Question

Humans can bite with a force of approximately 810 n. if a human tooth has the young's modulus of bone, a cross-sectional area of 1.5 cm2, and is 1.8 cm long, determine the change in the tooth's length during an 8.10 ✕ 102 n bite.

Answer 1

The change in the tooth's length during an 810 N bite is approximately 6.48 x 10^-6 meters.

Step-by-step explanation:

Define the given values:

Force (F) = 810 N

Young's modulus of bone (E) = 1.5 x 10^10 Pa

Cross-sectional area (A) = 1.5 x 10^-4 m^2

Original length (L) = 1.8 x 10^-2 m

Calculate the change in length using the stress-strain relationship:

Stress (σ) = F / A

Strain (ε) = ΔL / L

Stress is proportional to strain within the elastic limit, so σ = Eε

Combining these equations, we get ΔL = F * L / (E * A)

Substitute the given values and solve for ΔL:

ΔL = 810 N * 1.8 x 10^-2 m / (1.5 x 10^10 Pa * 1.5 x 10^-4 m^2)

ΔL ≈ 6.48 x 10^-6 m

Therefore, the tooth's length compresses by approximately 6.48 micrometers during the bite.