Answer:
a) P=974,028.25 Pascals
b) P=159,154,943.1 Pascals
Explanation:
Pressure
It's measured as the ratio of the force F applied perpendicular to a surface of area A. Its units are Pascal, PSI, atmospheres, bars, mm Hg, among many others.
[tex]\displaystyle P=\frac{F}{A}[/tex]
a)
Our man has a weight of 765 Nw. When he lies on the bed of nails, his weigh will be (uniformly) distributed among them all. It there are 1000 nails, each one will take a force of
[tex]\displaystyle F=\frac{W}{1000}=\frac{765 N}{1000}=0.765\ N[/tex]
The flattened point on each nail has a radius of 0.500 mm = 0.0005 meters, we can compute its area as a circle
[tex]A=\pi r^2=\pi 0.0005^2=7.854*10^{-7}\ m^2[/tex]
The pressure of each nail will be
[tex]\displaystyle P=\frac{0.765\ N}{7.854*10^{-7}\ m^2}[/tex]
[tex]\displaystyle P=974,028.25 \ Pascals[/tex]
Or equivalently
[tex]\displaystyle P=141.27 \ PSI[/tex]
b)
We can similarly calculate the pressure exerted on the skin by an acupuncture needle of radius 0.100 mm (0.0001 m) applied with a force of 5 N
[tex]A=\pi r^2=\pi 0.0001^2=3,1416*10^{-8}\ m^2[/tex]
[tex]\displaystyle P=\frac{5\ N}{3,1416*10^{-8}\ m^2}[/tex]
[tex]\displaystyle P=159,154,943.1 \ Pascals[/tex]
Or equivalently
[tex]\displaystyle P=1570.74 \ atmospheres[/tex]
