Passage Osteoporosis is a degenerative bone condition in which healthy bone degenerates into porous bone. Because bone provides the structural integrity that allows the musculoskeletal system to bear weight, osteoporosis is associated with a higher risk of bone fracture.Researchers conducted an experiment designed to assess the strength and elasticity of osteoporotic bone relative to normal bone. Osteoporotic and normal bone samples with identical physical dimensions were collected and placed within an pneumatic compression device, as shown in Figure 1. Figure 1 Bone compression device loaded with a bone sampleThe force required to compress the bone samples longitudinally (lengthwise) by a given distance was measured, with the results shown in Figure 2. Figure 2 Relationship between force and compression for normal and osteoporotic bonesResearchers observed that bone samples returned to their original dimensions for deformations not exceeding 1% of the original length L 0 . For each deformation, the associated strain ε is defined as the change in length of an object ΔL divided by the object's original length (Equation 1). Equation 1Based on these observations, researchers concluded that both osteoporotic bone and normal bone behaved as an elastic material under a wide range of applied forces. -Compared to osteoporotic bone, the work required to compress normal bone by 2 mm is:

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11ecba2d_12c6_19ba_a3bf_796f54e974d7_MD0008_00 Mechanical work describes the transfer of energy that occurs through the application of a force (F) to move an object over some distance (d) or the application of pressure (P) over some change in volume (ΔV): 11ecba2d_12c6_40cb_a3bf_fb8b97658089_MD0008_00 Consequently, in a graph of force versus distance, the area under the curve is equal to the associated work because within the above equation, F corresponds to a y-axis value (a force) and d corresponds to an x-axis value (a displacement from the equilibrium point). Figure 2 shows that the application of a compressive force results in the displacement of the samples of both bone types away from their equilibrium positions (ie, original, noncompressed length). As such, the compressing machine performs mechanical work as the surface of the bone is displaced some distance from its equilibrium position. The corresponding work performed over 2 mm of compression can be visualized graphically as the area A_T occupied by a triangle with a base b that is 2 mm (0.002 m) in length and a height h that is equal to the applied change in force: 11ecba2d_12c6_40cc_a3bf_e1d5f4ce4953_MD0008_00 Applying this relationship, the work performed on the normal bone (W_n) and on the osteoporotic bone (W_o) may be calculated as follows: 11ecba2d_12c6_40cd_a3bf_53133ae891de_MD0008_00 11ecba2d_12c6_40ce_a3bf_9b98b19d8170_MD0008_00 Accordingly, the ratio between W_n and W_o is: 11ecba2d_12c6_40cf_a3bf_4d91d77e2840_MD0008_00 Therefore, it can be concluded that the work needed to compress normal bone by 2 mm is 4/3 times greater than the work needed to compress osteoporotic bone by 2 mm (Choice C). Educational objective: Work is an energy transfer that takes place due to a force acting over some distance. In a graph of the force acting on the object versus the distance the object is displaced, the corresponding work performed on the object is equal to the area under the curve.

Passage Osteoporosis Is a Degenerative Bone Condition in Which Healthy Bone