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The limiting stress of a typical human bone is $0.9 \times 10^{8} N m^{- 2}$ while young's modulus is $1.4 \times 10^{10} N m^{- 2}$ . How much energy can be absorbed by two leg bones without breaking if each has a typical length of 50cm and an average cross sectional area of $5 c m^{2}$ ?

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435 J

290 J

490 J

145 J

answer is A.

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Detailed Solution

$W = \frac{1}{2} Fe = \frac{1}{2} \frac{F^{2} l}{AY} = \frac{1}{2} {(\frac{F}{A})}^{2} \frac{A l}{Y}$

$W_{net} = W_{1} + W_{2} = 2 W = {(\frac{F}{A})}^{2} \frac{A l}{Y}$

$= \frac{81 \times 10^{14} \times 5 \times 10^{- 4} \times 50 \times 10^{- 2}}{14 \times 10^{9}}$

$= \frac{81 \times 25}{14} = 145 J$

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