Let’s start with the simplest demonstration of the problem. A bed of nails.
Any one nail would go through a standard vest, if you put the weight of a person on it. However, if you collect a large number of nails together, a person can lay on them without any damage, even without wearing a vest.
Because the force is distributed across all the nails.
Now back to our example:
There are many kinds of bullets, many kinds of vests. Let’s simplify first:
Assume this is not an armor piercing bullet and the vest is Kevlar with no plating.
The bullet strikes the vest and flattens out a little. It looks a bit like a mushroom. The vest spreads this impact out over a much broader area. The force transfers from the bullet to the vest. It’s the same amount of force, but spread out over a large space. The force from this larger impact still transfers to the body, but it does not penetrate.
A knife does not spread the force out. The pressure is applied at the sharp point of the blade, which cuts through the fibers of the vest. The vest cannot distribute the force over a larger area since it’s physically being cut apart.
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