when tested on low friction rails, water (messy) or dry ice plucks. (although the experiment described here is adequate for demonstration
 purposes , a more complex torsion balance apparatus using metrology similar to Henry Cavendish’s 1706 experiment to measure the force of gravity 
between masses is recommended for evaluating true thrust output).
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