MadSci Network: Physics

Re: will bagged marbles break when they are dropped off a building

Date: Tue Mar 22 05:03:28 2005
Posted By: Ed Stammel, Faculty, Computer, SUNY Delhi
Area of science: Physics
ID: 1106859422.Ph


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

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