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Xelga [282]
3 years ago
8

When subjected to a force of compression, the length of a bone (compression Young's modulus 9.4 x 109 N/m2, tensile Young's modu

lus 1.6 x 1010 N/m2) decreases by 3.7 x 10-5 m. When this same bone is subjected to a tensile force of the same magnitude, by how much does it stretch?
Physics
1 answer:
Anarel [89]3 years ago
7 0

To solve this problem it is necessary to apply the definition of Young's Module which states that

Y_1 = \frac{\frac{F}{A}}{\frac{\Delta l_0}{l}}

Where,

F = Force

A = Cross sectional Area

L = Length

L_0 = Initial Length

We need to find the ratio between the two values when the another values are constant, that is

\frac{Y_1}{Y_2} = \frac{\frac{\frac{F}{A}}{\frac{\Delta l_1}{l}}}{\frac{\frac{F}{A}}{\frac{\Delta l_2}{l}}}

\frac{Y_1}{Y_2} = \frac{\Delta l_2}{\Delta l_1}

Re-arrange to find \Delta l_2,

\Delta l_2 = \frac{9.4*10^9}{1.6*10^{10}}*3.7*10^{-5}

\Delta l_2 = 2.17*10^{-5} m

Therefore the bone stretch around 2.17*10^{-5} m

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