A disk between vertebrae in the spine is subjected to a...

A disk between vertebrae in the spine is subjected to a shearing force of 600 $\mathrm{N}$ . Find its shear deformation, taking it to have the shear modulus of $1 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}$ . The disk is equivalent to a solid cylinder 0.700 $\mathrm{cm}$ high and 4.00 $\mathrm{cm}$ in diameter.

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Key Concepts

Shear Stress

Shear stress is the force applied parallel to the surface area of a material, and it is calculated by dividing the applied force by the area over which the force is distributed. It quantifies the intensity of the shear force acting on the material.

Shear Strain

Shear strain measures the deformation of a material due to shear stress. It is defined as the ratio of the displacement experienced by the material to its original dimension in the direction perpendicular to the force.

Shear Modulus

The shear modulus is a material property that represents the rigidity of a material under shear stress. Defined as the ratio of shear stress to shear strain, it indicates how resistant a material is to deformation when subjected to an applied force.

Geometric Area Calculation for Cylinders

Calculating the area of a circular cross-section is essential when determining the stress applied to cylindrical objects. It involves using the formula A = ?r², where r is the radius of the circle, to accurately compute the area over which the force acts.

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