Ok I'm an asshole....I had already written this up. It's Friday and I was feeling intellectually unstimulated during a coffee break.
Now I freely admit any part of this could be wrong or off...most people here know how terrible my math can be...please remember to show your own work if you want to try to pick this apart.
Neglecting air friction (the reason sling stones are so smooth), and of course assuming 2 dimensions (no vector calculus on Bullshido, I refuse to be that big a snot-nose).
F = m*a = 3,600 N = (3,600 kg*m/s^2)Since we don't know the actual weight of the bullets, let's assume m = 1.3 kg (approx 3 lb) bullet, making a = 2,780 m/s^2, about 282 Gs on the stone. That seems like a lot, but keep in mind this is because the stone has a relatively low mass (1.3) compared to the impact force measured (3,600 newtons). Making the stone heavier would decrease the amount of acceleration required to achieve a 3.6 kN strike (heavier rock = more force).
a = 3,600 N / m
Slings can't really use heavier rocks/bullet effectively due to lost range...their greater mass means the Earth's natural acceleration pulls their trajectory downward sooner than for the lighter stones (heavier bullets fall straight down to earth sooner). Note I didn't say faster...please don't try to conflate the gravitational constant of Earth's acceleration with multivariate ballistics calculus.
To overcome this problem, the ancients built siege weaponry capable of hurling larger stones.
But as far as the receiving helmet/skull/brain knows:
3,600 N / 5kg (Unhelmeted head) = rapid brain acceleration of 73 Gs (3600N = 5kg*a, a = 720 m/s^2)
If you factor in a liberal ~50% absorption rate (based on NFL video and 21st century helmet tech) you come to about 360 to 400 m/s^2 = ~40 G of brain acceleration and the subsequent traumatic oscillation which happens to be about the same as in the NFL video, reported to result in TBIs such as concussions, CTE, subdermal hematoma, stroke, and even death.
And that's with helmets.
Footnote: Keep in mind that these are ideal calculations in a vacuum, air resistance will ultimately lower the actual velocity achieved...the 3,600 Newtons is detected on the target and not on the stone, so I think it's safe to take air friction out of the equations entirely.