The tibia is a lower leg bone (shin bone) in a human. The maximum strain that the tibia can experience before fracturing corresponds to a 1 % change in length. A. Young's modulus for bone is about Y = 1.4 x 10 N/m². The tibia (shin bone) of a human is 0.35 m long and has an average cross-sectional area of 2.9 cm. What is the effective spring constant of the tibia?
B. If a man weighs 750 N, how much is the tibia compressed if it supports half his weight?
C. What is the maximum force that can be applied to a tibia with a cross-sectional area, A = 2.90 cm?

a

b

c

Explanation:

From the question we are told that

    The Young modulus is  

     The length is  

      The  area is  

Generally the force acting on the tibia is mathematically represented as

           derived from young modulus equation

Now this force can also be mathematically represented as

So

substituting values

    Since the tibia support half the weight then the force experienced by the tibia is  

 From the above equation the extension (compression) is mathematically represented as

substituting values

From the above equation the maximum force is