Ultimate tensile or compressive strength (UTS or UCS), Young\'s modulus (Y) 1. T
ID: 1284698 • Letter: U
Question
Ultimate tensile or compressive strength (UTS or UCS), Young's modulus (Y)
1. The figure compares the skeleton of a cat to that of an elephant. Relative to its height, the elephant's leg bones are proportionally much thicker than the cat's. Since the strength of bone is determined by UCS, which is roughly the same for all animals, the leg bones must increase with increasing size of the animal in order to distribute the weight over a larger area, so as not to increase the stress in the bone. To see why the diameter of the bones must increase proportionally more than the length as the size of the animal increases, consider the following. Suppose we scale the person (from the question above) up by a factor of 5.0 in all dimensions, i.e., Ra = 28.25 mm, Rb = 84.75 mm, etc. What is the mass of this person?
2. If this scaled-up person were to stand on one leg, what stress would be applied to the femur? Express your answer as percentage of the UCS. Ignore the weight of the leg.
Tissue UTS or UCS (MPa) Y (MPa)compact bone (compression) 162 10600
tendon 54 250
intervertebral disc (compression) 11 6
vertebrae 3.5 410
skeletal muscle 0.11 0.02
hyaline cartilage (synovial joints) 2.9 24
skin (face) 3.8 0.3 Ultimate tensile or compressive strength (UTS or UCS), Young's modulus (Y) 1. The figure compares the skeleton of a cat to that of an elephant. Relative to its height, the elephant's leg bones are proportionally much thicker than the cat's. Since the strength of bone is determined by UCS, which is roughly the same for all animals, the leg bones must increase with increasing size of the animal in order to distribute the weight over a larger area, so as not to increase the stress in the bone. To see why the diameter of the bones must increase proportionally more than the length as the size of the animal increases, consider the following. Suppose we scale the person (from the question above) up by a factor of 5.0 in all dimensions, i.e., Ra = 28.25 mm, Rb = 84.75 mm, etc. What is the mass of this person? 2. If this scaled-up person were to stand on one leg, what stress would be applied to the femur? Express your answer as percentage of the UCS. Ignore the weight of the leg.
Explanation / Answer
1. Add 1000 to whatever the mass was from 'the question' above.
2. r2^2-r1^2=6384.5=cross sectional area
take the mass found from question one and multiply it by acceleration (9.8 m/s^2) to get the force.
Force/Area = Stress
Stress/162*100 = your answer.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.