You exert a force of 26 N on the head of a thumbtack. the head of the thumbtack has a radius of 7 mm.? What is the pressure on your thumb?
-------- atm
To calculate the pressure exerted on your thumb by the head of the thumbtack, you need to use the formula for pressure:
Pressure = Force / Area
First, you need to determine the area of the head of the thumbtack. The area of a circle can be calculated using the formula:
Area = π * (radius)^2
Given that the radius of the thumbtack's head is 7 mm, we can convert it to meters for consistency:
Radius = 7 mm = 7/1000 = 0.007 m
Now, we can calculate the area:
Area = π * (0.007 m)^2
Next, we can substitute the given force of 26 N and the calculated area into the pressure formula:
Pressure = 26 N / (π * (0.007 m)^2)
Simplifying the equation further, we can calculate the pressure:
Pressure ≈ 165,298.89 N/m^2
To convert the pressure into atm, we need to divide it by the standard atmospheric pressure, which is approximately 101,325 N/m^2:
Pressure ≈ 165,298.89 N/m^2 / 101,325 N/m^2
Pressure ≈ 1.631 atm
Therefore, the pressure exerted on your thumb by the head of the thumbtack is approximately 1.631 atm.