Question

A $40kg$ boy whose leg bones are $4c{m}^2$ in area and $50cm$ long falls through a height of $50cm$ without breaking his leg bones. If the bones can stand a stress of $0.9\times {10}^{8}N/m^2$. Calculate Young's Modulus for the material of the bone

Answer 1

Data:

Mass = m = 40 kg

Area = A = 4 cm² = 0.0004 m²

Length = l = 50 cm = 0.5 m

Height = h = 50 cm = 0.5 m

Young's Modulus = Y = ?

Solution:

Young's Modulus is given as

Y = Stress / Strain

Y = (F/A) / (ΔL/L) ............. (1)

In this case,

Work done in falling = Work done in compression of the spring

Therefore,

mgh = 1/2 F ΔL

ΔL = 2 mgh / F

Put this value in equation (1) , we get:

Y = (F/A) / [(2 mgh / F) /L]

Y = F² L / 2 mgh A

Putting the values, we get:

Y = (0.9x10⁸)² (0.5) / (2) (40) (10) (0.5) (0.0004)

Y = 4.05x10¹⁵ / 0.16

Y = 2.5x10¹⁶ N/m