What is this spring's natural length?

Calculus Level 1

When the spring is stretched from 10 centimetres to 12 centimetres, the work done is 6 Joules. When the spring is stretched from 12 centimetres to 14 centimetres, the work required is 10 Joules. What is the spring's natural length natural length in centimetres?

(Hint: Use Hooke's Law: The force required to extend or compress a spring x beyond its natural length is F(x)=kx, where F(x) is the force required to compress or stretch the spring beyond its natural length x and k is a constant that reflects the stiffness of the spring. This law holds true for values of x that aren't too large, that is when x does not lead to the deformation of the spring.)


The answer is 8.

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