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Mechanical Properties of Solids

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Question : 17 of 21
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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?
Solution:  
Here, Compressional force, F=5×104NF=5 \times 10^{4} \mathrm{N}
Diameter, D=5.0×10−4mD=5.0 \times 10^{-4} \mathrm{m}
∴\therefore radius, r=D2=2.5×10−4mr=\frac{D}{2}=2.5 \times 10^{-4} \mathrm{m}
Area, A=πr2=227×(2.5×10−4)2A=\pi r^{2}=\frac{22}{7} \times (2.5 \times 10^{-4})^{2}
Pressure at the tip, P=?P=?
Using the relation, P=FA,P=\frac{F}{A}, we get P=5×104227×(2.5×10−4)2P=\frac{5 \times 10^{4}}{\frac{22}{7} \times (2.5 \times 10^{-4})^{2}}
=0.255×1012Pa=0.255 \times 10^{12} \mathrm{Pa}
=2.55×1011Pa=2.55 \times 10^{11} \mathrm{Pa}
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