Question

A novel biomaterial was tested for its tensile properties. The experiment was conducted using a cylindrical sample of this material, which was 10 cm long with 1 cm diameter. When a tensile force of 50 kN was applied, this cylindrical sample elongated by 4 mm. Based on the experimental results described above and the tensile moduli of different tissues given in the table below, this biomaterial would be a suitable replacement for \(\underline{\hspace{2cm}}\). 
\[\begin{array}{|c|c|} \hline \textbf{Tissue} & \textbf{Tensile modulus} \\ \hline \text{Bone} & \text{5 – 20 GPa} \\ \hline \text{Tendon} & \text{0.5 – 1 GPa} \\ \hline \text{Ligament} & \text{20 – 400 MPa} \\ \hline \text{Articular cartilage} & \text{3 – 10 MPa} \\ \hline \end{array}\]

• A. Bone
• B. Tendon
• C. Ligament
• D. Articular cartilage

Hint:

When selecting biomaterials for replacements, ensure their tensile modulus matches closely with the tissue they are replacing.

Answer 1

The Correct Option is A

The tensile modulus is a measure of the stiffness of a material. We can calculate the tensile modulus for this biomaterial using the Hooke's Law formula: \[ \text{Stress} = \frac{F}{A}, \text{Strain} = \frac{\Delta L}{L_0} \] Where:
- \( F = 50 \, \text{kN} = 50,000 \, \text{N} \) (applied force),
- \( A = \pi \left( \frac{d}{2} \right)^2 = \pi (0.5)^2 = 0.785 \, \text{cm}^2 = 7.85 \times 10^{-5} \, \text{m}^2 \) (cross-sectional area of the sample),
- \( \Delta L = 4 \, \text{mm} = 4 \times 10^{-3} \, \text{m} \) (elongation),
- \( L_0 = 10 \, \text{cm} = 0.1 \, \text{m} \) (original length).
First, calculate the stress: \[ \text{Stress} = \frac{50,000}{7.85 \times 10^{-5}} = 6.37 \times 10^8 \, \text{N/m}^2 \] Next, calculate the strain: \[ \text{Strain} = \frac{4 \times 10^{-3}}{0.1} = 0.04 \] Now, use the formula for tensile modulus: \[ \text{Tensile modulus} = \frac{\text{Stress}}{\text{Strain}} = \frac{6.37 \times 10^8}{0.04} = 1.59 \times 10^{10} \, \text{N/m}^2 = 15.9 \, \text{GPa} \] Since the tensile modulus of Bone lies within the range of 5 – 20 GPa, the correct answer is (A).