|MadSci Network: Physics|
Angela, Cool question!! Was this prompted by the same kind of thinking required to answer the question: “Can you save yourself in a falling elevator by jumping up into the air just before the elevator hits?” The answer to that one is a definite take the stairs if the elevator is at all untrustworthy! Now what about the marbles? During the period of time when the marbles are accelerating in response to gravity the marbles will be in a “weightless” state with respect to each other. If the bag were loose enough the marbles would be floating around and probably bumping gently into one another. Given a high enough building and enough time, the bag would reach a terminal velocity because of air resistance. The marbles; being protected from the wind by the bag, would fall slowly to the bottom of the bag while the bag reaches a maximum speed. The bag would go at a constant speed somewhere over 100 miles per hour. Eventually however the bag of marbles will run out of altitude and hit something. What happens to the marbles will depend upon what they land on. If they land on solid concrete most of the marbles are doomed. The bag may offer some protection and perhaps the dynamics of a group of slippery spheres will allow some to dissipate energy laterally. But what if they hit something softer? If they land in deep water I expect most would survive. If the rate at which the velocity is decreased (the rate of acceleration) is low enough I think all could survive. Like participants in an “egg toss” who have learned how to catch eggs by allowing the action of their hands and arms to bring the eggs to rest gently, it is possible to save the marbles. If they strike a slanted surface which gradually becomes level, they might survive. This is analogous to why ski jumpers don’t kill themselves when they land at over 100 mph. The slanted hill spreads the loss of velocity over a much greater time. Which brings us to some empirical discussions? What does time have to do with it? According to Newton the change in velocity of a moving object is directly related to the force and the time it takes to create the change or mv=ft. Assuming your marbles are all going v and have a mass of m then the force they receive is mv/t. Since mv is the same for all of the marbles then f is equal to k/t (k is a constant easily calculated by weighing a marble and finding its terminal velocity). Therefore if we can figure the amount of force it takes to break a marble, we could easily calculate whether a certain impact will break it. The breaking force could be tested using a variety of materials testing procedures. If you want to go the inexpensive route see how many bricks piled on a marble are required to shatter it. We would now know the probability of a marble breaking … that is we would if we knew exactly how long it took to stop a moving marble. This is not so easy! Given an inelastic marble striking a hardened steel plate at exactly 90 degrees we can estimate that the time would be less than a thousandth of a second. In this case a single marble dropped from a high building would most surely shatter. I am afraid that the only way you will ever know the real answer is to contact David Letterman and see if he’ll throw your bag out a window. Ed Stammel email@example.com
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