Question

8.
An artificial denture with ultimate strength of 10 ^7Nm^-2 breaks when the
jaws exerted a normal force of just 2N while eating. Estimate the area in
which the force acted on the denture,
​

Answer 1

Given :

The ultimate strength of artificial denture = $10^{7}$ $\[N/{m^2}\]$

The force exerted while eating = 2N

To Find:

We have to find the area in which the force acted on the denture.

Solution:

The ultimate strength of a material is the maximum stress it can withstand an applied load. The value is determined by dividing the load at the failure by the original cross-sectional area. Its unit is $\[N/{m^2}\]$.

Ultimate strength = $\frac{Load}{Area}$

    ⇒     Area   =  $\[\frac{{Load}}{{Ultimate\,Strength}}\]$

                       = $\[\frac{2}{{{{10}^7}}}\,{m^2}\]$

                       $\[\begin{array}{l} = 2 \times {10^{ - 7}} \times {10^6}\,m{m^2}\\\\ = 2 \times {10^{ - 1}}\,m{m^2}\\\\ = 0 \cdot 2\,m{m^2}\end{array}\]$

∴ The cross-sectional area of the denture = 0·2 $\[m{m^2}\]$