High-impact activities are hard on the joints and can cause significant damage t

Question

High-impact activities are hard on the joints and can cause significant damage to the cartilage in the knees. Peak loads on the knees can be as much as 8 times the person's body weight. If the cartilage in the knee of a 63 kg person has a cross-sectional area of 10.34 cm2, what is the maximum change in thickness of the cartilage, if its unstrained thickness is 4.20 mm?

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

Explanation / Answer

mass of the person = 63 kg

So the peak force that can act on the knees (F)= 8 x 63 x 9.8 = 4939.2 Pa

cross-sectional area of 10.34 cm2 (A)= 10.34 x 10-4 m2

Y(cartilage) = 24 MPa

thickness = 4.2 mm = 4.2 x 10-3m

F/A = Y(change in dimension/original dimension)

4776789.2 = 24000000(change in thickness/ 4.2 x 10-3)

So change in the thickness = 8.36 x 10-4 m = 0.836 mm

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