One of the heroes of the novel by N.G. Chernyshevsky (what to do?), Tempering his will, slept on a board with nails (points up). Estimate how many nails the hero’s bed should have been, considering that its weight is 70 kg, the point of each nail has an area of 0.1 mm2, and human skin can withstand a pressure of 3 MPa?
From the beginning, we will translate all data into the SI system:
pressure p = 3 MPa prefix m (mi) means 0.001 = 10-3, then p = 0.003 Pa or
p = 3 * 10-3 Pa. We convert the area S = 0.1 mm2 into m2, 1mm = 0.001m, and 1mm2 = 0.000001m2 or 10-6 m2, then S = 0.0000001 m2 = 10-7 m2.
We know that the pressure – p, the greater, the greater the force, in this case, the weight of the body – F, acting per unit area, and the less, the greater the area S.
formula p = F \ S, body weight can be found by the formula F = mg, where m is the mass of a person, g is the acceleration of gravity, constant = 9.8 m \ s2 or about 10 m \ s2.
we also know the area of one nail, and their n-number.
We substitute all this in the formula p = F \ S = mg \ nS, from this formula we find the n-number of nails by the formula:
n = mg \ pS = 70 (kg) * 10 (m \ s2) \ 3 * 10-3 (Pa) * 10-7 (m2) ~ 2.3 * 1012 or ~ 230,000,000,000 pieces