Anvils made of single crystals of diamond, with the shape as shown in Fig. 9.14, 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?


Here the Compressive force will be transmitted from the wide ends to the narrow end so there will be pressure at the Narrow end or the tip, which is also Experiencing force in opposite direction, from the lower end in order to keep it stationary, since forces must be balanced i.e. equal and opposite on each member of anvil the free body diagram disassembling each member of anvil has been shown in the figure



We know Pressure is force acting per unit area and is given by


P = F/A


Where P is the pressure, F is the force, and A is the surface area in contact


Now here the force on the Tip of anvil is


F = 50000 N = 5 × 104 N


We are given diameter of the tip


d = 0.50 mm


so the radius of the tip is


r = d/2 = 0.50mm/2 = 0.25 mm


i.e. r = 2.5 × 10-4 m


now since the tip is a circular area of a circle is given by


A = πr2


Where A is the area of circle,


r is the radius


Putting value of r we get area of the Tip as


A = π × (2.5 × 10-4 m)2


Solving we get area


A = 1.96 × 10-7 m2


So putting value of F and A we get pressure




So the pressure at the tip of anvil is 2.55 × 1011 Pa


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