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

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.)

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Nho 6 months 2021-08-04T12:31:29+00:00 1 Answers 23 views 0

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    2021-08-04T12:33:06+00:00

    Answer:

    The  force is  F =  3587.2 \  N

    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 =  \frac{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 =  \frac{F}{A}

    =>      F  =  P * A

    =>       F  =  1.54*10^{-6}  *  2.33*10^{9}

    =>      F =  3587.2 \  N

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