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## Thermodynamics and the JFK Assassination

There has been an ongoing debate about the physics of the fatal shot that struck President Kennedy in the head.

Although there is very strong evidence that the fatal shot came from the right rear (where the sixth floor sniper's nest in the Texas School Book Depository was located) JFK's head and body move backward and to the left with significant speed immediately after the head shot. Conspiracy theorists point to this rearward kick of the body as evidence of a shot from the grassy knoll which was located ahead and to the right of the President.

There is no question that matter exited the President's head with significant speed. A simple kinematic analysis shows that the forward ejection of matter from the head can carry more rearward momentum than the incoming bullet possessed, due to the sudden release of pressure built up in the skull as the bullet passed through. This was discussed in a 1976 Physics Today article by Nobel physicist Luis Alvarez. But Alvarez could not explain the physics of this pressure build up saying that one would "have to ask someone more knowledgeable in the theory of fluid mechanics than I am".

Experts have suggested that it is possible to generate the kind of pressure sufficient to burst the skull if the bullet generates a shock wave (ie. it passes through the head at a speed greater than the speed of a compression wave in the brain). The problem is that the speed of a compression wave in water (which the brain consists largely of) is about 5000 fps or 2.5 times the speed of a Mannlicher-Carcano bullet.

I think that it is simply a matter of the first law of thermodynamics:

$$\Delta KE = \Delta Q = \Delta U + \Delta W = \Delta (PV)$$

where $\Delta W$ is the work done by the system

Assuming that the head is filled with a liquid in a confined volume, if the bullet slows down it has to cause compression or produce heat. If the volume is confined, no work is done by the system (until the skull ruptures), so we have:

$$\Delta KE = V\Delta P$$

All the bullet has to do is deform sufficiently in entering the back of the skull to create enough drag force as it passes through the brain to slow down. By the first law, it will convert that loss of kinetic energy to pressure. So:

$$\frac{1}{2}m_{bullet}(v_i^2-v_f^2) = V\Delta P [/itex] In order to duplicate the result using the same ammunition used by Oswald (copper jacketed 6.5 mm. 160 grain (10 gram) bullets fired from an Mannlicher Carcano rifle at about 2000 feet/sec.) one just has to make the bullet slow down enough in passing through the target. Assuming the volume was about 2 litres (.002 m^2)(average weight of human head is 4.5-5 kg), the initial speed of the bullet was 600 m/s and the exit speed 150 m/s, (mass .010 kg): the loss of KE is about 1700 J., which means that: [tex]\Delta P = 1700/.002 = 850000 Pa$$ or about 8.5 atmospheres.

Can anyone find a material flaw in this analysis?

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