A 40kg boy whose leg bones are 4cm² 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 X 10^8 N/m². Calculate Young's Modulus for the material of the bone.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
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/m²
Answer:
Explanation: I hope this helps you.