Magazine article Science News

# Strings and Springs Net Mechanical Surprise

Magazine article Science News

# Strings and Springs Net Mechanical Surprise

## Article excerpt

Intuition can sometimes lead one astray. Consider a weight hanging from a spring, which in turn is suspended by a piece of string from an identical spring attached to the ceiling. Cutting the connecting string would send the weight and the lower spring plummeting to the floor.

Now add two "safety" strings to the original arrangement. One string joins the upper end of the lower spring to the ceiling. An identical string joins the lower end of the upper spring to the weight. Both safety strings initially hang limply.

When the taut string in the middle is cut, the safety strings prevent the weight from plunging all the way to the floor. Intuition suggests that, given the safety strings' slack, the weight will end up hanging somewhat lower than before. However, for certain combinations of springs, string lengths and weights, the opposite is true.

In the Aug. 22 NATURE, applied mathematician Joel E. Cohen of Rockefeller University in New York City and physicist Paul Horowitz of Harvard University argue that under a broad range of conditions, cutting the linking string and letting the safety strings carry the load actually pulls the weight above its initial position and closer to the ceiling.

The idea for this startling demonstration arose out of Cohen's long-standing interest in mathematical models of biological competition, especially models that produce counterintuitive outcomes. One model involving traffic flow, discovered in 1968 and now known as Braess' paradox, demonstrates that adding extra roads to a congested transportation network may actually increase the amount of congestion rather than alleviate it. …

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