Question

A 85-kg person stands on one leg and 90% of the weight is supported by the upper leg connecting the knee and hip joint – the femur. Assuming the femur is 0.65 m long and has a radius of 2.00 cm, by how much will the bone be compressed (in meters)?

Answer 1

The bone is compressed to 4.213*10⁻⁶ m.

Step-by-step explanation:

Given that ,

Mass of the person M = 85 kg,

Length of femur L =0.65 m

Radius of femur r = 0.02 m

To find,

Compression of the bone l = ?

The Young's Modulus is given by Y=
`(FL)/(lA)`

Young's modulus of human femur bone is Y = 9.4 *10⁹ Pa

Rearranging formula ,

l =
`(FL)/(YA)`

Weight supported by femur bone is 85 *0.9 =76.5 Kg

Area = π r² =3.14* (0.02)² = 0.001256 m

The length of compressed bone is

l =
`(76.5*0.65)/(9.4GPa*0.001256)` =
`(49.725)/(0.0118GPa)` =4213.89 *10⁻⁹

l = 4.213*10⁻⁶ m

The bone is compressed to 4.213*10⁻⁶ m.