The spinal column has normal curvature for stability, but this curvature can be increased, leading to increased shearing forces on the lower vertebrae. The spinal column (consisting of 26 vertebral segments separated by discs) provides the main support for the head and upper part of the body. Most bone fractures are not caused by compression but by excessive twisting and bending. Bones can support loads comparable to that of concrete and steel. This is one reason that bones can be long and relatively thin. Its shear modulus is not only greater than its Young’s modulus, but it is as large as that of steel. For example, shear moduli are less than Young’s moduli for most materials. Where S is the shear modulus and F is the force applied perpendicular to L 0 and parallel to the cross-sectional area A.Įxamination of the shear moduli in Table 1 reveals some telling patterns. Rearranging this toġ k \fracL_0 Δ x = S 1 A F L 0 , Note that this force is a function of the deformation Δ L-it is not constant as a kinetic friction force is. Where Δ L is the amount of deformation (the change in length, for example) produced by the force F, and k is a proportionality constant that depends on the shape and composition of the object and the direction of the force. In equation form, Hooke’s law is given by Second, the size of the deformation is proportional to the force-that is, for small deformations, Hooke’s law is obeyed. First, the object returns to its original shape when the force is removed-that is, the deformation is elastic for small deformations. For small deformations, two important characteristics are observed. Even very small forces are known to cause some deformation. A change in shape due to the application of a force is a deformation. If a bulldozer pushes a car into a wall, the car will not move but it will noticeably change shape. Now you want to find > 0 so that if x 5 < then 3 < x 5 < 5. We now move from consideration of forces that affect the motion of an object (such as friction and drag) to those that affect an object’s shape. 2 Answers Sorted by: 9 Assuming your algebra is correct (I didnt check it carefully), you have shown that x 1 2 < 1 if and only if 3 < x 5 < 5. Determine the change in length given mass, length and radius.Describe with examples the young’s modulus, shear modulus and bulk modulus.Discuss the three types of deformations such as changes in length, sideways shear and changes in volume.Explain Hooke’s law using graphical representation between deformation and applied force.By the end of this section, you will be able to:
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