Question

A solid cylinder of cortical bone has a length of 500mm, diameter of 2cm and a Young’s Modulus of 17.4GPa. Determine the spring constant ‘k’. Please explain.

Answer 1

The spring constant k is
`1.115* 10^(9) N/m`

Solution:

As per the question:

Length of the solid cylinder, L = 500 mm =
`500* 10^(- 3) = 0.5 m`

Diameter pf the cylinder, D = 2 cm = 0.02 m

As the radius is half the diameter,

Radius, R = 1 cm = 0.01 m

Young's Modulus, E = 17.4 GPa =
`17.4* 10^(9) Pa`

Now,

The relation between spring constant, k and Young's modulus:

`kL = EA`

where

A = Area

Area of solid cylinder, A =
`2\piR(L + R)`

`0.5k = 17.4* 10^(9)* 2\piR(L + R)`

`k = (17.4* 10^(9)* 2\pi* 0.01(0.01 + 0.5))/(0.5)`

k =
`1.115* 10^(9) N/m`

Young's modulus, E is the ratio of stress and strain

And

Stress =
`(Force or thrust)/(Area)`

Strain =
`(length, L)/(elongated or change in length, \Delta L)`

Also

Force on a spring is - kL

Therefore, we utilized these relations in calculating the spring constant.