# What $$is$$ the spring constant?

Classical Mechanics Level 4

Consider a helical steel spring of shear modulus $$G$$. Let the thickness of the wire be $$2r$$ and the coil radius be $$R$$.

Let the number of turns of the wire be $$n = 8$$.

Estimate the force constant (in S.I. units) of the spring.

Details and Assumptions:

• $$r = 1\text{ mm}$$.

• $$R = 6 \text{ cm}$$.

• $$G_{shear} = 78\text{ GPa}$$.

• Assume small enough pitch.

• Determine axial force constant considering shear forces only.

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