Question

Bone has a Young's modulus of about

1.8 x 100 Pa. Under compression, it can
withstand a stress of about 1.58 x 10° Pa be-
fore breaking.
Assume that a femur (thigh bone) is 0.54 m
long, and calculate the amount of compression
this bone can withstand before breaking.
Answer in units of mm.

Answer 1

Answer: 4.74 mm

Step-by-step explanation:

We can solve this problem with the following equation:

`Y=(stress)/(strain)` (1)

Where:

`Y=1.8(10)^(10) Pa` is the Young modulus for femur

`stress=(F)/(A)=1.58(10)^(8) Pa` is the stress (force
`F` applied per unit of transversal area
`A`) on the femur

`strain=(\Delta l)/(l_(o))`

Being:

`\Delta l` the compression the femur can withstand before breaking

`l_(o)=0.54 m` is the length of the femur without compression

Writing the data in equation (1):

`Y=((F)/(A))/((\Delta l)/(l_(o)))` (2)

`1.8(10)^(10) Pa=(1.58(10)^(8) Pa)/((\Delta l)/(0.54 m))` (3)

Isolating
`\Delta l`:

`\Delta l=((1.58(10)^(8) Pa)(0.54 m))/(1.8(10)^(10) Pa)` (4)

`\Delta l=0.00474 m` (5) This is the compression in meters

Converting this result to millimeters:

`\Delta l=0.00474 m (1000 mm)/(1 m)=4.74 mm`