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’

Answer 1

The spring constant is
`1.09*10^(9)\ N/m`

Step-by-step explanation:

Given that,

length = 500 mm

Diameter = 2 cm

Young's modulus = 17.4 GPa

We need to calculate the young's modulus

Using formula of young's modulus

`Y=((F)/(A))/((\Delta l)/(l))`....(I)

`Y=(Fl)/(\Delta l A)`

From hook's law

`F=kx`

`k=(F)/(x)`

`F=k*\Delta l`....(II)

Put the value of F in equation

`Y=(k*\Delta l* l)/(\Delta l A)`

`Y=(kl)/(A)`

We need to calculate the spring constant

`k = (YA)/(l)`....(II)

We need to calculate the area of cylinder

Using formula of area of cylinder

`A=2\pi* r* l`

Put the value into the formula

`A=2\pi* 1*10^(-2)*500*10^(-3)`

`A=0.0314\ m^2`

Put the value of A in (II)

`k=(1.74*10^(10)*0.0314)/(500*10^(-3))`

`k=1.09*10^(9)\ N/m`

Hence, The spring constant is
`1.09*10^(9)\ N/m`