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.
a) What is the average force exerted by each nail on the professor's body?
b) 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?
a) 79.2*9.8/1950= 0.398N
Just need help with b.
so 0.398/1.26 × 10^–6 m2=3.16x10^-7Pa
divide the force on each nail by the area of the nail head to get Newtons per square meter or Pascals of pressure.
To find the average pressure at each contact, we need to use the formula:
pressure = force / area
For this case, the force exerted by each nail on the professor's body is given as 0.398 N (from part a), and the area of contact at the head of each nail is given as 1.26 × 10^–6 m^2.
So, the average pressure at each contact can be calculated as:
average pressure = force / area
= 0.398 N / (1.26 × 10^–6 m^2)
To simplify this calculation, we can start by converting the given area from scientific notation to standard notation:
average pressure = 0.398 N / 1.26 × 10^–6 m^2
= 0.398 N / (1.26 / 10^6) m^2
= 0.398 N / (1.26 × 10^3) m^2
= 0.398 N / 1.26 × 10^3 m^2
To divide by a fraction, we can multiply by its reciprocal:
average pressure = 0.398 N * (1.26 × 10^3 m^2) / 1
Now, we can simplify the expression:
average pressure = 0.398 N * 1.26 × 10^3 m^2
= 0.398 * 1.26 × 10^3 N * m^2
Multiplying the numerical values:
average pressure = 0.50148 N * m^2
Hence, the average pressure at each contact is approximately 0.50148 N/m^2.
To find the average pressure at each contact, we need to divide the force exerted by each nail by the area of contact.
Given that the force exerted by each nail is 0.398 N (as calculated in part a), and the area of contact at the head of each nail is 1.26 × 10^–6 m^2, we can use these values to find the average pressure.
The formula to calculate pressure is:
Pressure = Force / Area
Substituting the known values into the formula gives us:
Pressure = 0.398 N / (1.26 × 10^–6 m^2)
To simplify the calculation, we can convert the area from scientific notation to standard decimal notation:
Pressure = 0.398 N / 0.00000126 m^2
Dividing the force by the area gives us:
Pressure = 316.6667 N/m^2
Rounding to an appropriate number of significant figures, we find that the average pressure at each contact is approximately 317 N/m^2.
Therefore, the average pressure at each contact point is 317 N/m^2.