On Thu, Dec 9, 2010 at 12:44 PM, Gary Antonick <gantonick@post.harvard.edu> wrote:
Hi all,
I recently posed a simple mechanics question to a bunch of university faculty. Pretty much everyone got it wrong.
What I'm wondering is.. why? Am trying to explore this a bit. Might make an interesting story.
Here's the question. You have a Newton's Cradle. The first ball has twice the mass it normally would. You swing it so it hits the second ball. What happens? a. the last ball flies out b. the last two balls fly out c. something else
Turns out the answer is c.
No one gets this right. OK. Bill Gosper got it right. In fact, he's completely unraveling the problem. And Neil Bickford was essentially there. Maybe I should have asked more people in math-fun.
But I asked 20 university faculty (physics and engineering, mainly) and they all got it wrong. Except one guy who had to simulate it first.
What's going on?
Here are two factors tat I think contribute to getting the answer b. The first is that people have done the experiment of swinging not one ball of double mass, but two balls of single mass, towards the stationary balls, and observed behavior b. Since the two balls stay together when you do this, it seems a natural assumption that welding together two balls that are staying together anyway would not change the behavior. It is surprising to me that two balls a tiny distance apart (so that the first hits the stationary balls first, and then the second swinging ball hits the first) exhibit a behavior different from the two balls welded together, yet one in which the two balls do not separate from each other. The second reason people produce the wrong answer b is that an effective shortcut in problems like this is "guess an answer, and verify that it satisfies the conservation laws". In a problem with sufficiently few degrees of freedom, there is a unique behavior that satisfies the conservation of energy and momentum, so if the guess passes these tests, it must be correct. Behavior b conserves energy and momentum, but is not the only possibility that does so, and turns out to be the wrong one. Andy
- Gary
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