Question

The triangular plate is fixed at its base, and is given a horizontal displacement of 5 mm. Determine the shear strain at?

Answer 1

Shear deformation is calculated using the shear modulus, shearing force, and the dimensions of the object experiencing stress. For a disk in the spine with given dimensions and materials, shear deformation can be obtained by relating shear stress and shear strain with the help of the object's dimensions and the applied force.

Step-by-step explanation:

To calculate the shear deformation of a disk subjected to a shearing force, we can use the relationship that shear strain (γ) is equal to shear deformation (Δx) divided by the original height (h) of the item being deformed. This is given by γ = Δx / h. Shear stress (τ) can be determined by dividing the shearing force (F) by the area (A), τ = F / A. Using the shear modulus (G), which is the ratio of shear stress to shear strain, G = τ / γ, we can solve for the shear deformation: Δx = (F / A) * (h / G).

To solve for the shear deformation of the disk between vertebrae subjected to a shearing force of 600 N, the given shear modulus of the disk material (G) is 1 x 10⁹ N/m², the height (h) is 0.700 cm (which needs to be converted to meters), and the diameter (d) provided is 4.00 cm (which also should be converted to meters to find area A).

To find A, we use A = π * (d/2)², and then we can place the values into the equation to calculate Δx. This will provide the shear deformation experienced by the disk under the shearing force.

Answer 2

To find the shear deformation of a vertebra, one needs to calculate the shear stress and then use the shear modulus to obtain the shear strain. The procedure involves applying formulas for shear stress and strain based on given force and dimensions.

Step-by-step explanation:

The student asked to find the shear deformation of a cylindrical vertebra subjected to a shearing force of 500 N, given that the vertebra is 3.00 cm high and 4.00 cm in diameter. To solve this, we need to use the formula γ = τ/G, where γ is the shear strain, τ is the shear stress (F/A), and G is the shear modulus (which must be provided or known from other sources).

First, calculate the shear stress: τ = F/A, where F is the shearing force (500 N) and A is the cross-sectional area of the vertebra. The area can be found using the formula for the area of a circle, A = π*(d/2)². Secondly, once we have the shear stress, we can use the shear modulus provided for similar materials (as we don't have the exact value for the vertebra) to calculate the shear strain.

The procedure would be similar for the disk between vertebrae with a given shear modulus. Calculating the shear deformation for the disk would follow the same methodology with its particular force, dimensions, and shear modulus value.