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Problem 12 Easy Difficulty

If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, What is the natural length of the spring?

Answer

Natural length of the spring is 8 $\mathrm{cm}$

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Video Transcript

This is a natural in this l and by hook slow. We have some months l to Tillman cell cakes. The it's peers who whoa, equal six with a look. Hey, Bill. So we need another equation. It's Gethers to get both variable. The case constant of this spring will not wait. Well, happy to calculate it. So this one is actually on self equals. Two k times l squared minus two minutes. L square increasing along. I was the second equation. It's the same thing, but in a difference value bill. So that's another condition which use 20 equals two k times, four months elsewhere. Minister Valls months ever squared. Okay, so we have because you wanted to conserve for Kanell. Two variables to equation and perfectly we're gonna have illegals. Eight said natural length of our of our spring is eight. We have the sole cable because the thing is, this a trick. We're gonna use one number two to a limit K. So the only thing I'm equating this l would have so okay. And this whole results