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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 :

okpalawalter8

Answer:

The  force is  [tex]F = 3587.2 \ N[/tex]

Explanation:

From the question we are told that

   The  diameter is  [tex]d = 1.4 \ mm = 0.0014 \ m[/tex]

    The pressure is  [tex]P = 2.33*10^{9} \ N/m^2[/tex]

Generally the radius is mathematically represented as

        [tex]r = \frac{0.0014}{2}[/tex]

        [tex]r = 0.0007 \ m[/tex]

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

       [tex]A = \pi r^2[/tex]

=>     [tex]A = 3.142 * 0.0007 ^2[/tex]

=>    [tex]A = 1.54 *10^{-6}[/tex]

Generally the pressure is mathematically represented as

        [tex]P = \frac{F}{A}[/tex]

=>      [tex]F = P * A[/tex]

=>       [tex]F = 1.54*10^{-6} * 2.33*10^{9}[/tex]

=>      [tex]F = 3587.2 \ N[/tex]

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