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 ?

Explanation

Diameter of the narrow end of the anvil, `d = 0.50 m m = 0.5 xx 10 ^(-3) m`
Area of cross section of trip
`A = (pi d ^(2))/( 4) " "[because r = (d)/(2) ]`
`= (22 xx (0.5 xx 10 ^(-3)) ^(2))/(7 xx 4)`
`=0.19643 xx 10 ^(-6) m ^(2)`
Stress(=pressure at the narrow end of the anvil)
`sigma = (F)/(A) = (50000)/(0.19643 xx 10 ^(-6)) `
`therefore sigma = 254543.6xx10 ^(6)`
`therefore sigma ~~2.54xx 10 ^(11) N m ^(-2) or Pa`