Question

Nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. What force (in N) must be exerted on a nail with a circular tip of 1.45 mm diameter to create a pressure of 2.33 ✕ 109 N/m2? (This high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)

Answer 1

The force is
`F = 3587.2 \ N`

Step-by-step explanation:

From the question we are told that

The diameter is
`d = 1.4 \ mm = 0.0014 \ m`

The pressure is
`P = 2.33*10^(9) \ N/m^2`

Generally the radius is mathematically represented as

`r = (0.0014)/(2)`

`r = 0.0007 \ m`

The cross-sectional area of the nail is mathematically represented as

`A = \pi r^2`

=>
`A = 3.142 * 0.0007 ^2`

=>
`A = 1.54 *10^(-6)`

Generally the pressure is mathematically represented as

`P = (F)/(A)`

=>
`F = P * A`

=>
`F = 1.54*10^(-6) * 2.33*10^(9)`

=>
`F = 3587.2 \ N`