Question

In a classroom demonstration, a 79.2-kg physics professor lies on a "bed of nails." The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board. While the professor is lying down, approximately 1950 nails make contact with his body.

If the area of contact at the head of each nail is 1.26 × 10 –6 m2, what is the average pressure at each contact?

Answer 1

Answer on Question#37463 - Physics - Other

In a classroom demonstration, a 79.2-kg physics professor lies on a "bed of nails." The bed consists of a large number of evenly spaced, relatively sharp nails mounted in a board so that the points extend vertically outward from the board. While the professor is lying down, approximately 1950 nails make contact with his body. If the area of contact at the head of each nail is $1.26 \times 10^{-6} \mathrm{~m}^2$, what is the average pressure at each contact?

Solution:

Average pressure at each contact:

Pressure = $\frac{\text{Force}}{\text{Area}}$ (in this case the number of nails)

$$p = \frac{mg}{N \cdot S_0} = \frac{79.2 \, \text{kg} \cdot 9.8 \, \text{N/kg}}{1950 \cdot 1.26 \cdot 10^{-6} \, \text{m}^2} = 316 \, \text{kPa}$$

Answer: the average pressure at each contact is equal to $316 \, \text{kPa}$.