Calculate the pressure exerted on the floor by the heel if it has an area of 1.45 cm2 and the woman's mass is 58.0 kg. Express the force in N/m2 and lb/in
To calculate the pressure exerted on the floor by the heel, you need to divide the force exerted by the area of the heel.
First, let's convert the mass from kilograms to newtons, as force is measured in newtons. The formula to convert mass to force is:
Force (in newtons) = Mass (in kilograms) × Acceleration due to gravity (approximately 9.8 m/s^2)
Given the mass of the woman is 58.0 kg, we can compute the force:
Force = 58.0 kg × 9.8 m/s^2
Force ≈ 568.4 N
Next, let's calculate the pressure.
Pressure = Force ÷ Area
Given the area of the heel is 1.45 cm^2, we need to convert it to square meters:
Area (in square meters) = Area (in square centimeters) / 10,000
Area = 1.45 cm^2 / 10,000
Area ≈ 0.000145 m^2
Now, we can substitute the values into the pressure equation:
Pressure = 568.4 N / 0.000145 m^2
Pressure ≈ 3,923,448.28 N/m^2
To convert the pressure to lb/in^2 (pounds per square inch), you need to know the conversion factor:
1 N/m^2 ≈ 0.000145 lb/in^2
Multiply the pressure in N/m^2 by the conversion factor to get the pressure in lb/in^2:
Pressure (in lb/in^2) = 3,923,448.28 N/m^2 × 0.000145 lb/in^2
Pressure ≈ 568.4 lb/in^2
Therefore, the pressure exerted on the floor by the heel is approximately 3,923,448.28 N/m^2 and 568.4 lb/in^2.