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Imagine three different masses are hung from a spring alongside a ruler. The first mass (F=mg=W=110 N) shows a displacement of 40 mm, the second mass (F=mg=W=240 N) shows a dis. of 60 mm, and the final mass of unknown weight is at 30 mm. Here's where I am having trouble: I need to find out a) which mark the spring will be at if there is no mass on the spring and b) the weight of the final mass.

I'm confused! If I use Hooke's Law, F= -kx, I can find the spring constant k when I know the force and the position x, but how do we find k if we do not know x? I imagine we use an equation for work by a spring force,

Ws= (1/2)k*xinitial^2 - (1/2)k*xfinal^2

which involves finding the initial and final x positions to find work...but I cannot figure out how to set this up. Perhaps I am leaving out another crucial equation or step? Hmmm..... Any help in setting up the problem would be appreciated. Thank ya'll -

Ever so lost,

Gin