Physics - Elasticity Question with Solution | TestHub

When a force $F$ acts along a rod of length $l$ and cross-sectional area $A$, its stress is $\frac{F}{A}$. Strain is the fractional length change $\frac{\Delta l}{l}$. Young's modulus $Y$ is the ratio of stress to strain. The table lists average moduli.

Rigid solids such as bone have moduli of order $10^{10}N/{\mathrm{m}}^2$ and can lengthen by no more than 1% without breaking. Stretching changes atomic distances, creating a restoring force through changes in internal energy. Soft biological tissues differ from rigid solids. These soft materials are elastomers: long molecular chains joined by sulfur cross-links. Stretching elongates the chains until they are almost parallel, as shown. Elastomers may expand to three times their original length.

Unstretched (left); stretched (right).

$Y=\frac{3\rho RT}{M}.$

Here $\rho$ is density, $R$ is the universal gas constant ($8.3J/(\mathrm{mol}\mathrm{K})$), $T$ is absolute temperature and $M$ is the mean molecular weight between cross-links. Unlike rigid solids, an elastomer's modulus varies with applied stress between $10^5$ and $10^{7}N/{\mathrm{m}}^2$.