If a compressive force of 3.3×104 N3.3 \times 10^4 \mathrm{~N} is exerted on the end of a 22 cm22 \mathrm{~cm} long bone of cross-sectional area 3.6 cm23.6 \mathrm{~cm}^2, (a)(a) will the bone break, and (b)(b) if not, by how much does it shorten?


Answered 2 years ago
Answered 2 years ago
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a) Compressive strength can be looked at as a maximum stress a material can take. If the stress is greater, the material will break.

Sc=17107N/m2S_c=17\cdot 10^7\,\,\rm{N/m^2}

stress=FA=3.31043.6104stress=\frac{F}{A}=\frac{3.3\cdot 10^4}{3.6\cdot 10^{-4}}

stress=9.1107N/m2<Scstress=9.1\cdot 10^7\,\,\rm{N/m^2} < S_c

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

b) The elongation can be calculated:

Δl=strainl0\Delta_l=strain \cdot l_0

Δl=stressEl0\Delta_l=\frac{stress}{E} \cdot l_0

Δl=9.11071510922\Delta_l=\frac{9.1\cdot 10^7}{15\cdot 10^9} \cdot 22


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