The force was provided by pressure that was built up inside the head by the bullet and suddenly released.
We know that there was pressure built up because the skull opened up and matter exploded out of the head in wide directions. We can see that in the zfilm.
As you know, the bullet passing through tissue creates a temporary cavity around it. But in a head, there is no ability to expand the volume. The brain, like water, is almost incompressible so a very small compression of volume increases the pressure tremendously. So the energy deposited in the head builds up pressure. When that pressure is released by the rupturing of the skull (likely initiated by the bullet exiting through the front of the head) matter is propelled out of the opening from the tremendous force (pressure x area).
If the pressure increase was just one atmosphere (1 bar or just over 100 kPa or 100,000 N/m^2) and the area of the skull that opened up was (estimating the size of the opening) was, say, 10 cm x 10 cm (4"x4") or .01 m^2, the total force on the matter expelled (force=Pressure x area) would have been 1000 N. if the matter expelled was 400 grams or .4 kg, then the acceleration would have been:
a=F/m=1000/.4= 2500 m/s2.
So in 10 ms. or 1/100th of a second, the speed would have been v=at=2500/100=25m/s That represents a momentum change of .4 x25 = 10 kg m/s and an equal and opposite momentum change to the head. Since the total incoming bullet momentum was .01g x 610 m/s =6.1 k m/s, the momentum of the recoiling head exceeds the maximum forward momentum imparted by the bullet. So head goes backward.
I'm not certain I agree with these calculations. But putting this aside, you say that after 10 ms, the head started to move backwards. If so, how is it, that according to the study by Physics Graduate Student William Hoffman, in his work for Josiah Thompson for the book "Six Seconds in Dallas" measured JFK's head at frame 313, two inches, or 5 cm, forward of the 312 position, by frame 313?
Why did the head immediately, or almost immediately (after just 10 ms) start moving backwards, and yet ended up 2 inches forward?
Provide me with a possible scenario. Don't use the excuse "Well, we can't tell exactly what happened". Just give us a possible scenario. That would be good enough.
We can use the following time system. z312.0 is when the shutter opens on frame 312. z312.5 is when the shutter closed on frame 312.
So, I need to see something like the following:
z312.5 - the bullet strikes.
during z312.5-z312.7, the head moves forward 2.5 inches, or 6.25 cm, at a rate of 12.5 mph.
z312.7 - the head explodes and the head starts moving backwards, at a rate of 0.6 inches per frame, or about 0.6 mph.
z313.5 - the head has moved back to a position where the head is 2.0 inches ahead of the position in frame 312.
This scenario is clearly impossible, for the bullet to push the head forward at 12.5 mph.
But what possible scenario, not a scenario you can 'prove', but a possible scenario, that would allow the head to start moving backwards after 10 ms, and still have the head 2 inches ahead of it's frame 312 position by the time the shutter closed at frame z313.
So, to summarize:
Questions:
Is there a possible scenario that fits the William Hoffman data?
Is this scenario in accordance with Classical Physics?
Is so, what is that scenario?