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November 28, 2006
Optimum Pitch for a Slinky
Last night a friend dropped a cell phone from the top of some stairs, and we next heard a series of clear thumps as the tiny metallic item proceeded to yield to the force of gravity. When I realized what was happening, I studied the staircase closely. It appeared to have a rather steep pitch. In other words, tall steps with narrow horizontal surfaces on which to place a foot. You cannot have wide feet for this staircase without increased risk of trippage.
Anyway, staring at the stairs for a second made me think of a toy I used to have. Slinky.
Those of us who were born before 1980 may remember the Slinky Craze that overtook elementary schools across America. Like Transformers and My Little Ponies, you just had to have one. They came in colors. They came in plastic. They came in metal. They came in boxes.
The metal ones made the smooth slinky sound when they slinked, making them more desirable amongst my circle, but if you messed them up they were messed up permanently. Tradeoffs.
So thinking about slinkies and upon closer inspection of the stairs, all of a sudden I had a burner of a scientific inquiry.
What I wondered is this. What is the optimum pitch for stairs for a slinky to properly "step" down? I mean, some stairs are steep and others are broad. So, what is the best slope for slinkies to best do their thing? If you have read this far and don't know what I'm talking about, please read this Wikipedia explanation before proceeding.
Now, then.
We are back in front of the steep stairs. You have Slinky, stairs, and a ruler. You have to determine the optimum pitch (that is to say, the change in y-dimension over the change in the x-dimension), or:
delta y
_______
delta x
People who have studied linear algebra will know this to be the "slope." m. This is the quantity we are looking for. We want to figure out the optimum m value to build the stairs in our dream homes so our future slinkies will have a good time getting from the top of the stairs to the bottom, without running into themselves or missing steps. Like Tiny Metallic Phone.
Anyway, you really want to be sure that you are with me here. Let's try this experiment together. Okay, here we go. Best of luck, fellow physicists! Ready, on your marks, get set, Go! A-ha! And slinky begins to slink.
We are using the metallic ones so you get the nice slinky slink sound. [Please pause for a moment to imagine the slinky sound.]
Okay, I think the numbers are in. Yes! They are. Thank you, gentlemen. May we have the winner, please. A Google query into "Optimum Pitch" for Slinky yielded the following revelations.
According to this site, we have a nonanswer. "Once optimum phase shift is approached, things change fast. As little as 45 degrees change in phase shift can make a large difference in directive gain, while a 180 degree error can be devistating [sic]. Accidentally stumbling on the optimum value seems unlikely."
But we have another slinky investigation that's provided new and different information. According to this person's “Slinky Walking Speed vs. Angle” experiment, the ideal pitch has been determined to be.... a range! Somewhere between 24 and 41 degrees.
Voila! And there we have it.
Posted by Dipika at 2:03 PM | Comments (0) | TrackBack
November 13, 2006
meta-post, #331
d: hey! you are writing a post!
a: yeah.
d: oh, there's nothing on DANDAN. Is that why you are posting?
a: yeah, don't you know? I only do laundry when there's no more underwear.
Posted by Akira at 1:59 PM | Comments (0) | TrackBack
dairy of a sushi helper #3
a: Oh, my god, the uni guy came in today, and I had one.
d: ??
a: Uni guy. He sells just uni, out of a cooler box he carries from a restaurant to a restaurant.
d: Like a drug dealer.
a: Huh? well, yeah. So, this guy comes in randomly and Boss goes, oh, that's the uni guy. He sells Boss two tiny boxes, each for $25. Expensive, huh?
a: he used to do this all the time, this uni guy, but he quit, he told me.
d: Why?
a: I don't know, but he started up again, apparently, just a few weeks ago. He came in the other night, and no one recognized him or knew what he was up to. Then he went, "do you remember me? I used to sell you uni. I quit, but I am doing it again."
d: So, was it good?
a: Awesome. $3 a pop, with employee discount. But so sweet and melt-in-your-mouth soft. Boss was like, "I can't serve this to customers. It's too good."
Posted by Akira at 1:31 PM | Comments (0) | TrackBack