## Related questions with answers

If a compressive force of $3.3 \times 10^4 \mathrm{~N}$ is exerted on the end of a $22 \mathrm{~cm}$ long bone of cross-sectional area $3.6 \mathrm{~cm}^2$, $(a)$ will the bone break, and $(b)$ if not, by how much does it shorten?

Solution

Verifieda) Compressive strength can be looked at as a maximum stress a material can take. If the stress is greater, the material will break.

$S_c=17\cdot 10^7\,\,\rm{N/m^2}$

$stress=\frac{F}{A}=\frac{3.3\cdot 10^4}{3.6\cdot 10^{-4}}$

$stress=9.1\cdot 10^7\,\,\rm{N/m^2} < S_c$

The stress is smaller than the compressive strength, therefore $\textbf{ the bone will not break}$.

b) The elongation can be calculated:

$\Delta_l=strain \cdot l_0$

$\Delta_l=\frac{stress}{E} \cdot l_0$

$\Delta_l=\frac{9.1\cdot 10^7}{15\cdot 10^9} \cdot 22$

$\boxed{\Delta_l=0.13\,\,\rm{cm}}$

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