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. -Which of the following expressions is equal to U_el, the elastic potential energy stored within a compressed bone?

Question

Quizplus · Accepted Answer

11ecba2d_12c8_b1db_a3bf_d3d0504f960e_MD0008_00 Stretching or compressing an elastic object away from its equilibrium point (ie, its position at rest) increases its elastic potential energy (U_el), which is a form of energy that depends on the configuration of elastic objects. U_el is stored within an elastic object because work must be done against the elastic force F_el generated when an elastic object is displaced. Consequently, U_el quantifies the capacity of an elastic object to do work in the future using energy stored by work completed on the object in the past. The magnitude of potential energy stored within elastic, spring-like objects is a function of the displacement from equilibrium (x) and the spring constant (k), a measure of the relative elasticity or stiffness of the spring-like object: 11ecba2d_12c8_b1dc_a3bf_dbb98dc8a1cb_MD0008_00 For the experiment described in this question, x is equal to the change in length (ΔL) of the bone sample because the initial length of the bone sample L₀ corresponds to the equilibrium position prior to compression. Making this substitution into Equation 1 and solving for x gives: 11ecba2d_12c8_b1dd_a3bf_e7f253d0000f_MD0008_00 11ecba2d_12c8_b1de_a3bf_2f12ed3e3360_MD0008_00 Because the passage states that compressed bone acts like a spring-like object, the above expression for displacement can be substituted into the equation for elastic potential energy to yield: 11ecba2d_12c8_b1df_a3bf_dba4ec4979c3_MD0008_00 Therefore, the magnitude of the potential energy stored within a compressed bone sample may be expressed as a function of the strain (ε) experienced by that sample (Choice A). Educational objective: Elastic potential energy describes the potential energy that results from displacing springs and other elastic objects away from their equilibrium point. Elastic potential energy is related to the spring constant and the magnitude of displacement from equilibrium point.

Passage Osteoporosis Is a Degenerative Bone Condition in Which Healthy Bone