throwing chocolate at people, how dangerous can it be?
-
I don't know how to answer this. Whatever you're planning it sounds brilliant.
Using my brother as the test subject I can tell you that if whacked hard using the flat side of a 600g bar it causes sudden sharp pain and great annoyance. This can be counteracted by offering him a piece of the now shattered in to pieces chocolate.
As an estimate I would say the breaking has reduced the chocolate to about 2.5 chunks per segment.
If I hit him with the narrow edge I believe there would have been much less damage to the chocolate and more to his head.
If we take it that chocolate behaves like concrete we assume isotropic and negligible tensile strength for calculations. Then looking at the second moment of area of the profile of the bar we see that in the X axis ((B*H^3)/12) = 37 434 375mm^4
IN the Y axis ((H*B^3)/12)=53 710mm^4
Therefore in bending the profile offers 700 times greater resistance and must therefore fail in compression in the form of shear.
The compressive strength of chocolate is something not even Google can find and I don't fancy casting a 100mm cube and strength testing it in the labs to find out. So lets say same as a medium stiff clay at 80kpa.
With an area of contact of no more than 5 square centimeters. 80kpa = 0.8N/mm^2 and therefore the failure load is approx 0.8*500 = 400 Newtons. or 40kg
That's gonna be unpleasant as a dead load. If you take it as live the force will be greater.
Now how fast can you hit. An average baseball throw is 28m/s as is on the end of an arm and outside of pendulum travels faster say 30m/s for easy maths.
Mass of head > 5 kg therefore acceleration will be less than 1g so not going to cause internal damage
F=ma
Watching a ball hit a wall and stop in high speed camera takes 0.025 seconds.
Using SUVAT equations v=u+at where 0=30+a*0.025 a=1200m/s^2
F=MA
F=0.6*1200 = 720 newtons
Or 72 kg resting on your head. A human skull should be O.K. with that so no fracture but may split the skin.
720/500mm^2=1.44N/mm^2 This means you should exceed the plastic limit of the chocolate and cause deformation.
Since chocolate has no tensile strength this deformation will result in cracking.
I think that's the most troll mixed with physics I can manage in one day. The maths kinda works but its accuracy as an actual model is probably rubbish. If you'd like to try it out get some ballistics gel and 1/4" ply (approx skull bone) to simulate for real tests.
Hope this helps.
Regards
Mark
Using my brother as the test subject I can tell you that if whacked hard using the flat side of a 600g bar it causes sudden sharp pain and great annoyance. This can be counteracted by offering him a piece of the now shattered in to pieces chocolate.
As an estimate I would say the breaking has reduced the chocolate to about 2.5 chunks per segment.
If I hit him with the narrow edge I believe there would have been much less damage to the chocolate and more to his head.
If we take it that chocolate behaves like concrete we assume isotropic and negligible tensile strength for calculations. Then looking at the second moment of area of the profile of the bar we see that in the X axis ((B*H^3)/12) = 37 434 375mm^4
IN the Y axis ((H*B^3)/12)=53 710mm^4
Therefore in bending the profile offers 700 times greater resistance and must therefore fail in compression in the form of shear.
The compressive strength of chocolate is something not even Google can find and I don't fancy casting a 100mm cube and strength testing it in the labs to find out. So lets say same as a medium stiff clay at 80kpa.
With an area of contact of no more than 5 square centimeters. 80kpa = 0.8N/mm^2 and therefore the failure load is approx 0.8*500 = 400 Newtons. or 40kg
That's gonna be unpleasant as a dead load. If you take it as live the force will be greater.
Now how fast can you hit. An average baseball throw is 28m/s as is on the end of an arm and outside of pendulum travels faster say 30m/s for easy maths.
Mass of head > 5 kg therefore acceleration will be less than 1g so not going to cause internal damage
F=ma
Watching a ball hit a wall and stop in high speed camera takes 0.025 seconds.
Using SUVAT equations v=u+at where 0=30+a*0.025 a=1200m/s^2
F=MA
F=0.6*1200 = 720 newtons
Or 72 kg resting on your head. A human skull should be O.K. with that so no fracture but may split the skin.
720/500mm^2=1.44N/mm^2 This means you should exceed the plastic limit of the chocolate and cause deformation.
Since chocolate has no tensile strength this deformation will result in cracking.
I think that's the most troll mixed with physics I can manage in one day. The maths kinda works but its accuracy as an actual model is probably rubbish. If you'd like to try it out get some ballistics gel and 1/4" ply (approx skull bone) to simulate for real tests.
Hope this helps.
Regards
Mark