Question

Bone has a Young's modulus of about

1.8 x 100 Pa. Under compression, it can
withstand a stress of about 1.59 x 108 Pa be-
fore breaking.
Assume that a femur (thigh bone) is 0.53 m
long, and calculate the amount of compression
this bone can withstand before breaking.
Answer in units of mm.

Answer 1

505.62 mm

Step-by-step explanation:

Young's modulus of a material is given by,

`Y=(Stress)/(Strain)`

Stress is the force experienced by the material per unit area (which is why stress has the same units as pressure).

Strain is the ratio between the change in length/area/volume to the original length/area/volume of the material (and hence a dimensionless quantity). Basically, it gives us a measure of the change in dimensions due to the stress experienced.

So, for the given problem,

`Y=(Stress)/(\Delta L/L)`

or,
`1.8*100=(1.59*108)/(\Delta L/0.53)` (since we need to find the compression of the bone at the critical stress point)

or,
`\Delta L=(1.59*108*0.53)/(1.8*100) m=0.50562m=505.62mm`