| MadSci Network: Physics |
The question: "How to maximize the amount of force of a rubber band? Since rubber bands obey to hooke's law, f=kx. if the rubber band were cut into a straight line, instead of the circular shape it is, wouldn't this increase the maximum possible displacement x, while keeping constant k, thus maximizing force? or is this logic incorrect? would a rubber band have more force as a circle or as a line? how would you maximize the amount of force a rubber band can exert?"
The answer: When you cut the rubber band and make it a straight band (rather than a "loop") k gets effectively halved because there is only one strand of material resisting the pulling movement. So at first glance one might say that it is exactly the same as simply using the rubber band as a loop: twice the distance but half the "spring" constant means the same force is realized.
But not so fast! That is true: At twice the distance the force is the same, but there is something that is different: the potential energy. The potential energy of a "spring" is 0.5 k x2 (see elastic potential energy at hyperphysics, for instance). For the cut band we have k' = 0.5 k and x' = 2x, so the potential energy of the cut band is 0.5 * 0.5 k * (2x)2 = 0.25 k 4x2 = k x2, which is exactly twice as much as the potential energy of the uncut band! So if you cut the band you get the same force at twice the distance, but it takes twice the energy to stretch it, and you will get twice the kinetic energy out of the band (if the mechanism that uses the potential energy is 100% efficient)!
John Link, MadSci Physicist
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