String Series, Number B

The Puzzler

RAY: Here's what you do. You tie one end of the string to the Zippo lighter. And you might not realize it, but you have constructed a pendulum.

TOM: Oh, man.

RAY: You then take the lighter, and you'll light the other string at both ends and you immediately set the pendulum a-swinging, as they say, and you know it's going to take 30 minutes for that string to burn up. And what you do while the string is burning...

TOM: You count pendulum swings.

RAY: You count pendulum swings, and of course, everyone knows that a pendulum's cycle is independent of its amplitude. That's why pendula were so popular in clock use. Because as the pendulum seemed to slow down, it really didn't slow down. As the amplitude of the cycle decreased, the time it took for it to swing from point A all the way to point B on the other side and then back to point A?

TOM: Remains the same. A little-known fact about pendulums.

RAY: Well, it's only true if the arc is small. If it gets too big, then there are other mathematics that get involved. Much too complex for me to explain here because I don't understand it. So, you count the number of swings, and when the thing has burned up completely, you say, "Ha. It took 30 minutes for--" let's pick a nice number like 300 swings of the pendulum. Therefore, if I divide this by five...

TOM: Which will be six minutes.

RAY: Thirty divided by five, so 300 divided by five is 60 swings of a pendulum, and so you set it a-swinging again, and you count up to? Six minutes. So who’s the winner?

TOM: The winner is Ed Krystlemeyer, from Mt. View, Wyoming. Congratulations!

[ Car Talk Puzzler ]

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