Anvils made of single crystals of diamond, with the shape as shown in Figure, are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of $0.50\; mm$, and the wide ends are subjected to a compressional force of $50,000 \;N$. What is the pressure at the tip of the anvil?
Medium
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Diameter of the cones at the narrow ends, $d=0.50 mm =0.5 \times 10^{-3} m$
Radius, $r=\frac{d}{2}=0.25 \times 10^{-3} m$
Compressional force, $F=50000 N$
Pressure at the tip of the anvil
$p=\frac{\text { Force }}{\text { Arear }}=\frac{F}{\pi r^{2}}$
$=\frac{50000}{\pi\left(0.25 \times 10^{-3}\right)^{2}}$
$=2.55 \times 10^{11} Pa$
Therefore, the pressure at the tip of the anvil is $2.55 \times 10^{11} \;Pa$
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