A compressive force of 26 x 104 N is exerted on the end 01 a

A compressive force of 2.6 x 10^4 N is exerted on the end 01 a 23 cm long bone of cross-sectional area 3.8 cm^2 The elastic modulus for bone is 1.5 x 10^10 N/m^2 and the compressive strength for bone is 1.7 x 10^8 N/m^2. Will the bone break By how much does it shorten

Solution

For a body with a force F being acted upon an area of A, the stress is defined as the ratio of force and cross sectional area. That is stress= F/A

Further strain as defined as the ratio of change in length to original length. That is, strain = L / L

Also, the modulus of elasticity is defined as the ratio of the stress and strain. That is, E = (F/A) / (L / L)

Part A.) The given body is being exerted over by a force of 2.6 x 10⁴ N over the area of 3.8 cm²

Hence, the stress = F/A = 2.6 x 10⁴ / 3.8 x 10^-4 = 0.684 x 10⁸ N/m²

As the stress is smaller than the compressive strength of the bone, it will not break.

Part B.) Now, we know that the modulus of elasticity = E = 1.5 x 10¹⁰ N/m²

That is, E = (F/A) / (L / L) = 0.684 x 10⁸ / (L / 0.23)

or, 1.5 x 10¹⁰ = 0.684 x 0.23 x 10⁸ / L

or, L = 0.10488 x 10^-2 m

Therefore the required change in length = 0.10488 cm