Question

A man weighing 765 N lies on a bed of nails. Find the average pressure exerted by a nail on his skin if there are 1000 nails and the flattened point on each nail has a radius of 0.500 mm.

Calculate the pressure exerted on the skin by an acupuncture needle of radius 0.100 mm applied with a force of 5.00 N.

Answer 1

a) P=974,028.25 Pascals

b) P=159,154,943.1 Pascals

Step-by-step 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.

`\displaystyle P=(F)/(A)`

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

`\displaystyle F=(W)/(1000)=(765 N)/(1000)=0.765\ N`

The flattened point on each nail has a radius of 0.500 mm = 0.0005 meters, we can compute its area as a circle

`A=\pi r^2=\pi 0.0005^2=7.854*10^(-7)\ m^2`

The pressure of each nail will be

`\displaystyle P=(0.765\ N)/(7.854*10^(-7)\ m^2)`

`\displaystyle P=974,028.25 \ Pascals`

Or equivalently

`\displaystyle P=141.27 \ PSI`

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

`A=\pi r^2=\pi 0.0001^2=3,1416*10^(-8)\ m^2`

`\displaystyle P=(5\ N)/(3,1416*10^(-8)\ m^2)`

`\displaystyle P=159,154,943.1 \ Pascals`

Or equivalently

`\displaystyle P=1570.74 \ atmospheres`