Young's modulus for bone under compression is about 9 ×10^9...

Young's modulus for bone under compression is about $9 \times 10^{9} \mathrm{Pa}$, and the breaking stress is about $2 \times 10^{8} \mathrm{Pa}$ a. A leg bone of length $30 \mathrm{cm}$ when unstressed is stressed to its breaking point. What is the change in length of the bone? b. If the bone has a diameter of $3 \mathrm{cm},$ how much weight can it support just before it breaks?

Young's modulus for bone under compression is about $9 \times 10^{9} \mathrm{Pa}$, and the breaking stress is about $2 \times 10^{8} \mathrm{Pa}$
a. A leg bone of length $30 \mathrm{cm}$ when unstressed is stressed to its breaking point. What is the change in length of the bone?
b. If the bone has a diameter of $3 \mathrm{cm},$ how much weight can it support just before it breaks?

Key Concepts

Young's Modulus

Young's modulus is a material property that quantifies its stiffness and resistance to elastic deformation under load. It defines the proportionality between stress (force per unit area) and strain (relative change in length) in the elastic region of the stress-strain curve, making it central to understanding how materials deform when subjected to forces.

Stress and Strain

Stress is the internal force per unit area in a material resulting from an applied external force, while strain is the measure of deformation representing the relative change in dimensions (such as length). These concepts are key to analyzing how materials respond to loads, particularly in the elastic regime where they return to their original shape after the stress is removed.

Breaking Stress

Breaking stress is the maximum stress that a material can withstand before failure or fracture occurs. It represents the material's strength limit, and exceeding this threshold results in permanent deformation or complete structural failure.

Hooke's Law

Hooke's law states that, within the elastic limit, the strain produced in a material is directly proportional to the applied stress. This law provides the fundamental relationship used to compute elastic deformations in materials when a known force is applied, and is essential for solving problems involving elastic deformation.

Cross-Sectional Area

The cross-sectional area is critical in determining how an applied force is distributed within a material. It is used to calculate stress by dividing the applied force by the area, which in turn is necessary to assess the material's ability to bear loads and predict failure under compression or tension.

Transcript

Please give Ace some feedback