During a wrestling match, a 147-kg wrestler briefly stands on one hand during a maneuver designed to perplex his adversary. By how much does the upper arm bone shorten in length? The bone can be represented by a uniform rod 38.0 cm in length and 2.10 cm in radius. Assume Young's modulus for bone under compression is 9 
109 N/m2.
+33665 Young's modulus (E) is Stress/Strain
Stress = force/unit area = mass*g/(pi*radius2)
Strain = change in length/original length = δL/L
Hence:
δL = L*mass*g/(pi*radius2*E)
$${\mathtt{deltaL}} = {\frac{{\mathtt{0.38}}{\mathtt{\,\times\,}}{\mathtt{147}}{\mathtt{\,\times\,}}{\mathtt{9.8}}}{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{0.021}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)}} \Rightarrow {\mathtt{deltaL}} = {\mathtt{0.000\: \!043\: \!903\: \!185\: \!783\: \!3}}$$
Note that I've turned length measurements into metres.
δL ≈ 4.4*10-5m = 0.044 mm
.
+33665 Young's modulus (E) is Stress/Strain
Stress = force/unit area = mass*g/(pi*radius2)
Strain = change in length/original length = δL/L
Hence:
δL = L*mass*g/(pi*radius2*E)
$${\mathtt{deltaL}} = {\frac{{\mathtt{0.38}}{\mathtt{\,\times\,}}{\mathtt{147}}{\mathtt{\,\times\,}}{\mathtt{9.8}}}{\left({\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{0.021}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}\right)}} \Rightarrow {\mathtt{deltaL}} = {\mathtt{0.000\: \!043\: \!903\: \!185\: \!783\: \!3}}$$
Note that I've turned length measurements into metres.
δL ≈ 4.4*10-5m = 0.044 mm
.
