I need to find an equation describing how much force would be needed to break a

Question

I need to find an equation describing how much force would be needed to break a water balloon and I'm not entirely sure as to how to approach it. We'll assume that the applied force is the result of the balloon impacting the ground from a free fall.

I'm guessing here that the breakage of the balloon is the result of a combination of a shear stress from impact and maybe hoop or longtitudinal stress from the water inside of the balloon, but I may be way off base here. Guidance would be appreciated.

Explanation / Answer

I assumed a spherical water balloon weighing about 1 kg (that is, a few pounds), and after a quick calculation, I worked out that the terminal velocity of the water balloon is about 50 m/s. Well, the change in momentum will be something less than (mass)*(velocity), because clearly not all of the water will just come to a complete stop (most of it will splash and continue going down, right?) Still, to be conservative let's say 2/3 of the mass comes to a complete stop on your head, so the impulse = change in momentum times 2/3: I = 2/3*(50 m/s)*(1 kg) =33.333 kg m/s Now, the average force will be I/(time duration of impact. What should we use for the time of impact? I have no idea! But let's come up with a reasonable guess. So, Let's say the impact only lasts for .1 seconds. Or, to make it even scarier, how about .075 seconds. So, then, the average force will be I/(.075 s): F = 444.4 Newtons.

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