Question

The legs of a weight lifter must ultimately support the weights he has lifted. A human tibia (shinbone) has a circular cross section of approximately 3.6 cm outer diameter and 2.30 cm inner diameter. (The hollow portion contains marrow.)If a 90.0 kg lifter stands on both legs, what is the heaviest weight he can lift without breaking his legs, assuming that the breaking stress of the bone is 150 MPa ?

Answer 1

Answer:

249003822308.05008 N

Explanation:

F = Force

$\sigma$ = Breaking stress of bone = 150 MPa

$d_2$ = Outer diameter = 3.6 cm

$d_1$ = Inner diameter = 2.3 cm

Area of the bone is assumed to be a hollow cylinder

$A=\dfrac{\pi}{4}(d_2^2-d_1^2)$

Stress is given by

$\sigma=\dfrac{F}{A}\\\Rightarrow F=\sigma A\\\Rightarrow F=\dfrac{150\times 10^6}{\dfrac{\pi}{4}(0.036^2-0.023^2)}\\\Rightarrow F=249003822308.05008\ N$

The maximum weight the person can lift without breaking his legs is 249003822308.05008 N