Question

There is a disk of cartilage between each pair of vertebrae in your spine. Young's modulus for cartilage is 1.0 × 106N/m2. Suppose a relaxed disk is 4.0 cm in diameter and 5.0 mm thick.

Part A If a disk in the lower spine supports half the weight of a 80 kg person, by how many mm does the disk compress?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the person = m = 80 kg

Weight supported by the disk of cartilage = F

F = mg/2

F = (80)(9.81)/2

F = 392.4 N

Young's modulus for the cartilage = E = 1 x 10⁶ N/m²

Diameter of the disk of cartilage = D = 4 cm = 0.04 m

Cross-sectional area of the disk of cartilage = A

A = D²/4

A = (0.04)²/4

A = 1.2566 x 10^-3 m²

Thickness of the disk = L = 5 mm = 5 x 10^-3 m

Amount the disk compresses by = L

Stress in the disk = = F/A

Strain in the disk = = L/L

L = 1.56 x 10^-3 m

L = 1.56 mm

A) Amount the disk compresses by = 1.56 mm