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Between each pair of vertebrae of the spine is a disc of cartilage of thickness 0.5 cm. Assume the disc has a radius of 0.04 m. The shear modulus of cartilage is 10 N/m² A shear force of 10 N is applied to one end of the disc while the other end is held fixed. What is the resulting shear strain?

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Final answer:

Shear strain is determined using the shear modulus of the material and the force applied. The shear strain for a disc of cartilage between vertebrae under a shear force, given the shear modulus, can be calculated using the cross-sectional area and the applied force.

Step-by-step explanation:

When a shear force is applied to a disc of cartilage between vertebrae, it experiences a deformation known as shear strain. This strain can be calculated using the shear modulus (also known as the modulus of rigidity) of the material, which is a measure of its stiffness when subjected to shear stress. To find the shear strain, use the formula: shear strain = shear force / (shear modulus × area).

Since the disc of cartilage is approximated as a solid cylinder, with its dimensions given as height and diameter, the area is the cross-sectional area of this cylinder, which can be found using its radius. In the provided example, the shear modulus of the cartilage is given as 1.0 × 10⁹ N/m², with a shear force of 600 N, a height of 0.700 cm, and a diameter of 4.00 cm (implying a radius of 2.00 cm). Given these parameters, the shear strain of the disc can be determined.

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