How much energy does it take to breach a sternum with a knife?

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Dryson
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The question I have is this. If a 9x19mm parabellum pistol round is able to breach the sternum of the chest at 561 joules of energy how many joules would it take to breach the sternum of the chest using a knife two inches wide by eight inches long?

I am uncertain of the conversation process but I have been following the Jodi Arias case and I find it hard to believe that she could exert the same amount of joules as a 9 x 19 mm pistol round.
 
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Unless you get into something extraordinarily convoluted and impractical, there is no conversion factor. A gun imparts blunt-force (although extremely concentrated) trauma while a knife is sharp-force. They simply don't work on the same principles. (There are some oddball overlaps such as ballistic knives, but that's really not worthy of consideration in the context of your question.)
I'm not familiar with that case, other than the fact that I inadvertently saw something about it on an ad for some dreck like "Nancy Grace". If you are asking whether or not she could manually administer a 9 mm bullet with the same energy that a pistol would, the answer is "no".
That doesn't seem to be your question, though, so I'm at a bit of a loss to understand exactly what you're asking. Can you be more specific, keeping in mind that you have to explain what the case is about?
 
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There is no direct conversion between the energies involved in each case. The pressure at the very tip of the knife would be the main factor governing how well it could penetrate - that's why people sharpen knives. chisels and other tools. Other factors would be the angle of taper at the end of the knife - how easily it could part the tissue and force its way in. Of course, energy is always relevant in any physical interaction but it is very hard to equate the energy imparted over a relatively long time by muscles and the energy imparted in a fast bullet impacting.
The ability to damage a body will vary from one bullet design to another, even with the same impact velocities and masses.
This ia all too damned grisly for me, really.