Question

The ratio of the tensile (or compressive) strength to the density of a material is a measure of how strong the material is "pound for pound." (a) Compare tendon (tensile strength \(80.0 \mathrm{MPa}\), density $1100 \mathrm{kg} / \mathrm{m}^{3}\( ) with steel (tensile strength \)\left.0.50 \mathrm{GPa}, \text { density } 7700 \mathrm{kg} / \mathrm{m}^{3}\right)$ which is stronger "pound for pound" under tension? (b) Compare bone (compressive strength \(160 \mathrm{MPa}\), density $1600 \mathrm{kg} / \mathrm{m}^{3}$ ) with concrete (compressive strength $\left.0.40 \mathrm{GPa}, \text { density } 2700 \mathrm{kg} / \mathrm{m}^{3}\right):$ which is stronger "pound for pound" under compression?

Short answer

Answer: Tendon is stronger "pound for pound" under tension, and concrete is stronger "pound for pound" under compression.

Step-by-step solution

Calculate the strength-to-weight ratio of tendon and steel for tensile strength

First, we calculate the strength-to-weight ratio for tendon and steel using the tensile strength values and densities given in the exercise. Tendon ratio = (Tensile strength of tendon) / (Density of tendon) Tendon ratio = (80.0 MPa) / (1100 kg/m³) Tendon ratio = (80 × 10^6 N/m²) / (1100 kg/m³) Steel ratio = (Tensile strength of steel) / (Density of steel) Steel ratio = (0.50 GPa) / (7700 kg/m³) Steel ratio = (0.50 × 10^9 N/m²) / (7700 kg/m³)

Compare the strength-to-weight ratio of tendon and steel

Now, let's compare the strength-to-weight ratio of tendon and steel to determine which is stronger "pound for pound." Tendon ratio = (80 × 10^6 N/m²) / (1100 kg/m³) ≈ 72727 N·m/kg Steel ratio = (0.50 × 10^9 N/m²) / (7700 kg/m³) ≈ 64935 N·m/kg Since tendon ratio (72727 N·m/kg) > steel ratio (64935 N·m/kg), tendon is stronger "pound for pound" under tension.

Calculate the strength-to-weight ratio of bone and concrete for compressive strength

Next, we calculate the strength-to-weight ratio for bone and concrete using compressive strength values and densities given in the exercise. Bone ratio = (Compressive strength of bone) / (Density of bone) Bone ratio = (160 MPa) / (1600 kg/m³) Bone ratio = (160 × 10^6 N/m²) / (1600 kg/m³) Concrete ratio = (Compressive strength of concrete) / (Density of concrete) Concrete ratio = (0.40 GPa) / (2700 kg/m³) Concrete ratio = (0.40 × 10^9 N/m²) / (2700 kg/m³)

Compare the strength-to-weight ratio of bone and concrete

Now, let's compare the strength-to-weight ratio of bone and concrete to determine which is stronger "pound for pound." Bone ratio = (160 × 10^6 N/m²) / (1600 kg/m³) ≈ 100000 N·m/kg Concrete ratio = (0.40 × 10^9 N/m²) / (2700 kg/m³) ≈ 148148 N·m/kg Since concrete ratio (148148 N·m/kg) > bone ratio (100000 N·m/kg), concrete is stronger "pound for pound" under compression.