Question

Common sports injuries result in the tearing of tendons and ligaments due to overstretching. If the anterior cruciate ligament (ACL) in an athlete’s knee has a length of 1.80 cm, a breaking point of 187 MPa, and a Young’s modulus of 600 MPa, how far must it be stretched from its relaxed length to tear it?

Answer 1

Young's Modulus is 600 MPa for knee

and that it will tear the ligaments if  the breaking point stress greater than 187 MPa is imposed on it.

If the effective diameter of the knee is 1.80cm,

what is the maximum force that can be imposed on it (before breaking, I assume) Here's what I've done:

where L is length of the knee = 1.8 cm = 0.018 m

y=Stress / Strain=600 MPa

Strain= Strain=ΔL / L​= Change in Length​ / Original Length

Stress= 187 MPa

so ΔL / L​ = stress / y

ΔL = stress x L / y

= 187 x 0.018 / 600

= 0.0056 m

therefor, ΔL = 0.018 - 0.0056 = 0.0124 m

so therefor, 0.0124 m or 1.24 cm is the length at which it can bear the stretching