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

Answer:

The spring constant is $1.09\times10^{9}\ N/m$

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

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$....(I)

$Y=\dfrac{Fl}{\Delta l A}$

From hook's law

$F=kx$

$k=\dfrac{F}{x}$

$F=k\times\Delta l$....(II)

Put the value of F in equation

$Y=\dfrac{k\times\Delta l\times l}{\Delta l A}$

$Y=\dfrac{kl}{A}$

We need to calculate the spring constant

$k = \dfrac{YA}{l}$....(II)

We need to calculate the area of cylinder

Using formula of area of cylinder

$A=2\pi\times r\times l$

Put the value into the formula

$A=2\pi\times 1\times10^{-2}\times500\times10^{-3}$

$A=0.0314\ m^2$

Put the value of A in (II)

$k=\dfrac{1.74\times10^{10}\times0.0314}{500\times10^{-3}}$

$k=1.09\times10^{9}\ N/m$

Hence, The spring constant is $1.09\times10^{9}\ N/m$