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Springs

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The spring constant decreases.

Think about Young's Modulus (E)

E = tensile strength/tensile stress = Force per Area/Extension per Length = (F/A)/(x/l) = Fl/xA

if

E = Fl/xA

then

F = (EA/l)x = kx

so

k = EA/l

if you increase the length by adding coils, your k decreases by the length corresponding to the number of coils added. With this same logic, if you cut the coil into 2 parts, you will increase k by 2