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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