Braessa

Braessa, a trickster rogue of the Paradox Parlour, cuts the middle string, and the hanging weight goes up.

The Physics

Two identical springs hang in series, joined by a short string, with the weight at the bottom. Two longer “safety” strings hang slack, one from the support to the lower spring and one from the upper spring to the weight. When the short string is cut, the load is carried by two parallel paths, each a spring plus a long string, so each spring carries half the weight. If the strings are long enough the weight ends up higher than before.

series: k_eff = k/2 → parallel: k_eff = 2k

• k: stiffness of each spring (N/m)
• k_eff: effective stiffness of the support

This is the mechanical analogue of Braess's paradox from traffic networks (Dietrich Braess, 1968), where adding a road can slow everyone down. The spring and string version is by Joel E. Cohen and Paul Horowitz (Nature 352, 699, 1991), who also gave an electrical version.

Honest caveat: No energy rule is broken. The rise depends on the string lengths. The weight rises because the support becomes stiffer, and the energy comes from rearranging the springs' stored energy.

On the sticker

Braessa holds the blade that cuts the string, with a glowing arrow pointing up. Printed text: BRAESSA with the line CUT IT, IT RISES. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.