Calculating sling projectile speed from video.

[CuriousStrang]

https://www.youtube.com/watch?v=6IQ15ymhR2M

This clip from the history channel as is titled, attempts to address the likelihood of David killing Goliath with a sling.

As you can see in the video, the pro Slinger when testing the force on a load cell, got a reading of 3.62 kN or 3620 N.

Unless I'm completely butchering this would be simple calculation (which wouldn't surprise me)...if the force is 3620 N, and we assume the sling stone used is 1 kg, wouldn't the final acceleration come out to be 3620 Meters/Sec^2? That seems awfully high...(though I would assume it decelerates very quickly over a greater distance) Keep in mind that I'm trying to be conservative here by giving that small stone a much greater mass than it should have, to come out with a lower speed. Afterall, a baseball which is much larger than that stone, only has a mass of 0.145 kg.

Anyway, is the acceleration right or wrong? Because what I'm getting is really hard to believe.

 

[256bits]

Looks about right.

I bet the stone used would be closer to 0.1 kg, then at impact the acceleration would proportionally higher.

 

[CuriousStrang]

That's pretty crazy...

Even if we keep with the conservative 3620 meters/sec^2 figure...I have to wonder how many firearms could shoot projectiles at that speed within the same distance.

That's why I'm having such a hard time digesting this figure. It seems astounding, but maybe I'm simply underestimating the sling...

 

[256bits]

Well it did say in the video, that the "crack" or "snap" was the sonic boom, which I did not hear.
It could be the stone travels near the speed of sound or around 340m/s, which is darn fast. Goliath never saw it coming.

 

[CuriousStrang]

Hmm I was able to hear the snap/crack?

Low volume?

And again that's the thing that's astonishing to me, ~340 m/s is the speed of sound, which would make 3620 m/s over mach 10? '

 

[JHamm]

The acceleration of the rock when it strikes the sensor is not the same as its velocity before it strikes unless the time it took to decelerate in seconds happened to be the mass of the object in kgs.

 

[tony_physic]

Surely f=ma.
with a force of 3620 and a mass of 0.1
3620/0.1 = a
36200 = a.
distance traveled on impact = 0.05m
dist = 1/2at^2 which gives a time to stop of .0016Secs
which leads to velocity on impact of only 59m/s

 

[sophiecentaur]

I take issue with the way the whole thing is dealt with on the video. That stuff about a sonic snap would just be describing the snap of the end of the sling after the stone had left it (a whip crack of the tail of the sling with the knot in it). That is irrelevant nonsense and just there for effect and to impress non-thinkers and non-Physicists. A schoolboy can make his school tie or a towel snap with no trouble.
The whole thing boils down to Kinetic energy and not force.
First of all, forget whether he actually threw the stone (which would account for a small loss and, of course, a huge problem with accuracy - but he was dead lucky and the story wouldn't have been told if he'd missed).

The same situation would obtain with a light hammer, with the stone as the head and with a long handle. Certainly, a half kilo hammer, with a longish shaft could easily be wielded and make a hole in someone's skull. It's easy to make a dent in a steel plate, using a modest ballpeign hammer - that's what they're used for. You may say that it's not a fair comparison and that you are still 'pushing' when a hammer lands on its target but without the swing before impact, in which you are giving the head all that KE, the hammer does nothing.
But David didn't actually need to have killed Goliath with his stone. Even my rusty memory tells me that he cut off his head PDQ after he fell - so he may have only been stunned / unconscious and needed to be finished off with the sword.

TV presentations of stuff like this, involving 'experts' who are committed to a magical / religious explanation are usually full of holes. This is typical.

BTW, that Spanish guy was really hot stuff with his sling!