You understand the Slinky, yet have you ever before wondered how it walks under stairs, or why it appears to hang in midair once dropped? Scientists have peered right into these phenomena because that decades, however now a Princeton professor has actually mathematically proved that the answers can be discovered in her junior high physics class.

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Slinkies gets their “walking” capability from 2 properties: wave motions and also Newton’s laws. As soon as a Slinky sit atop a staircase, gravity acts upon the toy, keeping it still. Knock over the Slinky, and also Newton’s 2nd law comes right into play. As middle school physics course may have actually taught you, this legislation states the providing pressure to an item increases that acceleration. Gravity starts to administer this force, as soon as the Slinky is cast down a stairway. This movement is continual through a directional wave that ricochets transparent the coil and also stops when the toy hits the bottom that the stairs. Contradictory to how it looks, the Slinky doesn’t walk, it somersaults.


A rainbow Slinky somersaults under a staircase photo via CRC_Studio/Getty Images

“This is all straightforward Newtonian physics. Force equates to mass time acceleration,” claimed Bob Vanderbei, a mathematician in ~ Princeton University. But the Slinky captivates both scientists and also YouTube stars alike since when dropped from a an excellent height, it shows up to “float” because that a break-up second. Scientists have actually been researching this phenomenon for more than 25 years making use of high speed cameras, math proofs and lots the Slinkies.

Vanderbei newly wrote an short article for American mathematics Monthly the quantified the reasons why the fall slinky action this way.

“It’s the mix of the Slinky pulling upward and gravity accelerating downward, and also those two results cancel each various other out,” Vanderbei said. Both the these effects can be described by relatively simple algebra, and some no so simple calculus.


Vanderbei illustrates the falling Slinky. Photo by Robert Vanderbei

You can think the the Slinky coils together being 98, loosely associated objects. As soon as one coil hits another, the facility of massive is moved down the slinky as it starts to bunch together. You deserve to see an interactive version of this on Vanderbei’s website.

“There is no floating effect,” said Michael Wheatland of the university of Sydney, who has also studied the Slinky. “The facility of mass falls with acceleration g. It’s simply that the coils above the facility of mass autumn faster, and also the ones below slower.”

Because the fall slinky is administrate by straightforward Newtonian physics, the force of gravity is yes, really the only constant you need. This concept means if you dropped a slinky indigenous a helicopter, impede the reality that there would certainly be wind native the rotors blow in every direction, these falling slinky physics would certainly still apply.

“The scale of things doesn’t matter, as lengthy as we are here on Earth,” Vanderbei said. “Things don’t change if gravity is constant, yet if we were extending native the moon come the Earth, that would certainly be a an extremely different setup.”

In this scenario, the please of this 238,000-mile long Slinky would certainly take hours or maybe even days at such a huge scale, and also that’s no to cite the impact of the moon’s heaviness tugging ~ above the Slinky too. Also, given that the planet is spinning as soon as per day, points would get messy. Great luck untangling a Slinky wrapped native Beijing to Beirut.

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Vanderbei couldn’t really think of any kind of practical applications for the fall Slinky, however he believes the toy is great for getting people interested in the ar of mathematics.