What the heck answer 5

Here is the original item:

The winner this week is Frank of Action-Reaction. The answer (maybe this was easy) was an inertia ball. I don't know if that is the technical term or not. The basic idea is that you hang this ball from a string and attach a string to the bottom. If you pull slowly on the bottom string, the top string breaks. But, if you pull very fast the bottom string breaks.

I was going to make a demo video, but Dale Basler already did a great job on this one.

Inertia Ball from Dale Basler on Vimeo.

So, instead of a demo video let me look at the conditions to break a string. First, some simplifications. Suppose that the ball of mass m is supported by a string. I will model this string as though it were a spring (which shouldn't be too hard because you just replace the "t" with a "p") with a spring constant of k. Also, I will model the string at the bottom as a spring with the same spring constant (these will be very stiff spring-strings with a very high spring constant). Here is a diagram:

So, the bottom spring is pulled down with a speed (at the end of the spring) of v. Which spring breaks first? Well, let me say that the string (spring) will stretch up to a certain force. Then it will break. Let me label the position of the mass as r_m and the position of the end of the bottom spring as r_s and this bottom of the spring has a constant velocity. Then the magnitude of the force in the bottom spring would be:

And what about the top spring? This is a little more complicated. Let me write down what I can for the forces in the y-direction:

So maybe this is enough for an answer. Both the bottom and the top spring force have a r_m term in them. The top term also has this mg term in it where the bottom spring as a v term in it. If v is small, and mg is large then the mg term will dominate and make the top spring break first. If v is large, then the bottom spring force will increase very vast while the top spring will depend on the large mass to move.