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A disk between vertebrae in the spine is subjected to a shearing force of 625n. find its shear deformation, taking it to have a shear modulus of 1.6 x 10⁹ n/m². the disk is equivalent to a solid cylinder 0.8 cm high and 5.5 cm in diameter. what is the shear deformation?

User Civilu
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Final answer:

The shear deformation of a spinal disc subjected to a shearing force can be calculated using the shearing force value, the shear modulus of the material, and the dimensions of the disc modeled as a cylinder. The formula involves calculating the area of the cylinder's cross-section and using it, along with the shearing force and shear modulus, to find the shear deformation.

Step-by-step explanation:

When a disk between vertebrae in the spine undergoes a shearing force, we can calculate its shear deformation by using the shear modulus. The problem provided specifies a shearing force of 625 N and a shear modulus of 1.6 x 109 N/m2. The disk is modeled as a solid cylinder with a height (h) of 0.8 cm and a diameter (d) of 5.5 cm.

Shear deformation (Δx) can be calculated using the formula:

Δx = (F * h) / (A * G)

where F is the shearing force, A is the area of the cylinder’s cross-section, G is the shear modulus, and h is the height of the cylinder. Converting the dimensions to meters to match the SI units of the shear modulus, we have h = 0.008 m and d = 0.055 m. The area, A, of the cylinder's cross-section is found using the formula for the area of a circle:

A = π * (d/2)2

Substituting the values:

A = π * (0.055/2)2

Now, we can calculate the shear deformation:

Δx = (625 N * 0.008 m) / (A * 1.6 x 109 N/m2)

First, compute the area, A, then substitute it back into the deformation equation to find Δx.

User Colin Nicholson
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